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Beyond Einstein and E =mc2
Science is infinite
Ajay Sharma
Contents
Chapter 1
Einstein derived L =mc2 For Newton’s Perception [pp.3-24]
Chapter 2
Contradictions In Einstein’s Derivation Of ∆L=∆mc2 [pp.24-60]
Chapter 3
Derivation Of Generalized Form Of Mass Energy Equation, ∆E =Ac2∆m [pp.60-81]
Chapter 4
Applications Of Equation ∆E =Ac ∆m In Understanding The Origin Of Universe.
[pp.81-98]
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Chapter 5
Applications of generalized mass energy inter-conversion equation in Nuclear Physics
and Nuclear Reactors [99-120]
Chapter 6
Rest Mass Energy Erme = Mrmec2 Is Derived From Non- Existent Equation.[121-137]
Chapter 7
Frequently Asked Questions: Based on previous chapters [137-157]
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Preface
The spirit or essence of science is lighting one lamp from the other.
Einstein is the greatest due to his matchless imagination and unsurpassed intuition, which of
course proved consistent with experimental findings in due course of time. But Einstein’s
immortal intellectualism confronts with mathematical analysis and logic which is regarded as
the first and the foremost requirement in physics, as no human brain is perfect. This work is
the complete tribute to Einstein's work and philosophy on mass energy inter conversion.
Einstein may not be knowing but he provided mathematical equation for Newton’s
hypothesis of inter-conversion of light energy and mass.
Newton has quoted in his book ‘Optiks’ in 1704 that
"Gross bodies and light are convertible into one another..."
After about 200 years i.e. in 1905 Einstein derived mathematical equation for Newton’s
perception i.e. mass-light energy equation L =mc2 from which he speculated E=mc2. While
deriving mass-energy inter conversion equation Einstein took special values of the involved
parameters but did not discuss many other feasible cases. On such significant topic ‘short
cuts’ are not justified. Further Einstein did not follow the common practice of giving
references of the existing literature in the research papers, on which his work is based upon.
Based upon current experimental situation, theoretical analysis and future
assessment, E=mc2 has been extended to E = Ac2 m. The author intends to interact in
future through other book titled ‘Archimedes and Newton Generalized.’ In this book 2265
years old Archimedes principle is generalized, Newton’s three laws are made more practical
and stress has been given understanding of law of Gravitation by constructing elusive water
and glycerine barometers.
I am indebted to my critics and promoters within the house e.g. my late mother Mrs
Kala Rani Sharma, poet father Mr Dev Dutt Sharma and wife Anjana Sharma. Otherwise it
would have been difficult to maintain enthusiasm over three decades on such topics. Also
diligent efforts of staff of the press are gratefully acknowledged.
Some people have years and years for criticism but really no moments
for constructive suggestions. The knowledge is infinite and suggestions from one and all are
humbly solicited, so that subject matter which is just introduced may be improved. Einstein’s
E=mc2 in some sense is based upon Newton’s hypothesis, the generalized equation E = Ac2
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m is result of critical analysis of Einstein’s E=mc2 and this work needs more sophisticated
experimental observations in future. Thus science is like lighting one lamp from the other.
AJAY SHARMA,
Shimla . August 2012
Email
[email protected], www.AjayOnLine.us
Beyond Einstein and E =mc2
Science is infinite
Ajay Sharma
Chapter 1
Einstein derived L =mc2 For Newton’s Perception
First Glimpse

Many scientists have contributed to concept of mass energy inter-conversion. Also
qualitative and quantitative equations were also put forth by various scientists.

S. Tolver Preston(1875), Jules Henri Poincaré (1900) , Olinto De Pretto (1903)
Fritz Hasenohrl(1904) etc. developed equations and conceptual basis regarding
inter-conversion of mass and energy .

But the real credit for mass light energy inter-conversion equation goes to Einstein,
who derived equations for Newton’s perception as L =mc2, under certain conditions.
4

From L =mc2 Einstein speculated E=mc2, which is not justified scientifically.

In Einstein’s derivation there are four variables e.g. number of light waves, energy
of the light waves, angles at which light waves are emitted and velocity v. These
variables have numerous values, but Einstein has taken only special or handpicked
values of the variables.
 If all the values of the variables are taken then result is L  mc2 or
L
=Ac2 m. Thus Einstein’s derivation is not complete.
1.0
Mass energy inter-conversion before Einstein.
The word ‘energy’ derives from energeia which was coined by Aristotle for first time [1].
German Gottfried Wilhelm Leibniz [1646-1716] put forth idea of vis viva (from the latin
living force) as mv2 and stated that it is conserved [2-3].
vis viva or living force = mv2
(1.1)
where m is mass of body and v is its velocity.
In 1807, Thomas Young [1773 -1829] was first to use term ‘energy’ instead of vis viva [4-5].
Energy = mv2
(1.2)
French mathematician Gustave Coriolisis [1792-1843] was first to define work as product of
force and displacement.
W =FScos Φ
(1.3)
where W is work , Φ is angle between force and displacement S.
In 1829, Coriolisis [4-5] described kinetic energy as
Kinetic Energy =
mv 2
i.e.
2
mv 2
2
(1.4)
Further mass is quantity of matter contained in the body, the real understanding of mass
started when Newton defined second law of motion in the Principia. [6]. Newton also stated
inter conversion of light energy to mass [7], thus initiated important debate on this issue.
According to Newton,
"Gross bodies and light are convertible into one another...",
Mass energy inter-conversion processes are the oldest in nature and constitute the
basis of various phenomena. Further the energies have various forms (e.g.
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sound energy,
heat energy,
chemical energy,
energy emitted volcanic reactions
nuclear energy,
magnetic energy,
electrical energy,
energy emitted in form of invisible radiations,
energy emitted in cosmological
and astrophysical phenomena energies co-existing in various forms etc.) which are
converted into mass. At different times various scientists have studied this significant topic in
different ways and study is continuous process even now.
Many scientists and philosophers have discussed about inter-conversion of mass to energy at different times.
Even an illiterate knew that more the wood or grass he would burn more heat or light energy would be
produced. He may not be aware of Einstein’s work but conclusion is obvious, more mass of wood is consumed,
more energy is emitted. Before Einstein many scientists contributed to the discussion of inter-conversion of
mass to energy. It is equally possible that there may be many more scientists whose contributions are not
recorded or may have been destroyed or purposely annihilated, hence their names are not in this list of
contributors.
Aristotle [384-322 BC] believed that all matter on earth consisted of four pure substances or
elements, which were earth, air, fire, and water [1]. Here fire may be regarded as energy.
Antoine Lavoisier (1743-1794) French Chemist was the first to formulate a law of
conservation of matter in chemical reactions i.e. matter can neither be created nor be
destroyed but can be transformed from one form to other form [8].
Newton [7] has quoted in his book ‘Opticks’ in 1704 that
"Gross bodies and light are convertible into one another...",
No immediate reason is known for Newton’s intuition. It implies that energy is other form of
mass. Neither Lavoisier nor Newton gave any mathematical equation relating to mass- energy
inter-conversion, hence the deduction is qualitative only. The speed of light c (3×109 m/s)
was not defined in Newton’s time, however now c plays a significant role in such cases.
S T Preston [9], an English scientist in his book Physics of the Ether in 1875, gave and applied
equation ΔE  Δmc2 (proportionality form) apparently.
In one example, Preston speculated that one grain could lift a 100,000-ton object up to
a height of 1.9 miles. Mathematically, if the calculations are based upon E = mc2 then mass of one
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grain (64.79891 milligram) emits energy equal to 5.832×1012 J, if completely annihilated. Also energy
required to lift (mgh) one hundred thousand ton (9.0718×107 kg ) to height of 1.9 miles ( 3.0577 ×103
m) is 2.7006×1012 J.
E= mgh = 2.7006×1012 J
(5.32)
The calculations imply that Preston used equation E = mc2 in form E  mc2. It is work of the
rarest or exceptional scientific perspicacity. Now Preston’s 137 years old book is in the
category of the rare books.
Jules Henri Poincaré [10,11] in 1900 applied the calculations in a recoil process and
E
reached at the conclusion in the form, mv =  2  c. From the viewpoint of dimensional
c 
analysis,
E
takes on the role of a ‘mass’ associated with radiation, which yields E=mc2.
2
c
Olinto De Pretto [12] speculated E=mc2, implying that when v = c, then E= mv2 (Leibniz’s
vis viva) becomes E=mc2, in 1903-04. Few years back some Italian scientists logically sought
priority of innovation of E=mc2 as they claimed E=mc2 is Italian idea before Einstein. Just
possible Einstein may have obtained E=mc2 by replacing L by E in L=mc2. In fact Einstein
initially derived L= mc2.
Fritz Hasenohrl [13, 14] in 1904, concluded
“to the mechanical mass of our system must be added an apparent mass which is given by,
m=
8E
where E is the energy of the radiation.”
3c 2
In a later paper he further improved result that mass exchanged is, m=
4E
. Thus in this case
3c 2
also E  mc2 .
Ebenezer Cunningham [15] has further improved Hasenohrl ‘s equation as
E =mc2
Frederick Soddi [16] in 1904 and M. Henri Becquerel both have predicted that in
radioactive emissions the mass of body decreases i.e. energy of radiations is at the cost of
mass. Thus higher the decrease in mass more would be energy of radiation and no conversion
factor was given, this inference is like above one. It also corresponds to E  m or E 
mc2. Hence more radiations are emitted, more mass of radioactive sample or source will
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decrease. But no conversion factor between decrease in mass of radioactive sample and
energy of radioactive radiations, was given by Frederick Soddi. This deduction can be
qualitatively experimentally verified. It is believed that Einstein was influenced by
radioactivity while he derived mass energy inter-conversion equation. In Sep. 1905 Einstein
has written
It is not impossible that with bodies whose energy-content is variable to a high degree (e.g.
with radium salts) the theory may be successfully put to the test.
The radium is over one million times more radioactive than uranium. It decays 3.7 × 1010
disintegrations per second, its salts like RaF2, RaCl2, RaI2 etc are also extremely radioactive. After
radioactive decay, the sample remains at rest. The energy content of radium is highly variable i.e.
emits radiations (hence energy) far more intensely than other radioactive samples.
Thus equation nearly similar to E =∆mc2 were suggested by many intellectuals. Einstein
derived under special conditions L =∆mc2 (as discussed in the forth coming discussions) , and
speculated without mathematical proof E =∆mc2 ( may have taken hint from existing
discussions as a section of thinkers believe). Further Einstein in Sep. 1905 paper did not
write E= ∆mc2. Consequently various scientists used equation E =∆mc2 and now it is
generalized as E = Ac2M, is suggested. So science progresses steadily and continuously.
2.0 Einstein’s approach in Sep. 1905 paper in which L =∆mc2 was derived and E
=∆mc2 was speculated?
Or
Description and Critical Analysis of Einstein’s Thought Experiment
In Einstein’s derivation [17] basic equation is
 v

1  c cos  

   
v2
1 2
c
(1.5)
where  is light energy emitted by body in frame (x,y,z) and  * is light energy measured in
system (ξ, η, ζ ), and v is velocity with which the frame or system (ξ, η, ζ ) is moving. This
equation was given in Einstein’s June 1905 paper in Section 7 and is called Doppler principle
for any velocity whatever. But there is no specific derivation to the equation in paper. Also
there are no references in the paper so that its origin may be quantitatively understood. Then
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this equation is used in derivation which is basically equation of conservation of energy.
Einstein derived L = ∆mc2 from this equation under special conditions and speculated E =
∆mc2 under all circumstances. Thus we find that E = ∆mc2 is speculated from L = ∆mc2
which is based upon eq.(2.2) and eq.(2.2) is not derived as in Einstein’s June 1905 paper. It
is really a strange situation about origin of E=∆mc2 and from equations it is derived.
Obviously many possibilities exist.
Einstein’s perception: Let a system of plane waves of light, referred to the system of
coordinates (x, y, z), possesses the energy l; let the direction of the ray (the wave-normal)
makes an angle ɸ with the axis of x of the system.
If we introduce a new system of co-ordinates (ξ, η, ζ ) moving in uniform
parallel translation with respect to the system (x, y, z), and having its origin of coordinates in
motion along the axis of x with the velocity v.
Thus v is the relative velocity between system (x, y, z) and system (ξ, η, ζ ) .
The body which emits light energy is considered stationary in the system (x,y,z) and also
remains stationary after emission of light energy in the system (xy,z).
Let E 0 and H 0 are energies in coordinate system (x, y, z) and system (ξ, η, ζ
) before emission of light energy, further E1 and H 1 are the energies of body in the both
systems after it emits light energy. Ei and Hi include all the energies possessed by body in two
systems. The various values of Ei’s and Hi’s are shown in Table I.
Table I. Energies emitted before and after emission by body in Einstein’s Sep. 1905
derivation.
Sr No
System (x,y,z)
System(ξ, η, ζ )
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1
Before Emission E0
Before Emission H0
2
After Emission E1
After Emission H1
Thus Einstein wrote various equations as Energy of body in system ( x,y,z ). Then Einstein
concluded that body emits two light waves of energy 0.5L each in system (x,y,z) where
energy is E0.
Energy before Emission = Energy after emission +0.5L + 0.5L
E 0 = E1 + 0.5L + 0.5L = E1 + L
(1.6)
Hence Einstein took all possible energies in account in the derivation.
Energy of body in system (ξ, η, ζ )
H 0 = H 1 + 0.5  L {(1 –
where  
v
v
cos  ) + (1+ cos  ) }
c
c
1
(1.8)
v2
1 2
c
H 0 = H 1 + L
(1.9)
Or ( H 0 – E 0 ) – ( H 1 – E1 ) = L [  –1]
Einstein calculated as
( H 0 – E 0 ) = K 0 +C =
( H 1 – E1 ) = K1 +C =
(1.7)
M bv2
+C
2
M av2
+C
2
(1.10)
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Einstein defined C as additive constant which depends on the choice of the arbitrary additive
constants of the energies H and E. The arbitrary additive constant C is regarded as equal in
both the cases. Thus value of C is purely arbitrary. Kinetic energy of body before emission of
light energy, K 0 (
(
M bv2
) and kinetic energy of body after emission of light energy, K1
2
M av2
).
2
K 0 – K1= L {
1
v2
1 2
c
– 1}
(1.11)
Einstein considered the velocity in classical region thus applying binomial theorem,


v2
v4
K 0 – K1 = L 1  2  3 4  .....................  1
8c
 2c

(1.12 )
Further Einstein quoted [1]
Neglecting magnitudes of fourth
v4
v6 v8
and
higher
,
……. orders, we may place.
c4
c6 c8
v2
K 0 – K1= L
2c 2
M bv2 M av2
v2
–
= L 2
2
2
2c
or L = ( M b  M a ) c 2 = mc 2
(1.13)
(1.14)
(1.15)
Mass of body after emission ( M a ) = Mass of body before emission ( M b ) –
L
(1.16)
c2
Then Einstein generalized the result for every energy and called mass of body is measure of
energy content (every energy that is included in a collection). Einstein further wrote in Sep.
1905 paper
If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact that the
energy withdrawn from the body becomes energy of radiation evidently makes no difference, so
that we are led to the more general conclusion that
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The mass of a body is a measure of its energy-content; if the energy changes by L, the mass
changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in
grammes.
However Einstein never wrote a character ‘E’ or E=mc2 . It is concluded that Einstein’s
statement means E= mc 2 . It can be obtained by replacing L (light energy) by E (energycontent or every energy). Einstein wrote:
or E = ( M b  M a ) c 2 = mc 2
(1.17)
Mass of body after emission ( M a ) = Mass of body before emission ( M b ) –
E
c2
(1.18)
When energy is emitted the mass decreases. Thus Einstein did not differentiate between Light
Energy and other energies in the derivation (both conceptually and mathematically), and
consequently replaced L (light energy) by E (every energy) to get eq.(1.17). The
characteristic equations for describing various energies are different, then it was not taken in
account.
Fadner [27] has rightly pointed out that in the paper Einstein neither wrote E= mc 2 nor E in
the paper. Thus Einstein was not confident while replacing L by E. It is also reflected by the
fact that title of the paper is
Does the Inertia of a Body Depend upon Its Energy-Content?
2.1 Typical Comments Regarding Classical Region Of Velocity (Not Given By Einstein).
Einstein’s derivation also offers the most mysterious and puzzling situation in science. It is
explained below, with help of equation,
Mmotion =
M rest
v2
1 2
c
(1.19)
Let the velocity is in classical region i.e. 10m/s (36 km/hr i.e. ordinary speed of vehicle), then
no increase in mass of object increases when it moves with this velocity. The speed of
aeroplane is over 400km/hr, and no increase in mass is observed. For proper understanding
the conceptual basis of Einstein’s derivation, consider the followings. Now expanding
eq.(1.19) by applying Binomial Theorem we get,
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Mmotion = Mrest [ 1+
v 2 3v 4
+
+……………]
2c 2 8c 4
(1.20)
(i) If velocity v =0 , then eq.(1.20) becomes
Mmotion = Mrest
(ii) If velocity v = 1cm/s (0.036 km/hr) in typical classical region
Mmotion = Mrest [ 1+ 5.55×10-22 +4.166×10-42 + ……………..]
(1.21)
Mmotion = Mrest + Mrest 5.55×10-22 + Mrest 4.166×10-42 + ……….
Here even term Mrest 5.55×10-22 is regarded as negligible compared to Mrest and
Mrest 4.166×10-42 is further negligible thus
Mmotion = Mrest
(1.22)
Thus term 5.55×10-22 has to be neglected only then both masses are equal.
(iii) Similarly the orbital velocity of the earth is 30km/s or 3,0000m/s i.e.
Mmotion = Mrest [1+
v
=10-4
c
v 2 3v 4
+
+……………]
2c 2 8c 4
Mmotion = Mrest [ 1+ 5×10-9 + 3.75×10-17+ ……………..]
(1.23)
Mmotion = Mrest + Mrest 5×10-9
(1.24)
+ Mrest 3.75×10-17
The mass of earth remain same 5.98×1024 kg always. Thus here also the term
v2
(5×10-9)
2
2c
is neglected compared to unity.
Mmotion [mass of earth in motion] = Mrest [mass of earth at rest]
(1.24)
If it is not neglected then mass of earth will be increase per second will increase by
significant amount i.e. 5×10-7 %. Thus we find that Mrest 5×10-9 and Mrest 5.55×10-22 are
neglected in the existing literature. This fact will be used in further interpretation. The various
terms neglected compared to unity are shown in Table II
Table II: Terms neglected in calculations and their effects.
13
Sr.
velocity
No.
Mrel = Mrest[ 1+
v 2 3v 4
+
+ …. ]
2c 2 8c 4
Neglected
Result
term
1
0
Mrel = Mrest
none
Mrel = Mrest
2
Earth’s orbital
Mrel =Mrest [ 1+ 5×10-9 +
5×10-9
Mrel =Mrest
velocity
3.75×10
-17
+ ………]
30km/s
or
3×104m/s
or
1,80,000km/hr
3
v=1cm/s
or
0.036km/hr
Kb –Ka
Mb =Ma
= L [ 1+ 5.55×10
-22
+4.166×10
-42
-22
5.55×10
+ ………-1]
Mass before
emission
or Mb =Ma
= Mass after
emission
2.2 Appearance of c2 in L= Δmc2 is apparently arbitrary.
If Einstein’s derivation is carefully analyzed, then it becomes clear that c2 is arbitrarily
brought in picture i.e. in equation L= Δmc2. We have eq.(1.12) as


v2
v4

K 0 – K = L 1  2  3 4  .....................  1
8c
 2c

(1.12)
Now consider the same case when velocity is 1cm/s or 0.036km/hr , under this conditions
eq.(12) becomes
M bv2 M av2
–
= L [ 1+ 5.55×10-22 +4.166×10-42 + ………..-1]
2
2
(i) Einstein has neglected term
M bv2 M av2
v2
–
= L 2
2
2
2c
(1.25)
3v 4
v2
retained
the
term
as
, and obtained equation
8c 4
2c 2
(1.14)
14
or L = ( M b  M a ) c 2 = mc 2
(1.15)
(ii) If the velocity is very-2 small then
1cm/s (typical classical region), then
v2
can be neglected compared to unity. If velocity is
2c 2
v2
is 5.55×10-22. Depending upon the orbital velocity
2
2c
of the earth (30km/s or 3,0000m/s i.e. v/c =10-4 ) the term
v2
2c 2
(5×10-9 ) can be neglected
compared to unity, only then the equation i.e
Mmotion [mass of earth in motion] = Mrest [mass of earth at rest]
is justified.
In typical classical region ( v =1cm/s )
v2
= 5.55×10-22 is neglected compared to unity ( as
2
2c
5×10-9 is neglected ) then
Mb (mass before emission) = Ma ( mass after emission)
(1.22)
Hence we find that L= Δmc2 is only obtained if the equation is written in particular way. It
is not obtained in all cases. Einstein obtained the equation L= Δmc2 following steps.
(i) Einstein started from the relativistic equation i.e. eq.(1.5)
(ii) After calculation using relativistic equation ,


v2
v4

K 0 – K = L 1  2  3 4  .....................  1
8c
 2c

(1.12)
Einstein applied the Binomial Theorem which implies calculations are reduced to classical
regions only.
(iii) Then Einstein neglected higher terms and retained only
v2
, thus
2c 2
L= Δmc2 is
obtained.
(iv) Now the term
v2
can also be neglected, in eq.(1.12) then we get
2c 2
Mb = Ma
Thus both L= Δmc2 and Mb = Ma are equally probable and but have entirely different
nature. Thus Einstein has brought c2 arbitrarily in equation L= Δmc2, hence in E= Δmc2.
There is no scientifically preferred reason that result
15
L= Δmc2
(1.15)
from Einstein’s derivation must be taken in account and result
Mb (mass before emission) = Ma (mass after emission)
(1.22)
must be neglected.
This discussion also validates the necessity of categorization of sub ranges of velocity in the
classical region or up to which magnitude of the term to be neglected comparatively.
2.3 If the measuring system is at rest (v=0), then Einstein’s derivation L = ∆mc2 is not
applicable. v can also zero if system (x,y,z) and system (ξ, η, ζ ) move with same velocity.
However in this case (when v =0) experimentally when light energy is emitted mass decreases. It is
serious limitation of Einstein’s derivation.
When the measuring system (ξ, η, ζ ) is at rest v = 0 then
 * =
Ho = H1 +L/2 +L/2
Eo = E1 + L
(Ho – Eo) – (H1 –E1) = 0
As body is at rest and measuring system (ξ, η, ζ ) is also at rest, then (Ho – Eo) or (H1 –E1) cannot
be interpreted as kinetic energy. Hence Einstein’s derivation is not applicable. Practically, there are
numerous cases when light energy is emitted by body and measuring system remain at rest( v=0).
Practical situation: A luminous body is at rest and emitting light energy.
Theoretical prediction: Einstein’s derivation predicts decrease in mass is not possible in this
case. Or Einstein’s derivation becomes invalid in this case.
Experimental situation: Actually luminous body emits light energy and its mass decreases.
But this decrease in mass cannot be measured by Einstein’s derivation.
Conclusions Thus Einstein’s derivation is not applicable under these conditions, however
mass is decreasing when light energy is being emitted. It is serious limitation of the
derivation as it becomes invalid. But experimentally the derivation is valid.
3.0 Einstein took only super special values of variables.
In Einstein’s derivation there are four variables which have numerous values e.g. number of
light waves, energy of light waves, angles at which waves are emitted and velocity etc. In
addition Einstein put another condition in the derivation that body remains at rest. These
variables affect the results and their impacts are discussed below. The following arguments
can be given that Einstein’s derivation is true under super special or handpicked conditions.
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3.1 Einstein’s Condition: Body remains at rest before and after emission of energy
Einstein [17] has put condition on state of the body: Let there be a stationary body in the
system (x, y, z), and let its energy--referred to the system (x, y, z) be E0. Let the energy of the
body relative to the system (ξ, η, ζ ) moving as above with the velocity v, be H0. The body
also remains stationary in system (x, y, z) after emission of energy.
Einstein also assumed that the body also remains stationary after emission of light energy.
But practically this condition (Luminous body is stationary) is NOT obeyed in many cases.
(i) The nuclear fission is caused by the thermal neutrons which has velocity 2,185m/s. The
uranium atom also moves as it is split up in barium and krypton, and emit energy. Thus
reactants and products are in motion. Initially reactants is in motion and also sets the products
in motion.
(ii) When a gamma ray photon of energy at least 1.02MeV, moves near the field of nucleus it
is split up in electron and positron pair [18]. The gamma ray photon is in motion and so is the
state of electron and positron pair. Thus reactants and products are in motion.
(iii) Similarly the particle and antiparticle moves towards each other for annihilation. The
particle and antiparticle collide then annihilation takes place. In nuclear fusion the atoms are
set in motion.
(iv) When a paper burns then it is also sets in motion and energy in various forms is emitted.
Also in volcanic reaction the reactants and products remain in motion.
(v) The fast neutrons are slowed down and called thermal neutron thus their velocities are not
necessarily uniform as can be variable while they cause fission of other nuclei.
(vi) When deuterium and titanium fuses, but only after these are set in motion under
conditions of high temperature. The velocity of the reactants is not necessarily uniform and
gradually they overcome the force of electrostatic repulsion. Thus practically Einstein’s
condition that luminous body (reactant) remain at rest, is not obeyed in many cases. It is true
in case of heavy radioactive source emitting radiations.
Chemical reactions were discovered in Einstein’s time. Einstein never discussed this
phenomenon in his works. So Einstein’s condition that body is stationary, emits light energy
and its mass decreases, is not justified in many cases.
3.2 Other Conditions On Einstein’s Derivation.
Einstein’s Sep. 1905 derivation [17] of L = mc2
is true under super special conditions
or handpicked conditions only. It is justified below. In the derivation of L = mc2 . Einstein
17
has considered a luminous body and measuring system in the mathematical treatment, there
are FOUR variables e.g.
(a) Number of waves emitted by luminous body,
(b) l magnitude of light energy emitted by body,
(c) Angle  at which light energy is emitted by body and
(d) Uniform velocity (relative velocity), v of both the systems.
Further values of various variables can be different.
3.3
Nature of v
According to Einstein: v is the relative velocity between system (x, y, z) and system (ξ, η, ζ
). If system (x,y,z) is at rest and system ( ξ, η, ζ ) moves with velocity v, then v is relative
velocity. If the system (x,y,z) and system (ξ, η, ζ ) both move with same velocity then relative
velocity v is zero. Further Einstein strictly took the value of velocity as UNIFORM.
The law of inter-conversion of mass and energy holds good if
(i) Velocity v is in classical region.
(ii) Velocity v is in relativistic region. Then mass of body increases with velocity as given by
eq.(1.19).
(iii) Velocity v is zero
(iv) Velocity v is variable or uniform
These variables have numerous values. The law of inter conversion of mass and energy
holds good under all conditions of velocity, but Einstein has considered just one i.e. constant
velocity is in classical region.
3.4 Einstein’s Guesswork of E =mc2 from L =mc2.
It is obvious that Einstein stated his work for light energy, from eq.(1) i.e.
 v

1  c cos  

   
2
v
1 2
c
(1.5)
where  is light energy emitted by body in frame (x,y,z) and  * is light energy measured in
system (ξ, η, ζ ), and v is velocity with which the frame or system (ξ, η, ζ ) is moving. . This
18
equation was given in Einstein’s June 1905 paper in section 7 and is called Doppler principle
for any velocity whatever. But there is no specific derivation to the equation. Then this
equation is used in derivation which is basically equation of conservation of energy. Using
this equation Einstein obtained equation
L =mc2
Light Energy emitted = (Mass annihilated)c2
Thus this derivation is for inter-conversion of light energy to mass, not for inter-conversion
of every energy to mass. Here Einstein’s guesswork came in picture when equation was
generalized for every energy.
Einstein wrote
‘ Neglecting magnitudes of fourth and higher orders we may place
L v2
K0 − K1 = 2 .
c 2
From this equation it directly follows that:
If a body gives off the energy L in the form of radiation, its mass diminishes
L
by c 2 . The fact that the energy withdrawn from the body becomes
energy of radiation evidently makes no difference, so that we are led to the
more general conclusion that:
The mass of a body is a measure of its energy-content; if the energy
changes by L, the mass changes in the same sense by
L
, the energy
910 20
being measured in ergs, and the mass in grammes.’
It is not impossible that with bodies whose energy-content is variable to
a high degree (e.g. with radium salts) the theory may be successfully put to the test. If the
theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing
bodies.
19
Now measuring the energy of radiations emitted by radioactive source, the decrease in mass
can be estimated. Then results can be compared be E =mc2.
4.0
Mass energy equation after Einstein’s work
Max Planck was compatriot of Einstein. He studied Einstein derivation E =mc2 or L =mc2
and pointed out its limitation [19-20]. However Planck did not point out the limitations which
are discussed here. Max Planck in 1907 made an in-depth investigation of the energy
"confined" within a body, but he did not use Einstein’s approach at all. Planck derived an
expression, m-M=
E
, for heat energy and mass and interpreted that
c2
” The inertia mass of body is altered by absorption or emission of heat energy. The
increments of mass of body are equal to heat energy divided by square of speed of light.”
Planck acknowledged Einstein’s previous derivation but did not agree with correctness of
Einstein’s derivation.
Work of predecessors
It is pertinent to mention that Einstein did not acknowledge work of his predecessors
implying that all work is done by him. But the basics of Special Theory Relativity i.e.
postulate of relativity existed before Einstein in one form or other. Similar is situation of
relativistic variation of mass, time dilation and length contraction etc. The equation for
relativistic variation of mass was given by Lorentz [21-22] in 1889 and 1904. The time
dilation was given by Larmor [23 ] in 1897. The length contraction was given physicist
George Francis FitzGerald [24] to explain negative results of Michelson Morely experiment
in 1889. So these phenomena existed before Einstein. So Einstein simply edited all existing
laws judiciously in an article but did not discover, invent or theorize them. If someone restates Newton’s laws and publishes in journal or book without mentioning name of Newton,
then it does not mean author gets credit of the innovation. Under the perceived condition
Newton cannot be deprived of the credit, similar is the situation of inventors and co-inventors
of relativity.
Purposely Einstein did not give any reference in his paper of already existing
concepts, indicating that nothing existed before and all is his original contribution. Also
these facts were not pointed out by Editor the German journal Annalen der Physik. If the
paper was sent by Editor to an expert for review, the same was also neglected by expert. Or
20
other possibility is that paper was published by Editor as Einstein sent it. However at that
time in the same journals authors gave references of the existing work.
Albert Einstein has given references his own others’ works in his papers, one
specific example is of the paper which he published in Annalen der Physik [57]. Einstein has
given references of work of J Stark. It is evident that Einstein was aware of existing facts in
scientific literature but did not acknowledge the contributing scientists.
Ezzat Bakhoum [25-26] has proposed that a total energy equation that satisfies the
Compton-de Broglie wave mechanics as well as theory of special relativity is
H = mv2
(1.26)
where H is total energy of particle, m is its mass and v is velocity. Bakhoum has put forth that
H=mc2 (or widely regarded as E=mc2) cannot do so simultaneously. The perception is
applied to explain various phenomena. Here it is assumed that H=mc2 is the maximum limit
of energy. Thus again the conversion factor between mass and energy is other than c2 is
suggested. Hence
E  mc2
Afterwards many scientists wrote critical papers on Einstein’s derivation but the same
were contradicted by other scientists hence not discussed here.
4.1 Generalized form of mass energy equation, ∆E =Ac2 ∆m
The author has pointed out the hidden limitations of Einstein’s Sep. 1905 paper or
derivation of E =mc2 , and hence suggested a generalized mass energy inter-conversion
equation ∆E =Ac2 ∆m. In equation ∆E =Ac2 ∆m , A is coefficient of proportionality like
numerous others existing in physics and depend upon inherent characteristics of the mass
energy inter-conversion process. The concept of co-efficient of proportionality is existing
since days of Aristotle. If A is equal to unity then ∆E =Ac2 ∆m becomes equal to E =mc2,
otherwise magnitude of energy predicted can be less or more than E =mc2. In many cases E
=mc2 is regarded as true but not experimentally confirmed in all cases. Thus ∆E =Ac2 ∆m
can be discussed in such cases [29-56]. All these aspects are discussed in the forthcoming
chapters.
5.0
Conclusions.
The ideas of inter-conversion of mass and energy existed in science since ancient days.
Many scientists contributed to the topic, and it is equally possible that doctrines of many may
21
have not seen the light of the day. Thus Einstein has provided mathematical equation for
Newton’s statement [7] that
‘gross bodies and light are inter-convertible to each other’.
Einstein’s derivation is under special conditions only, and hence is not general. This
derivation has some inconsistencies, which are pointed out for first time. The reason is that in
the derivation there are four variables and each variable have numerous values. Whereas all
possible values of variables are taken then inconsistent results are obtained. E =mc2 is
obtained when special values of the parameters are taken. All these aspects are discussed. The
generalized equation of mass energy inter-conversion, ∆E =Ac2 ∆m is also put forth and
applied in various physical phenomena. This aspect is elaborated in Chapters 3- 5.
Reference
[1] Hussey Edward Aristotle Physics Book III and IV Oxford University Press, USA
(1983)
[2] Smith Crosbie The Science of Energy - a Cultural History of Energy Physics in Victorian
Britain. University of Chicago Press , Chicago (1999).
[3] Prentiss, J.J. (Aug 2005). "Why is the energy of motion proportional to the square of the
velocity?". American Journal of Physics 73 no 8: 705 (Aug 2005).
[4] George E. Smith, Physics Today 59 Issue 10 pp 31-36. (October 2006)
[5] Jammer, Max Concepts of Force. Dover Publications; New Ed edition (December
23, 1998)
[6] Newton, I. The Principia: Mathematical Principles of Natural Philosophy (Trans.
I. B. Cohen and A. Whitman). Berkeley, CA: University of California Press, (1999).
[7] Sir Isaac Newton, Opticks, pp. CVX (1704; reprinted by Dover Publications, Inc., New
York, (1952).
[8] Donovan, Arthur, Antoine Lavoisier: Science, Administration, and Revolution.,
Cambridge University Press, (1993).
[9] S. T. Preston, Physics of the Ether, E. & F. N. Spon, London, (1875).
[10]
Poincaré, J.H. , Arch. neerland. sci., 2, 5,232 (1900)).
22
[11] Poincaré', J.H. , In Boscha 1900:252,
[12] Pretto, O. De “Ipotesi dell'etere nella vita dell'universo”, Reale Istituto Veneto di
Scienze, Lettere ed Arti, Feb. 1904, tomo LXIII, parte II, pp. 439-500 (1904).
[13] Hasenöhrl, F. Wien Sitzungen IIA, 113, 1039 (1904).
[14] Hasenöhrl, F. Ann. der Phys. 16, 589 (1905).
[15] Cummingham, E. The Principle of Relativity, p. 189 (Cambridge University Press,
1914).
[16] Soddy, F, Radioactivity: An Elementary Treatise from Standpoint of the Disintegration
Theory (“The Electrician “ Printing and Publishing, London, 1904).
[17] Einstein, A Ann. der Phys. 18 (1905) 639-641.
[18] Arthur Beiser, Concepts of Modern Physics, 4th edition (McGraw-Hill International
Edition, New York, 1987), pp. 25, 27, 420, 428 (1987)
[19] Planck, M, Ann. Phys. 26, 1 (1908)
[20] Planck , M Akad. Weiss. Physik. Math. K1. 13, 542 (1907)
[21] Lorentz H A Proc. Roy.Soc. Amst. 1 427-442 (1899)
[22] Lorentz H A Proc. Roy.Soc. Amst. 6 809-831 (1904)
[23 ] Larmor, J. (1897) "On a dynamical theory of the electric and luminiferous medium",
Phil. Trans. Roy. Soc. 190, 205–300 (third and last in a series of papers with the same
name).
[24] FitzGerald, George Francis (1889), "The Ether and the Earth's Atmosphere", Science 13
(328): 390
[25] E.G. Bakhoum, Physics Essays 15 (1) 2002 (Preprint archive: physics/
0206061)
[26] E.G. Bakhoum, Physics Essays 15 (4) 2002
[27] Fadner, W.L. Am. J. Phys. 56 2 , 144 (1988).
[28] Einstein, A Ann. der Phys. 17, 891-921 (1905).
[29] Sharma,
A American Journal of Scientific Research , Vol. 12 pp.67-112 (2010)
[30] Sharma, A Einstein’s E=mc2 Generalized Raider Publishing International (2007) New York , USA
23
[31] Sharma, A. Proceedings of Physical Science of 98th Indian Science Congress, Chennai,
p.194 (2011)
[32] Sharma, A Proceedings of the 4th international conference of IMBIC, Kolkata ,
pp. 211 (2010).
[33] Sharma, A Proceedings of the Natural Philosophy Alliance , Vol.6 No. 2 pp.
261-263 (2011).
[34] Sharma, A International Journal of Nuclear Science and Technology Vol. 3 No 4 pp. 370-77 (2007)
[35] Sharma, A. Galilean Electrodynamics, Vol. 18, No. 5, pp 99-100 (2007).
[36] Sharma, A. Kurt Godel Society Collegium Logicum Volume IX pp. 67-71 (2007)
[37] Sharma, A
Progress in Physics,
Vol. 3
pp. 76-83 (2008)
[38] Sharma, A. Concepts of Physics, Vol. III, No. 4, pp.345–373 (2006),
http://merlin.fic.uni.lodz.pl/concepts/2006_4/2006_4_351.pdf.
[39] Sharma, A. Abstract Book: 38th European Group of Atomic Systems (Euro physics
Conference), Isachia (Naples), Italy, p.53 (2006) .
[40]
Sharma, A. Abstract Book: A Century After Einstein Physics 2005, (Organiser
Institute of Physics, Bristol) University of Warwick, UK, 10–14 April. (2005)
[41] Sharma, A. Abstract Book 19th International Conference on the Applications of
Accelerators in Research and Industry, Fort Worth, Texas, USA, 20–25 August. 2005
[42] Sharma, A. Abstract Book , Oral presentation (lecture) on 21st September
2005, in The 5th British Gravity Meeting , Oxford, England.
[43] Sharma, A. Physics Essays, Vol. 17, pp.195–222 (2004)
[44] Sharma, A. Proc. Int. Conf. on Number, Time, Relativity, United Physical Society of
Russian Federation, Moscow, p.81 (2004)
[45] Sharma, A Acta Ciencia Indica Vol. XXIV P No. 4 pp.153-158 (1998).
[46] Sharma, A to be published in Galilean Electrodynamics, Massachusetts in , USA
[47] Sharma, A submitted for publication.
24
[48] Sharma, A Acta Ciencia Indica Vol. XXVI P. No. 1 pp.013-016 (1998).
[49] Sharma, A International Conference on World Year of Physics, University of Rajasthan , Jaipur pp.14
(2005)
[50] Sharma, A. 3rd international Young Scientists Conference, Kyiv National University , Scientific works
pp. 19 ( 2002).
[51] Sharma, A Journal of Theoretics Vol.6-5, pp.39-43 2004
[52] Sharma, A Beyond Einstein (monograph) accepted for publication to be published.
[53] Sharma, A Einstein’s Mass Energy Equation, Lambert Academic Publishers (2009) ,Saarbrucken ,
Germany
[54] Sharma, A. Journal of Vectorial Relativity . JRV (4) 1-28 (2009)
[55] Sharma, A. Concepts of Physics, Vol. V, No. 3, pp.553–558 (2006),
[56 ] Sharma A., Proceedings of International Conference on Computational Methods in
Sciences and Engineering 2003 World Scientific Co. USA, 585-586 (2003).
[57] Einstein, A.
Annalen der Physik 14 354-362 (1904).
Beyond Einstein and E =mc2
Science is infinite
Ajay Sharma
Chapter 2
Contradictions In Einstein’s Derivation Of ∆L=∆mc2
First Glimpse
 Einstein initially put forth equation
 v

1  c cos  

   
v2
1 2
c
in June 1905 paper apparently without mathematical derivation. Then derived
25
from this L =mc2 , further speculated E =mc2 by L by E. Thus the derivation is not
justified. There is no such example in history of science.
In Einstein’s derivation L =mc2 and mb = ma are two equally probable equations ,

but L
=mc2 is taken in account and mb = ma neglected.

In Einstein’s derivation there are four variables, and Einstein took super-special or handpicked
values of the variables to derive L =mc2.

If all values of parameters are considered, then results contradict ‘Law of Conservation of Matter’
i.e. when light energy is emitted, mass increases.
 Also under these conditions, the derivation gives L
 mc2
or L =Ac2 m, where A is co-
efficient of proportionality.
 Einstein speculated E =mc2 from L =mc2 , by simply replacing L by E without mathematical
derivation which is incorrect on conceptual basis.
1.0
Law is established after passing many stages.
How a law is established in science? It is an interesting question. A law or a principle is
established after passing two stages [1-28].
(i) Firstly scientist(s) formulate a law or principle for general cases (as far as possible) .
Then mathematical equations are formulated on the basis of perceptions. The
mathematical equations so obtained are theoretically checked for its consistency for
various cases or various values of variables. If the results are theoretically consistent
then that equation passes the first test. If theoretically results are not consistent, then the
law or principle and its mathematical equations are improved.
(ii) Secondly the predictions from mathematical equations are experimentally checked
over a wide range. If experimental results match, then again experiments are conducted
under different conditions. If results are repeatable then law or equation is
experimentally established.
In this regard it can be concluded that Einstein’s perception or
derivation has not passed the first test. Was this paper was published after review ? Or it
was published by Editor as Einstein sent it. Was there some other silent contributor who
did not come in picture? There are reasons that the name of Einstein’s first wife Maric
Mileva can be considered purposely. Due to responsibilities as mother and wife , she
26
could not complete the master’s degree, so even she had published one or 100 research
papers she would have not got PhD degree. So she might have silently contributed to
Einstein’s work, even remaining behind the curtain. Further Einstein’s Sep. 1905 paper
simply required basic knowledge of mathematics and physics which even an
undergraduate student have.
If Einstein has published a paper due to his own self inspiration or intuition , then
at some stage he might have extended or improved the same. The creativity does not
stop but continues and Einstein may have thought to improve his work at some other
stage, especially later half of Einstein’s career remain unproductive comparatively .
There is no satisfactory answer to these questions.
Further this paper has no reference and no acknowledgement. It implies that
such work did not exist in literature before , and everything is solely due to Einstein. But it
was responsibility of Editor to check all these aspects now a days. One can guess the situation
in Einstein’s time. What were rules and regulation of the journal in 1905? Before Einstein
about a year ago Olinto De Pretto has published the same equation E=mc2. The same
equation also follows from the work of Hasenöhrl published in the same journal. Other
scientists were giving references at that time. Did Einstein hid something or he never wanted
that reader should know others’ work on the topic? Sooner or later facts have to come to the
surface. Also Einstein never wrote E=mc2 in his Sep. 1905, this aspect is discussed by
Fadner in American Journal of Physics[29].
Even illiterates know that more mass is consumed more energy is produced. The thesis of
various scientists implies the same. Einstein’s speculated equation also states the same. The
nuclear reactions were discovered in early 1920s. But due to non-availability of any other
equation in 1920s, E=mc2 is used as there was no other way out. Also at that time some
scientists have too given similar equation e.g. Italian Olinto de Pretto [30] and Ebenezer
Cunningham [31], improving work of Fritz Hasenohrl [32].
At that time this equation was used as standard , as there are 7 days in a
week not 10 . So all the parameters or standards were calibrated in terms of E=mc2. Even
basic units of mass or energy ( ‘atomic mass unit’ or MeV) were defined in terms of
E=mc2. The data which was not found consistent with E=mc2 was neglected.
Few facts about atom bomb
It is generally believed that explosion of atom bombs in 1945 , supported the
27
equation E=mc2 , quantitatively. But truth is that E=mc2 is not quantitatively confirmed
in atom bomb explosions in Hiroshima and Nagasaki. The energy observed in devastation is
only 2% of the expected energy predicted by E=mc2. It is report of first US team which
entered Japan in Sep 1945 to assess loses. The details are available in the book , The Los
Alamos Primer written by Robert Serber [33]. He was member of the US team that visited
Japan to assess losses. This book is published by University of California, California. Where
98% energy has gone? It is yet not explained specifically and quantitatively. Hence this
equation E=mc2 should not be regarded as quantitatively confirmed in this case.
In this regard it is pertinent to mention that idea of atom bomb ( chain reaction)
was perceived by Leo Szilard [34 ] in early 1930s. At that time scientists did not pay much
heed to Leo Szilard’s proposal. When he wanted to present the idea to US President Franklin
D. Roosevelt, he failed to get appointment. Then Szilard was instructed to get the idea
approved by Einstein, who had no idea of the chain reaction and how to control it. Einstein
was a theoretical physicist and has nothing to do with experimental physics.
So Leo Szilard travelled to New York where Einstein was holidaying. Szilard
wrote the letter got is signed by Einstein and then it was considered . Also it was brought in
the notice of US President Franklin D. Roosevelt, that probably atom bomb has been formed
in Germany. Thus Manhattan Project for creation of atom bomb was established. Einstein
was not member of the team, Italian theoretical and experimental physicist Enrico Fermi
played a key role is producing sustained nuclear chain reaction. Thus Einstein was a silent
spectator of the process of preparation the most fatal weapon human has ever made. But
generally he is regarded as father of atom bomb.
Thus this equation was established on the basis of qualitative
observation which is not logical. Here we don’t question that mass is converted to energy or
energy is converted to mass both are true, people knew it since ages. But we are discussing
that whether conversion factor is ‘c2’ or different.
Conservation law
The conservation laws are not only the basis of the scientific formulations but also very
essential for the stability of a system or society. For example, let us imagine the state of
affairs in the most ancient society. Let one person A snatched a fruit from the other person B.
This highhandedness as disliked by B, compelled him to take fruit back from A and both may
even hurt each other in the process. In the process, as far as possible B would have taken back
28
the fruit from A or equivalent amount of other eatables such as flowers or sweet roots etc.
Therefore, whatever is the initial content with B before the tussle, as far as possible must be
equal to final content; it is an essential requirement for peace and contentment between two.
The same is the principle of judiciary system globally. This phenomenon can be understood
or discussed in view of general law of conservation. According to this perception
Initial quantity before event = Final quantity after event
This is an example from ancient times, as civilization grew, some consensus or understanding
was established that ‘this’ quantity is equivalent to ‘that’ quantity. For example, an apple is
equivalent to two mangoes or four guavas. In addition, if the person works in the fields then
his daily labor is equivalent to a few kilograms of grain. Thus, the concept of equivalence of
various quantities is as old as civilization itself. In addition, it will continue as long the
civilization lasts hopefully forever in one form of other. Now–a–days one common quantity
that can be exchanged in terms of other quantity known as is currency, which is globally
recognized, a say Dollar or Euro or New Indian Rupee etc.
In general, the law of conservation may be expressed in basic physics in terms of the
principle of dimensional homogeneity. This principle of dimensional homogeneity implies
that dimensions in each term of LHS and RHS of equation are the same. If the dimensions on
each term of LHS and RHS are not the same, then equation is not regarded as correct. In
addition, in chemical reactions, the number of atoms in the reactants and products are
unequal then it is not balanced, it is the application of conservation laws in terms of atoms.
The similar resemblance exists in mathematical equations. In an equation left hand
side (LHS) is always equal to right hand side (RHS) or may be understood as law of
mathematical conservation. These are a few elementary or qualitative or approximate
examples of conservation laws just for understanding that such ideas existed since inception
of humanity or civilization in different ways. Now a day, these are expressed scientifically in
terms of more specific and quantitative quantities in each scientific discipline.
The rise and fall of the laws
The laws fall due to both theoretical and experimental contradictions or inconsistencies. In
the history of science there are numerous examples, that laws were modified or generalized
or uprooted after long time of its use. Thus no law is static in science as laws have been
29
abandoned even after thousand years of use. The new theories so formed explained the
previous results as well as new findings. Here are few such interesting examples.
(i)
Aristotle (384-322 BC) asserted [35] that
‘speed of fall of body was proportional to the weight, and inversely proportional to
the density of the medium the body was falling through’.
Thus, heavier body (more weight) falls quickly than the lighter body. Nearly 30
years after the death of Aristotle it was even challenged in his native place Athenes by Strato,
but unsuccessfully. Galileo (1564-1642) in 1638 published his book The Discourse on Two
New Sciences (published in press in Leiden in the Netherlands), confirmed that all bodies fall
with same acceleration. Thus according to equation
S =1/2at2
(2.1)
the bodies fall equal distances in equal intervals of time (S is distance traveled, a is
acceleration and t is time). Thus, Aristotle’s views were replaced by Galileo’s perception
after about 2000 years. Since time of Galileo, the ‘idealization of reality’ in scientific
perceptions started in some sense.
(ii) For nearly 1800 years, we taught that the Earth is centre and the Sun revolves
around the Earth. It coincided with belief of the Holy Bible. When Galileo [36] published the
truth in 1632 the Dialogue Concerning the Two Chief World Systems, Inquisition prosecuted
him even at age of 63 in 1633. Now we read, teach, understand and preach that the Earth with
all planets revolve around the Sun. Now even the velocity of the Earth around the Sun is
estimated as 30 km/s or 1.08105 km/hr. Hence, problems, solutions and perceptions in
science vary with time.
(iii) Newton’s Corpuscular Theory of light, predicts that the speed of light must be
more in water (denser medium) than in air. It is experimentally found incorrect and Newton’s
Theory was replaced. However, it took somewhat more time and eventually Dutch scientist
Huygen’s Wave Theory of Light was accepted.
(iv) Likewise, Newton’s equation of velocity of sound in air has been replaced by
Laplace’s equation. Newton’s theory (Proposition 49 of Book II of the Principia) on velocity
of sound predicted that velocity of sound must be 280m/s whereas its actual experimental
30
value is 332m/s, which is a contradiction. The difference between predicted and measured
values of velocity of sound is 15.66 %. Thus, Frenchman Pierre Simon Laplace (1749-1827)
modified Newton’s equation. Laplace’s modified equation gave velocity of sound 330m/s,
which is nearly an exact value. Therefore, theories and perceptions in science change
depending upon experimental observations and theoretical analysis.
(v) Einstein’s Static Theory of Universe: Alexander Friedmann (1888-1925) of Russia
proposed that universe is expanding. Einstein intentionally proposed a modification of the
Friedmann’s equation and theorized in opposite sense that universe is STATIC not
expanding. He added a term, which he called the Cosmological Constant, a controversial term
in Cosmology. Einstein did not give any experimental proof that why he is suggesting that
Universe is Static, apparently he wanted to do something different from existing theory. Now
there are two main developments worth noticing.
(a) Friedmann discovered a serious mistake in Einstein’s mathematical proof.
Einstein in his equation divided with a term, which also becomes zero. Since division by zero
is not permitted in algebraic operations. Thus, Friedman maintained that Einstein’s
interpretation is incorrect. According to Gamow,
It is even taught to students of High School that division by zero is not allowed.
Einstein accepted the mistake and called it the biggest blunder of his life as quoted by
George Gamow [37]
”Much later, when I was discussing cosmological problems with Einstein, he
remarked that the introduction of the cosmological term was the biggest blunder of his life”.
George Gamow, My World Line, 1970
In addition, Einstein has said,
‘’Do not worry about your difficulties in Mathematics. I can assure you mine are still
greater’’.
Everybody sails on the same boat and only great souls like Einstein can accept it so humbly.
Einstein greatness can be described by his another quotation;
Imagination is more important than knowledge.
31
(b) Later on, it is experimentally confirmed that universe is expanding (Hubble’s Law)
in 1929, hence Einstein’s doctrine of static universe was abandoned. Thus, science is not
static; in many cases as new evidences come, old theories are modified or replaced. However,
Einstein abandoned his theory of static universe much later in 1930s. Thus, human brain must
not be regarded as perfect; superiority is definitely there in many cases comparatively.
It must be noted that the time when the old theories were formulated they explained
the existing results and appeared correct. It is only later when more and more experimental or
theoretical evidences emerged, old theories were extended or modified to accommodate
newer experimental results and facts.
2.0 Genuine cases neglected in Einstein’s derivation
It is described in Chapter 1 that there are four variables in Einstein’s derivation of L= Δmc2
, each variable may have numerous values. Thus numerous sub cases are possible and hence
L= Δmc2 may not be possible in all cases. Einstein’s light energy mass inter-conversion
equation
L= Δmc2
is obtained under special cases only.
In Einstein’s derivation eq.(2.2) is basic equation.
 v

1  c cos  

   
2
v
1 2
c
(2.2)
where  is light energy emitted by body in frame (x,y,z) and  * is light energy measured in
system (ξ, η, ζ ), and v is velocity with which the frame or system (ξ, η, ζ ) is moving. This
equation was given in Einstein’s June 1905 paper in Section 7 and is called Doppler principle
for any velocity whatever. But there is no specific derivation to the equation in paper. Also
there are no references in the paper so that its origin may be quantitatively understood. Then
this equation is used in derivation which is basically equation of conservation of energy.
Einstein derived L = ∆mc2 from this equation under special conditions and speculated E =
∆mc2 under all circumstances. Thus we find that E = ∆mc2 is speculated from L = ∆mc2
which is based upon eq.(2.2) and eq.(2.2) is not derived as in Einstein’s June 1905 paper. It
32
is really a strange situation about origin of E=∆mc2 and from equations it is derived.
Obviously many possibilities exist.
Einstein has taken super special or handpicked values of parameters. Thus for complete
analysis the derivation can be repeated with all possible values of parameters. In all cases the
law of conservation of momentum is obeyed (which is discussed in next sub-section).
(i) The body can emit large number of light waves but Einstein has taken only TWO light
waves emitted by luminous body.
Why one or n light energy waves are neglected?
(ii) The energy of two emitted light waves may have different magnitudes of energy but
Einstein has taken two light waves of EQUAL magnitudes (0.5L each).
Why other magnitudes (0.500001L and 0.499999L) are neglected by Einstein?
(iii) Body may emit large number of light waves of different magnitudes of energy making
different angles (other than 0º and 180º as assumed by Einstein).
Why other angles (such as 0º and 180.001º, 0.9999 º and 180º etc.) are neglected by Einstein?
Thus body needs to be specially fabricated; other forms of energy such as invisible energy are
not taken in account. Further body should emit light energy only, not other forms of energy.
(iv) Einstein has taken velocity in classical region (v<<c and applied binomial theorem in the
end) has not at all used velocity in relativistic region. If velocity is regarded as in relativistic
region (v is comparable with c), then equation for relativistic variation of mass with velocity
i.e.
Mrel =
M rest
v2
1 2
c
(2.3)
is taken in account. It must be noted that before Einstein’s work this equation was given
by Lorentz [38-39] and firstly confirmed by Kaufman [40] and afterwards more convincingly
by Bucherer [41]. Einstein on June 19, 1948 wrote a letter to Lincoln Barnett [42] and
advocated abandoning relativistic mass and suggested that it is better to use the expression for
the momentum and energy of a body in motion, instead of relativistic mass.
It is strange suggestion as Einstein has used relativistic mass in his work including in the
expression of relativistic kinetic energy [43] from which rest mass energy is derived [44-45].
33
So Einstein’s equation of inter-conversion of mass to energy highly depends upon velocity
theoretically whereas practically the mass energy inter-conversion phenomena are applicable
in all cases.
(v) Einstein has considered body emits light energy, but simultaneously body may also emit
heat energy which is not taken in account in Einstein’s derivation. A burning body emits
heat, sound, light energies and energy in form of invisible radiations simultaneously, along
with invisible radiations. For proper description of heat energy-mass inter-conversion we
need equation equivalent to eq.(2.2). Similar is the case of other energies. In nuclear
explosion energies co-exist in many forms e.g.
light energy,
sound energy,
heat energy ,
and energy in form of invisible of various radiations. Einstein has only considered Light
Energy and other energies are neglected to derive L = mc2.
Further Einstein has considered that body emits light energy in visible region. But energy can
also be emitted in the invisible region and Einstein did not mention at all about heat and
sound energies (emitted along with light energy). Thus energies other than light energy are
also emitted but neglected by Einstein in the derivation. So energies are not taken in account
completely. The various values of parameters neglected and taken in account in derivation are
shown in Table I.
Table I The values of various parameters considered by Einstein and neglected by
Einstein in the derivation of light energy mass equation L = mc2.
Sr
Parameters Einstein considered
No
Einstein neglected
(No reason was given by Einstein why
parameters are neglected).
1
No. of
light
waves
Two Light Waves
One, three, four or n waves
34
2
Energy of
Equal
Energies of the order of 0.500001L and
light wave
0.5L and 0.5L each
0.499999L are also possible. There are
numerous such possibilities, which need to
be probed. Bodies can emit more than two
waves. The invisible waves of energy are
not taken in account.
3
Angle
0
and 180
The angles can be 0
and 180.001 or
0.9999 and 180 are also possible. There
are numerous such possibilities which need
to be probed.
4
Velocity
Classical region
The velocity can be in relativistic region.
The velocity v can also be zero i.e. v = 0
when v~c mass increases
5
Velocity
Uniform and
The law of inter-conversion of mass to
in classical region
energy also holds good, when velocity is
variable.
Deductions: Einstein has taken only super-special values of parameters, and neglected many
realistic values.
3.0 Effects of general values of variables
If body recoils when waves of different light energy are emitted. Eq.(2.2) is main equation
in Einstein derivation .
(i) If light emitting body is at rest then relative velocity of measuring system (ξ, η, ζ) is only
‘v’. In this case recoil velocity is zero. Thus relative velocity is ‘v’.
(ii) If light emitting body recoils away from the body VR , then relative velocity will be
v + VR
35
(iii) If light emitting body is drifted towards the measuring system(ξ, η, ζ) with velocity VR
then relative velocity will be
v– VR
But in this case the recoil velocity VR is of the order of 5×10– 33 m/s and with this velocity
body can travel a distance of 1.57×10-24 m in 10 years ( which is undetectable , hence by
definition body is at rest). Thus in this case body is regarded as at rest.
If upon emission of light energy, the body may move towards or away from the observer
velocity becomes ( v± VR) or say (v + VR). Thus
 v  VR

1  c cos  

   
[v  V R ] 2
1
c2
(2.4)
Now this equation can be applied to study variation in mass when light energy emitted as in
case of eq.(2.4).
3.1 Conservation of momentum in general cases helps in calculations of recoil velocity.
The law of conservation on energy and momentum are two significant laws.
(i) In the derivation of L = mc2, the law of conservation of energy is taken in account as in
eqs.(2.5-2.6) i.e.
E 0 = E1 + 0.5L + 0.5L = E1 + L
(2.5)
Hence Einstein took all possible energies in account in the derivation.
Energy of body in system (ξ, η, ζ )
H 0 = H 1 + 0.5  L {(1 –
v
v
cos  ) + (1+ cos  ) }
c
c
(2.6)
Similar is the status in derivation under general conditions.
(ii) Further the law of conservation of momentum holds good in such cases and can be used
to calculate the recoil velocity, VR. The value of recoil velocity in this case turns out to be too
less i.e. 5×10-33 m/s.
This case is similar to recoil of the gun when bullet is fired, but here two waves are emitted.
It can be compared with the case that a person is standing with both arms stretched, holding
36
pistols in both hands and shots are fired. The momentum is conserved in both cases i.e.
when person remains at rest or moves (tends to move).
In all these cases initial momentum is equal to the final momentum of the system.
When system is at rest then both initial and final momenta of system are zero.
If person recoils then final velocity is such that initial momentum is exactly same as final
momentum.
The momentum is conserved irrespective of the fact that luminous body remains at rest or
recoils after emission of light energy [46].
In case of Einstein’s derivation momentum is conserved in both special and general cases.
(i) When light emitting body remains at rest after emission. In this case recoil velocity is zero
i.e. VR =0, it is calculated by applying law conservation of momentum.
(ii) When light emitting body recoils due to emission of two waves in different directions. In
this case velocity of recoil is non-zero and calculated by applying law of conservation of
momentum. Einstein did not consider this case.
Calculations recoil velocity in system (x, y, z)
The recoil velocity can be calculated by applying law of conservation of momentum,
initial momentum of the system = final momentum of the system
, then VR will affect equation of relativistic Doppler principle of light as in eq.(2.4) as
relative velocity will vary. If a bullet is fired from gun then system recoils in backward
direction.
The law of conservation of momentum can be used to calculate the velocity of recoil
in this case also. Let the body of mass 1 kg emits in two waves in visible region of
wavelength 5000ºA , it corresponds to
2hc

or 7.9512×10-19 J , and the energy is divided in
two waves.
Let body emits light energy (towards the observer, φ= 0º) 0.50001L i.e.
E1 = 3.975607×10-19 J
(2.7)
and momentum
p1 =
E1
= 1.325202×10-27 kg m/s
c
(2.8)
Secondly, the body emits light wave of energy (away from the observer, φ= 180º) 0.49999L
i.e.
37
E2 =3.975592×10-19 J
momentum p2 =
( 2.9)
E2
= 1.325197×10-27 kg m/s.
c
(2.10)
Let us assume that when the body emits light waves of energy in
system (x,y,z) and recoils (if it actually does) with velocity VR (say), the body will recoil
opposite to direction of wave having energy E1 ( more energetic wave).
Before emission of light energy
Initial momentum of waves + initial momentum of luminous body = 0 +0
(2.11)
After emission of light energy
Final momentum of waves + final momentum of body due to recoil= p1 – p2 + MVb
(2.12)
One wave having momentum p2 moves towards the direction in which body recoils and other
wave moves in the opposite direction ( M =1kg).
Here the energy of wave 1 is E1 (E1 = 3.975607×10-19 J, p1 =
E1
=1.325202×10-27 kg m/s),
c
which is more than energy of wave E2 (E2 =3.975592×10-19J, p2 =
E2
= 1.325197×10-27 kg
c
m/s. ).The wave 1 is emitted towards the observer system(ξ, η, ζ ) .
Thus body recoils in direction opposite to wave 1 is emitted. It is like a bullet is fired from
gun, then system recoils in backward direction. Hence here momentum p1 (bigger in
magnitude) have forward direction to measuring system (ξ, η, ζ ) is taken as negative.
The direction of recoil velocity VR will be opposite to that of p1.
The recoil velocity is calculated as 5×10-33 m/s, hence relative velocity of the (ξ, η, ζ )
becomes (v+VR) .
Then according to law of conservation of momentum we get
0 = p1–p2 + MbVR
( 2.13)
VR = (p1 –p2) /Mb = (1.325197×10-27–1.3252202×10-27) ×10-27
= –0.000005×10-27 = –5×10-33 m/s
(2.14)
Thus body recoil backwards. The velocity 5×10-33 m/s means body remains at rest, as 5×10-33
m/s is negligible. A body is said to at rest if it does not change its position w.r.t. to
surroundings. The velocity is too less to be detected. It is analogous to observation that a
CAR cannot move when head and rear lights are switched on.
38
Thus conservation of momentum requires that body should move with velocity 5×10-33 m/s
away from the observer as direction is opposite to p1. With this velocity the body will recoil
to immeasurably small distance i.e.
S(100 years) = 5×10-33 m/s × 3.14×107 ×100 = 1.57×10-23 m
(2.15)
S(10 years) = 1.57×10-24 m
which is undetectable by all means hence body can be regarded as at rest.
Thus body will tend to move with velocity 5×10-33 m/s( towards the observer) which is
immeasurably small or undetectable by all means, hence the body remains at rest by
definition of the rest.
This recoil velocity (VR ) i.e. 5×10-33 m/s is negligible compared to the velocity of the
measuring system i.e. v + VR = v+5×10-33 m/s = v
Size of nucleus = 10-14 m
S(100 years) = 1.57×10-9 size of nucleus
(2.16)
( 2.17)
S(10 years) = 1.57×10-10 size of nucleus
Thus body moves a distance of 1.57×10-24 m in 10 years which is immeasurable. Hence
body can be regarded as at rest by definition, as in case of Einstein’s derivation when two
waves are emitted. Even if this velocity is taken in account for the sake of completeness then
results are same as in previous case.
Even bigger numerical values are neglected in Physics e.g. in the relativistic variation of mass
Mmotion =
M rest
(2.18)
v2
1 2
c
Mmotion = Mrest [ 1+
v 2 3v 4
+
+……………..]
2c 2 8c 4
Mmotion = Mrest [ 1+ 5.55×10-18 +4.629×10-31+ ……………..]
Here velocity is regarded as 1m/s (3.6km/hr) in classical region and even term 5.55×10-18 is
regarded as negligible, thus
Mmotion = Mrest
Hence recoil velocity 5×10-33 m/s is also negligible. Thus equations for recoil momentum and
recoil kinetic energy KE recoil will be
Precoil = 5×10-33 kgm/s
(2.19)
KErecoil = 1.25×10-65 kgm2/s2
( 2.20)
This energy i.e. 1.25×10-65 J is equivalent to 2.99×10-66 calories.
39
Due to this uniform relative velocity v of the system (ξ, η, ζ ) will not change within
measurable limits, however effect of VR can be considered for completeness.
If body does not change its position so it can be regarded at rest by definitions, as
v+VR = v+5×10-33 m/s =v ,
and x+ 1.57×10-24 m = x
Thus the law of conservation of momentum helps us in calculations of recoil velocity, which
changes the magnitude of v. Hence equation of relativistic variation of light energy i.e.
Doppler principle for light for any velocities whatever, becomes as eq.(2.4).
 v  VR

1  c cos  

   
[v  V R ] 2
1
c2
(2.4)
Now if body recoils then eq.(2.4) has to be used instead of eq.(2.2) in calculation of energy.
4.0 L  ∆mc2 or L =A ∆mc2 and contradiction of law of conservation of matter
In the derivation Einstein [47] has included all types of energies of body in E and H [and
speculated with this basis, equation for every energy (or energy -content)]. While body
recoils small amount of heat energy, sound energy etc. may also be produced and energy is
dissipated against friction, depending upon velocity of recoil. In Einstein’s case recoil
velocity is zero.
Thus when body recoils then energies after emission are denoted by E1 and H1 (
as these take in account all type of energies in Einstein’s derivation). Einstein has written the
equations of conservation of energy in both the systems i.e. in system(x,y,z) and system (ξ, η,
ζ ). The conservation of energy implies inclusion and constancy of all type of energies. Also
in this case body remains at rest i.e. v+VR= v+5×10-33 m/s = v, and x+ 1.57×10-24 m = x (in
10 years). Even the recoil velocity is considered for the sake of completeness only to remove
any doubt over this sensitive issue.
Einstein has considered a body emitting two light waves of energy 0.5L each just
in opposite directions. Let in this case the luminous body emits two light waves of energy
0.500001L and 0.499999L in system (x,y,z) emitted in opposite directions. Then amount of
40
light energies measured in both systems are related as (equivalent to case of Einstein) as in
eq.(2.5) and eq.(2.6)
E0 = E1 + L
(2.21)
H0 = H1 + 0.500001 L  {(1 –
v  VR  cos 0 )} + 0.499999 L  {1– v  VR  cos180 }
c
c
(2.22)
where
 =
1
2

v  VR 
1
c2
The eqs.(2.21-2.22) correspond to law of consevation of energy, like eqs.(2.5) and eq.(2.6)
 v  VR 
H0 = H1 + L  [ 1– 0.000002
 ]
 c 
(2.22)
 v  VR 
H0 – E0 = H1 – E1 + L  [ 1– 0.000002
 ] –L
 c 
(2.24)
 v  VR 
(H0 – E0 ) – (H1 – E1) = L{  [1– 0.000002
 –1}
 c 
(2.25)
 v  VR 
K0 –K1 = L{  [1– 0.000002
 –1}
 c 
2

v  VR 
= L (1+
2c
2
 v  VR 
)[ 1– 0.000002
 –1]
 c 
 v  VR 
=L [1- 0.000002
 +
 c 
 v  VR 
K0 –K1 = L [– 0.000002
+
 c 
 v  VR 2
M bv2
– Ma 
2
2

Mb
v2
v  VR 
2
v  VR 2
2c 2
–1]
+...
v  VR 2 ]
(2.26)
2c 2

 = L [– 0.000002 v  VR

 c

– Ma = – 0.000004L / (v+VR )c +

+

v  VR 2 ]
2c 2
L
c2
The recoil velocity VR is already calculated eqaul to 5×10-33 m/s in eq.(2.14)
v+VR = v+5×10-33 m/s = v
(2.27)
41
M b – Ma = L [
∆mc2 = L[
L=
 0.000004 L
1
+ 2 ]
cv
c
 0.000004c
+ 1]
v
(2.29)
mc 2
 0.000004c   1
v
 0.000004c
= –120
v
L=
(2.28)
(2.30)
(if v=10m/s)
mc 2
mc 2
=
 120  1  119
(2.31)
or L =constant × ∆mc2
Further,
L  ∆mc2
or L =A ∆mc2
(2.32)
where A is coefficient of proportionality like many others in the existing physics. Its value
depends upon inherent characteristics of the process. The conversion factor between mass
and energy in L = ∆mc2 is c2 ( 9×1016 m2/s2) like a universal constant. Even some variations
in value of universal gravitational constant, G are considered but not in this case.
Whether the effects of recoil velocity are incorporated or not, the result remains the same as
velocity of recoil is 5×10-33 m/s.
4.1 Einstein’s Sep. 1905 derivation also contradicts the law of conservation of energy.
The eq.(2.28) also contradicts the law of conservation of energy. From the derivation
following derivation can be easily deduced.
Increase in mass of luminous body when Light Energy is emitted.
With slight variations in the variables in Einstein’s Sep. 1905 derivation we have already
derived eq.(28) as
M b – Ma = L [
1
 0.000004
+ 2 ]=
cv
c
 0.000004 L
L
+ 2
cv
c
(2.33)
0.000004 L L
– 2
cv
c
(2.34)
4L
133.3L
0.000004 L
= 6
=
8
cv
10  3  10  10
1017
(2.35)
M a = Mb +
42
L
L
1.11L
=
= 17
16
2
9  10
c
10
(2.36)
0.000004 L L 133.3L 1.11L
– 2 =
– 17 is positive quantity
cv
c
1017
10
M a = Mb +
133.3L 1.11L
– 17 = Mb + positive quantity
1017
10
(2.37)
Mass after emission of light energy =
Mass before emission of light energy + positive quantity
The Einstein’s derivation under these conditions clearly implies that
When luminous body emits light then mass of body increases.
It is contradiction of Law of Conservation of energy. Now following question are required to
be answered in view of the theoretical derivation.
(i) How energy is emitted?
(ii) How mass increases?
How does double increase happen simultaneously?
It implies that a candle once lit will keep on giving light and heat energies for infinite time, as
energy is emitted the mass of candle will increase spontaneously and automatically. But this
prediction is contrary to experiments.
Now %age difference (in energy) between Einstein’s special derivation and
generalized derivation can be calculated
%age increase = {
L
c2
L
 0.000004 L
–
(
+
)
}×
×100}
cv  VR )
L
c2
c2
= 1.2×104
(2.38)
which is exceptionally significant magnitude.
4.2 If the direction (angles) of waves is exchanged then results from Einstein’s
derivation are entirely different i.e. self contradictory results are produced.
In previous case it is regarded as waves of energy 0.500001L makes angle 0 with x-axis , and
wave of energy 0.499999L makes an angle 180 . If the angles are interchanged then result is
different. For example the derivation in this case predicts that
when body emits light energy then mass of body decreases more than L/c2
Thus Einstein’s Sep.1905 derivation gives different results under different conditions. But if
angles of the waves are interchanged then results are entirely different. It is justified below.
43
Ho = H1 + 0.499999  L[( 1 –
v  VR  cos0º)] + 0.500001 β L [1– v  VR  cos 180º)]
c
c
(2.39)
v  VR  )]
Ho = H1 + 0.499999  L[( 1–
c
+ 0.500001 β L [1+
v  VR  + 0.500001
Ho = H1 + 0.499999  L – 0.499999 β L
c
v  VR  )]
(2.40)
c
 L + 0.500001  L
v  VR 
c
Ho = H1 +  L + 0.000002  L
v  VR 
(2.41)
c
Eo = E1 + L
(Ho – Eo) = (H1– E1) +  L + 0.000002  L
v  VR  –L
(Ho – Eo) – ( H1 – E1) =  L + 0.000002  L
=  L [1 + 0.000002
( 2.42)
c
v  VR  –L
(2.43)
c
v  VR  ]– L
c
= L {  [ 1 + 0.000002
v  VR  ]– 1 }
c
2

v  VR  – 1 }
v  VR 
= L { ( 1+
)( 1 +0.000002
2c 2
c
2


v  VR 
v  VR 
= L{[1 + 0.000002
]+
– 1}
c
K0 –K1 = L { 1 + 0.000002
K0 –K1 =
L [ 0.000002
M bv2
– Ma
2
 v  VR 2


2

Mb – Ma = L [
∆mc2 = L [
v  VR 2
2c 2
+
2c 2
v  VR 2 – 1 }
2c 2
(2.44)
(2.45)
v  VR  + v  VR 2 ]
c
2c 2

v  VR  + v  VR 2 ]
 = L [ 0.000002

c
2c 2

0.000004
1
+ 2]
cv  VR 
c
0.000004c
+ 1]
v  VR 
(2.46)
(2.47)
(2.48)
44
L= [
mc 2
]
0.000004c
1
v  VR 
(2.49)
If v =10m/s
L=
mc 2
mc 2
=
0.000004c
0.000004c
1
1
v  VR 
10  5 10 33

=

mc 2
mc 2
=
120  1
121
So Einstein’s derivation does not give fixed value of energy corresponding to mass
annihilated.
L =constant × ∆mc2
(2.50)
Thus if Einstein’s derivation is critically analysed then general result is
L  ∆mc2 or L =A ∆mc2
(2.32)
where A is coefficient of proportionality.
Further
M b – Ma = L [
M a = Mb –
0.000004
1
+ 2]
cv  VR 
c
(2.51)
0.000004
L
– 2
cv  VR 
c
In this case result is
when body emits light energy its mass decreases more than
L
c2
Thus Einstein’s derivation gives self contradictions and contradictory results to law of
conservation of energy.
4.3 In the derivation Einstein used eq.(2.2) for relativistic variation of light energy,
which was given in the previous paper [8]. But this equation is only meant for light
energy not at all for other energies; hence any deduction from it must be applicable for
light energy only.
The equation
 v

1  c cos  

   
2
v
1 2
c
(2.2)
45
is not meant for
(i) sound energy,
In Doppler effect change in frequency of sound is estimated, not variation in mass. Likewise
eq.(2.2) is not associated with any other energy. The speed of sound is 332m/s and that of
light 3x108 m/s.
(ii) heat energy
There is no equation like eq.(2.2) which relates variation of heat energy. The similar is the
case of other types of energies.
(iii) chemical energy
(iv) nuclear energy
(v) magnetic energy
(vi) electrical energy
(vii) energy emitted in form of invisible radiations
(viii) attractive binding energy of nucleus
energy emitted in cosmological and astrophysical phenomena
(x) energy emitted in volcanic reactions
(xi) energies co-existing in various forms etc. etc.
Then why results based upon eq.(2.2) are applied to above energies (i –xi) ?
The reason is that all energies have different type of nature, and the energies are not
confirmed to obey the same equation.
Einstein initially derived ‘light energy’–mass inter-conversion equation L =∆mc2, then
speculated ‘every energy’ –mass inter conversion equation E =∆mc2 from
L =∆mc2. As
eq. (2.2) is only meant for light energy, not for other energies. Hence speculative transition to
E =∆mc2 from L =∆mc2 is absolutely without any mathematical basis.
4.4 If the measuring system is at rest (v=0), then Einstein’s derivation L = ∆mc2 is not
applicable. v can also zero if system (x,y,z) and system (ξ, η, ζ ) move with same velocity.
However in this case (when v =0) experimentally when light energy is emitted mass decreases. It is
serious limitation of Einstein’s derivation.
When the measuring system (ξ, η, ζ ) is at rest v = 0 then
 * =
(5.52)
Ho = H1 +L/2 +L/2
(5.53)
Eo = E1 + L
(5.54)
(Ho – Eo) – (H1 –E1) = 0
(5.55)
As body is at rest and measuring system (ξ, η, ζ ) is also at rest, then (Ho – Eo) or (H1 –E1) cannot
46
be interpreted as kinetic energy. Hence Einstein’s derivation is not applicable. Practically, there are
numerous cases when light energy is emitted by body and measuring system remain at rest( v=0).
Practical situation: A luminous body is at rest and emitting light energy.
Theoretical prediction: Einstein’s derivation predicts decrease in mass is not possible in this
case. Or Einstein’s derivation becomes invalid in this case.
Experimental situation: Actually luminous body emits light energy and its mass decreases.
But this decrease in mass cannot be measured by Einstein’s derivation.
Conclusions Thus Einstein’s derivation is not applicable under these conditions, however
mass is decreasing when light energy is being emitted. It is serious limitation of the
derivation it becomes invalid. But experimentally the derivation is valid.
4.5 Einstein has considered just two waves at angles 0 and 1 0, but if one angle is
slightly changed then the results change drastically. It can be understood in various
cases.
(a) Inconsistent results are obtained if one angle is slightly changed (180 to 180.01 ) in
Einstein’s derivation and other parameters remain the same. Now equation equivalent to
eq.(2.6) becomes,
H0 = H1 + 0.5  L [ (1 –
H0 =H1+ 0.5  L [1 –
v  VR  cos0 ) + (1 – v  VR  cos 180.01 )]
c
v  VR  + 1+0.9999 99984 v  VR  ]
c
H0 = H1+ 0.5  L [2 –0.000000015
(2.56)
c
c
v  VR  ]
(2.57)
(2.58)
c
E0 = E1+L
(Ho – Eo) – (H1 – E1) = 0.5  L[2 –0.00000015
K0 – K'1 = L{  [1 –0.0000 00015
=L{[1+
v  VR  ] – L
c
v  VR  ]–1}
c
v  VR 2 ] (1-0.0000 00007 v  VR  )-1}
2c 2
 v  VR 2
M bv2
– Ma 
2
2

(2.59)
c
2


v  VR  v  VR 
 =L[–0.0000 00007
+
]

c
2c 2

(2.60)
47
L
0.000000015L
+ 2
cv  VR 
c
M b – Ma =
M a = Mb +
0.000000015L L
– 2
cv  VR 
c
(2.61)
v=1m/s or 3.6 km/hr
0.000000015L
5L
=
cv  VR 
1017
(2.62)
L 1.111L
=
1017
c2
(2.63)
5L 1.111L
>
1017
1017
Mass after emission of light energy =
Mass before emission of light energy + positive quantity
(2.64)
It implies that when light energy is emitted the mass of the body increases. But it does not
happen actually. It is contradiction of law of Conservation of Energy/Mass. When a body
emits light energy or any types of energy the mass always decreases. It is the most serious
limitation.
%age increase in energy =
{
L
L
c2
0.000000015L
–
(
+
)
}×
×100 = 45
cv  VR 
L
c2
c2
(2.65)
(b) We can also discuss the case when the angle is slightly lesser than 180 i.e. 179.98. The
other parameters remain the same as in case of Einstein’s derivation. Now equation
equivalent to eq.(2.6) becomes,
H0 = H1 + 0.5  L [ (1 –
H0 = H1 + 0.5  L[1-
v  VR  cos0 ) + (1 – v  VR  cos 179.98 )]
c
v  VR 
c
c
+ 1+0.9999 99939
H0 = H1+ 0.5  L[2-0.0000 0006
v  VR 
c
]
v  VR  ]
(2.67)
c
E0 = E1+L
(Ho – Eo) – ( H1– E1) = 0.5  L[2-0.0000 0006
(2.66)
v  VR 
c
]–L
48
K0 – K1 = L{  [1 –0.0000 0003
=L{(1+
v  VR  ]–1}
c
v  VR 2 )[ (1-0.0000 0003 v  VR  ] -1}
2c 2
(2.68)
c
M bv2
– Ma
2
 v  VR 2


2

M b – Ma =
0.00000006 L
L
+ 2
cv  VR 
c
M a = Mb +
0.00000006 L
L
– 2
cv  VR 
c
2


v  VR  v  VR 
 = L{–0.0000 0003
+
}

c
2c 2

(2.69)
20
0.00000006 L
= 1017
cv  VR 
L 1.111L
=
1017
c2
Mass after emission = Mass before emission + positive quantity.
It is evident from the mathematical equations that when light energy is emitted mass of body
increases. It is contradiction of law of conservation of matter, as never verified
experimentally.
(c) Further another case can be considered if angle is 180.001 instead of 180 . The other
parameters remain the same as in case of Einstein’s derivation.
Einstein’s angle = 180
Now angle under consideration =180.001
The rest of parameters and derivation is same as that in case of Einstein.
H0 =H1 + 0.5  L [ (1 –
H0 = H1+ 0.5  L[1 –
v  VR 
c
cos0 ) + (1 –
v  VR 
c
cos 180.001 )]
(2.70)
v  VR  + 1+0.9999 99999 v  VR  ]
c
H0 = H1 + 0.5  L[2 –0.0000 00001
c
v  VR 
c
]
( 2.71)
E0 = E1+L
(Ho – Eo) – ( H1 – E1) =  L[2 –0.0000 000005
K0 – K1 = L[  (1-0.0000 000005
v  VR 
c
v  VR  ] – L
) –1]
c
49
=L[(1+
2c 2
 v  VR 2


2

M bv2
– Ma
2
(2.72)
c

v  VR  + v  VR 2 ]
 =L[–0.0000 00005

c
2c 2

L
0.000000001L
+ 2
cv  VR 
c
M b – Ma = –
M a = Mb +
v  VR 2 ) {1 –0.0000 00005 v  VR  }–1]
0.000000001L L
– 2
cv  VR 
c
(2.73)
L
0.333L
0.000000001L
=
=
17
cv  VR 
310
1017
L
c2
=
1.11L
1017
M a = Mb +
L
0.000000001L
– 2
cv  VR 
c
M a = Mb +
0.333L 1.111L
–
1017
1017
In previous case when angle under consideration is 180.01 then result is contradictory to
eq.(2.73). Thus decrease in mass is less than
L
. Thus Einstein’s derivation does not give
c2
unique value of ∆m . So Einstein’s derivation gives different results under different
conditions. The value of ∆m varies from one situation to other.
%age difference = {
L
c2
0.000000001L L
–
(–
+
)}×
×100}
cv  VR 
L
c2
c2
= 0.0000 00001×3×108 ×100 = 30
(2.74)
4.6 Relativistic Velocity: In the derivation Einstein has done calculations under classical
conditions of velocity (v<<c) and applied binomial theorem in the end. Thus derivation of L=
∆mc2 is under classical conditions, and hence is obviously applicable under similar
conditions. It implies that inter-conversion of mass energy takes place only under classical
conditions.
When v is in relativistic region then mass of body increases according to
eq.(2.2). As mass is annihilated, the energy is emitted. If velocity is in relativistic region mass
50
also increases. If in this region mass is annihilated to energy, then we need to find out how
much mass increases and then how much mass is annihilated to energy. The net
disappearance or annihilation of mass is converted into energy. This case would be of
particular interest in thermonuclear reaction (lighter nuclei are fused together) especially in
solar storms. When velocity is in relativistic limits, then mass of body increases. So in this
case both ‘increase’ in mass of body (due to relativistic variation of mass) and ‘decrease’ in
mass of body (due to conversion of mass to energy) has to be taken in account to draw
conclusion about release of energy.
Practically the inter-conversion of mass and energy also takes place under
relativistic conditions e.g. when a gamma ray photon (have speed approaching to c ) of
energy at least 1.02MeV, moves near the field of nucleus it is split up in electron and positron
pair. The nuclear fusion of hydrogen, requires temperature of the order of 108 K . It also sets
nuclei in motion. The neutrons which are produced as products in fission move with
velocities 1.954×107 m/s.
So it is limitation of Einstein’s derivation. Einstein’s Sep. 1905 derivation implies that interconversion of mass and energy takes place under classical conditions of velocity, whereas
experimentally the inter-conversion of mass and energy also takes place under relativistic
conditions.
4.7 When one wave is emitted  =90
Einstein has considered two waves of equal energy emitted in opposite directions, to derive
equation ∆L=∆mc2 . In Einstein’s case energy L is emitted in two equal waves of energy.
But the same can be obtained if one wave of light energy L is regarded as emitted making
angle of 90 along x-axis. All the calculations are done in identical way
H0 = H1 + L  (1–
v  VR  cos 90 )
(2.75)
c
H0 = H1 + L 
(2.76)
E0 = E1+ L
(2.5)
(Ho – Eo) – (H1 –E1) = L  –L = L (  –1)
(2.77)
K0 –K1
2

v  VR 
=L[1+
M bv2
– Ma
2
2c 2
 v  VR 2


2

2

v  VR 
–1] =L
2c 2

v  VR 2
= L

2c 2

51
M b – Ma =
L
c2
M a = Mb –
L
c2
or ∆L=∆mc2
(2.78)
which is Einstein’s perception. It also follow from single wave of light energy L emitted at
angle of 90°.
4.8 When one wave is emitted at angle,  = 9.999
Einstein has considered two waves of equal energy emitted in opposite directions, to derive
equation ∆L=∆mc2 . But the same can be obtained if one wave is regarded as emitted making
angle of 90 along x-axis. Now if the calculations are repeated taking angle 89.999° then
further interesting results are obtained.
H0 =H1 + L  ( 1–
v  VR  cos 89.999)
c
H0 =H1 + L  ( 1–0.000017453
v  VR  )
(2.79)
c
E0 = E1 + L
(2.5)
(Ho – Eo) – (H1 –E1) = L  ( 1–0.000017453
v  VR  ) –L
= L [  ( 1–0.000017453
c
v  VR 
c
-1}
2

v  VR  ) –1]
v  VR 
= L [ (1+
) ( 1–0.000017453
2c 2
M bv2
– Ma
2
M b – Ma = –
M a = Mb +
 v  VR 2


2

c
(2.80)

v  VR  +L v  VR 2
 = – 0.000017453L

c
2c 2

0.000034906 L
L
+ 2
cv  VR 
c
0.000034906 L
L
– 2
cv  VR 
c
0.000035L
35
1.166 L
= 6
=
8
cv
10  3  10
1013
L
L
1.11L
=
= 17
16
2
9  10
c
10
( 2.81)
52
Mass after Emission = Mass before emission+
1.166 L 1.11L
–
1013
1017
Mass after Emission = Mass before emission+ positive quantity
If the angle is changed to 89.999° from 90°. Thus again when light energy is emitted mass
increases, which is contradiction of Law Conservation of Matter. It again justifies the
limitation of Einstein’s derivation.
4.9 When two waves are emitted identically as in Einstein’s case. Only difference is that
in this case one angle is regarded as 0.9999 instead of 0. The other angle remains 1 0
and other parameters remain the same.
Now equation equivalent to eq.(2.26) becomes
H0 = H1+ 0.5  L [ (1 –
v  VR  cos0.9999 ) + (1 – v  VR  cos 180 )]
H0 = H1+ 0.5  L [ (1 –
v  VR  0.99984773 ) + (1+ v  VR  )]
c
(2.82)
c
c
c
H0 = H1 + 0.5  L –0.499923865  L
H0 = H1 +  L +0.000076135  L
v  VR  + 0.5 βL + 0.5
c
L
v  VR 
c
(2.83)
v  VR 
c
E0 = E1 + L
(Ho – Eo) – (H1 – E1) =  L +0.000076135  L
v  VR  –L
= L {  [1+0.000076135]
v  VR  –1}
= L {[1+
v  VR 2
2c
2
K0 – K1 = L [0.000076135
v  VR  –1]}
c
v  VR  + v  VR 2 –1]
2c 2
c
v  VR  + v  VR 2
2c 2
c
v  VR  + v  VR 2
c
c
][1+0.000076135
= L [1+0.000076135
= L [0.000076135
c
2c 2
]
]
(2.84)
53
2
M b v 2  v  VR 

–

2
2

M b – Ma = [
M a = Mb –

v  VR  + v  VR 2 ]
 = L [0.000076135

c
2c 2

0.000076135L
L
+ 2]
cv  VR 
c
(2.85)
0.000076135L L
– 2
cv  VR 
c
Thus decrease in mass is more than predicted by Einstein’s derivation.
4.10 The body emits light energy but mass does not increase i.e. mass remain the same
but energy is being emitted.
Let the luminous body emits two light waves of energy 0.500001L and 0.499999L are
emitted in opposite directions. For this case we have already derived eq.(2.28 )
M b – Ma = L [
 0.000004 L
 0.000004 L
1
L
+ 2 ]=
+ 2
cv
cv
c
c
(2.28)
In case it is assumed that the velocity of the system (ξ, η, ζ ) is 1200m/s , then
 0.000004 L
L
+ 2
cv
c
=–
L
c2
+
L
c2
=0
Mb =Ma
(2.86)
Thus the mass of body remains the same and energy is emitted form the body. It is again
contradiction of law of conservation of matter.
Hence this derivation has serious limitations. The various quantitative results are shown in
Table II
Table II Comparison of results under Einstein’s super special conditions or
handpicked conditions and general condition in sep. 1905 derivation.
Sr
Energy
Energy of
Angle
Angle
Mass after emission
Mass after
%age
.
of first
second
of
of
Ma
emission
differen
N
wave
wave
first
second
(ma)
ce
wave
wave
0
180
Decreases
NA
o
1
0.5L
0.5L
Ma = Mb –
L
c2
54
2
0.50001
0.49999L
0
180
L
3
0.5L
Increases
1.2×105
Increases
450
Ma = M b –
decreases
1800
L
0.00000006
+
cv
< L/c2
Ma = Mb +
0.00004
0.5L
0
180.01
L L
–
cv c 2
Ma = M b +
0.000000015
4
0.5L
0.5L
0
179.98
L L
–
cv c 2
L
c2
5
8
9
0.49999
0.500001
9L
L
0.50000
0.499999
1L
L
0.5L
0.5L
0
180
Ma = Mb –
0.000004
0
180
180.001
L L
–
cv c 2
Ma = Mb +
0.000004
0
Decreases
0.50000
0.499999
1L
L
0
180
> L/c2
Increases
1.2×104
Decreases
30
L
L
– 2
cv c
Ma = M b +
0.000000001
10
1.2×104
L L
cv c 2
< L/c2
Ma = M b
No
(v =1200m/s )
increase
NA
No
decrease
11
L
NA
90
NA
Ma = Mb –
12
L
NA
89.99
NA
Ma = M b +
L
c2
0.000034906
Decreases
NA
Increases
105
L L
–
cv c 2
Deductions: Einstein’s derivation contradicts Law of conservation of energy under general
conditions, and also implies that L α mc2 or L =A ∆mc2. Derivation is not applicable if v=0
and v is in relativistic region. Also under classical conditions ma=mb .
55
5.0 Conclusion:
Einstein derived L =∆mc2 under special conditions, i.e. two equal waves of light energy are
emitted exactly in opposite directions and body remains static in the process in system(x,y,z).
The system (ξ, η, ζ ) is moving with uniform velocity w.r.t. system(x,y,z). If the above
conditions vary, then results are not consistent. If Einstein’s derivation is completely analysed
then it also predicts
(i) Mass of body decreases less than
L
c2
(ii) Mass of body decreases more than
L
c2
Then these are examples of self contradictions.
(iii) Light energy is emitted but mass of luminous body remains the same.
How energy is emitted mass remains the same? It is not justified by any experiment.
(iv) Light energy is emitted mass increases.
How light energy and mass are emitted out of nothing ?
(v) Einstein’s Sep. 1905 derivation not only implies L α mc2 or L =A ∆mc2 (E α
mc2 or E =A ∆mc2), but also contradicts the Law of Conservation of Matter. Further the
discussion of applications of implies L α mc2 or L =A ∆mc2 (E α mc2 or E =A ∆mc2)
requires different discussion. This is only theoretical analysis of derivation of L = mc2 ( or
E = mc2 ) , and has no impact on the established experimental status of E = mc2.
Further experimental evidences can be investigated for various value of co-efficient of
proportionality A in weird mass energy inter-conversions reactions (Chemical reactions,
nuclear reactions, cosmological reactions and astrophysical reactions.) The concept of coefficient of proportionality exists since days of inception of science and Aristotle used the
same it is discussed in next chapter.
Appendix
Quasars and some heavenly bodies move with speed comparable with speed of light,
discuss eq.(2) in view of it.
Quasars and equation (2.2)
The eq.(2.2) has mainly two limitations i.e. under some conditions it does not obey law of
dimensional homogeneity and does not comply with of identity a2 –b2 = (a+b) (a-b).
56
The heavenly bodies like Quasars move with velocities tending to that of light (v→c). So
eq.(2.2) is interpreted in view of motion of quasars. Let us calculate the intensity of light
emitted by Quasars or other heavenly bodies which move with speed approaching to that of
light. Then interesting results are obtained as it violates dimensional analysis. This aspects is
discussed below as eq.(2.2) is central equation in derivation of L = mc2 ( from which E =
mc2 speculated).
(i) Inconsistency of dimensional homogeneity when velocity v approaches to c i.e.
v→c. We have eq.(2.2) as
 v

1  c cos  

   
2
v
1 2
c
(2.2)
In his June 1905 papers Einstein [43] himself has interpreted equations under this
condition (v=c) and  =0°. In eq. (2.2)  is the angle which emitted wave makes with x-axis.
If  = 0o, then
ℓ* = ℓ (1 – v/c) / √ (1 – v2 /c2)
(2.2)
The various values of velocity i.e. v =0.01c, v=0.5c, v = 0.9c etc. can be substituted
in eq.(2.2) algebraically. If the system [X,Y,Z] moves with velocity equal to that of light
which realistically or actually means that velocity v tends to c i.e. v → c or v=c (some
Quasars or other heavenly bodies may attain such high velocities) . Thus eq.( 2.2) becomes
ℓ* →0/0 or ℓ* = 0/0
[from unsolved eq.(2.2)]
which is undefined. The nature of eq.(2.2) should be such that
ℓ* = 0
should have been obtained . Eq.(2.2) introduced by Einstein in June 1905 paper without
derivation in June 1905 paper in section 7 titled Theory of Doppler's Principle and of
Aberration. In this paper Einstein has not given any reference so that origin of equation may
be traced.
Violation of dimensional analysis: The dimensions of LHS are M L2 T-2 [energy] and
that of RHS undefined. It is the inherent requirement that an equation must obey the principle
57
of dimensional homogeneity i.e. dimensions of LHS and RHS are the same, but it is not so in
case of eq.(2.2) under this particular condition. Hence under this condition the central
equation which leads to L = mc2 ( from which E = mc2 speculated) is not applicable.
Eq.(2) is relativistic equation, and yields significant results when velocity is in relativistic
region). Such central equation, which leads to such a basic principle, should be free from the
limitations.
(ii) Non-compliance of identity a2 –b2 = (a+b) (a-b) by eq.(2.2).
a2 –b2 = (a+b) (a-b) is a basic identity which is universally used in science. But it is not so in
case of eq.(2.2) which has central place in the present discussion.
The contradictory results are also self-evident if eq.(2.2) is solved and same condition
is applied i.e. {1–v2/c2} = (1–v/c) (1+v/c) is simple algebraic result.
When eq.(2.2) is solved with above algebraic identity we get
ℓ* = ℓ √ (1 – v/c) / √ (1 +v/c)
(2.87)
Now again if we apply the same condition the velocity v tends to c i.e. v → c above
equation becomes
ℓ* → 0
[from solved form of eq.(2.87) ]
Further if the velocity of Quasar or heavenly body is precisely equal to c (theoretically), then
we get v = c , ℓ* =0. Thus the same equation (in unsolved and solved forms) under similar
conditions (v → c) gives different results i.e. (ℓ* →0/0 and ℓ* → 0), which is never justified.
Thus, under some conditions, results from eq.(2.2) are not consistent with basic
identity of algebra and in addition, the result is not consistent with dimensional homogeneity.
Conclusion
The obvious conclusion from eq.(2.2) i.e.
 v

1  c cos  

   
v2
1 2
c
has serious limitations. This equation was quoted by Einstein in June 1905 paper [43] in
58
section 7 titled
Theory of Doppler's Principle and of Aberration. But there is no
mathematical derivation to equation . Had logical and mathematical derivation would have
been there, correction could have been made. Also there is no reference in the paper , which
may have helped finding the origin of the equation. The way equation was presented implies
that it was provided by Einstein in ready way.
References
[ 1] Sharma,
A American Journal of Scientific Research , Vol. 12 pp.67-112 (2010)
[2] Sharma, A Einstein’s E=mc2 Generalized Raider Publishing International (2007) New York , USA
[3] Sharma, A. Proceedings of Physical Science of 98th Indian Science Congress, Chennai,
p.194 (2011)
[4] Sharma, A Proceedings of the 4th international conference of IMBIC, Kolkata , pp. 211
(2010).
[5] Sharma, A Proceedings of the Natural Philosophy Alliance , Vol.6 No. 2 pp. 261-263
(2011).
[6] Sharma, A International Journal of Nuclear Science and Technology Vol. 3 No 4 pp. 370-77 (2007)
[7] Sharma, A. Galilean Electrodynamics, Vol. 18, No. 5, pp 99-100 (2007).
[8] Sharma, A. Kurt Godel Society Collegium Logicum Volume IX pp. 67-71 (2007)
[9] Sharma, A
Progress in Physics,
Vol. 3
pp. 76-83 (2008)
[10] Sharma, A. Concepts of Physics, Vol. III, No. 4, pp.345–373 (2006),
http://merlin.fic.uni.lodz.pl/concepts/2006_4/2006_4_351.pdf.
[11]
Sharma, A. Abstract Book: 38th European Group of Atomic Systems (Euro physics
Conference), Isachia (Naples), Italy, p.53 (2006) .
[12]
Sharma, A. Abstract Book: A Century After Einstein Physics 2005, (Organiser
Institute of Physics, Bristol) University of Warwick, UK, 10–14 April. (2005)
[13]
Sharma, A. Abstract Book 19th International Conference on the Applications of
Accelerators in Research and Industry, Fort Worth, Texas, USA, 20–25 August. 2005
[14]
Sharma, A. Abstract Book , Oral presentation (lecture) on 21st September 2005, in The 5th
British Gravity Meeting , Oxford, England.
[15] Sharma, A. Physics Essays, Vol. 17, pp.195–222 (2004)
[16]
Sharma, A. Proc. Int. Conf. on Number, Time, Relativity, United Physical Society of
Russian Federation, Moscow, p.81 (2004)
59
[17]
Sharma, A Acta Ciencia Indica Vol. XXIV P No. 4 pp.153-158 (1998).
[17]
Sharma, A to be published in Galilean Electrodynamics, Massachusetts in , USA
[19] Sharma, A submitted for publication.
[20] Sharma, A Acta Ciencia Indica Vol. XXVI P. No. 1 pp.013-016 (1998).
[21] Sharma, A International Conference on World Year of Physics, University of Rajasthan , Jaipur pp.14
(2005)
[22] Sharma, A. 3rd international Young Scientists Conference, Kyiv National University , Scientific works
pp. 19 ( 2002).
[23] Sharma, A Journal of Theoretics Vol.6-5, pp.39-43 2004
[24] Sharma, A Beyond Einstein (monograph) accepted for publication to be published.
[25] Sharma, A Einstein’s Mass Energy Equation, Lambert Academic Publishers (2009) ,Saarbrucken ,
Germany
[26] Sharma, A. Journal of Vectorial Relativity JRV (4) 1-28 (2009)
[27] Sharma, A. Concepts of Physics, Vol. V, No. 3, pp.553–558 (2006),
[28 ] Sharma A., Proceedings of International Conference on Computational Methods in
Sciences and Engineering 2003 World Scientific Co. USA, 585-586 (2003).
[29] Fadner, W.L. Am. J. Phys. 56 2 , 144 (1988).
[30] Pretto, O. De “Ipotesi dell'etere nella vita dell'universo”, Reale Istituto Veneto di
Scienze, Lettere ed Arti, Feb. 1904, tomo LXIII, parte II, pp. 439-500 (1904).
[31] Cummingham, E. The Principle of Relativity, p. 189 (Cambridge University Press,
1914).
[32] Hasenöhrl, F. Wien Sitzungen IIA, 113, 1039 (1904), Hasenöhrl, F. Ann. der Phys. 16,
589 (1905).
[33] Serber , R The Los Alamos Primer (U.S. Govt. first published as LA1, April 1946),
declassified 1965 , annotated book, 1992. also R . Serber (editor) , The Los Alamos Primer
pp. 38 , Univ. of California Press, (1992)
[34] Leo Szilard: His Version of the Facts : Selected Recollections and Correspondence.
Spencer R. Weart (ed.). Cambridge, MA.: The MIT Press
[35] Hussey Edward Aristotle Physics Book III and IV Oxford University Press, USA
(1983)
[36] Galileo, G. 1632, Dialogues concerning the two chief world systems, trans. S. Drake,
2nd edition 1967, University of California Press.
[37] Gamow, G., My World Line (Viking, New York). p 44, 1970
[38] Lorentz H A Proc. Roy.Soc. Amst. 1 427-442 (1899)
[39] Lorentz H A Proc. Roy.Soc. Amst. 6 809-831 (1904)
60
[40] Kaufmann , W. Phys. Z 4, 55 (1902) and Gott. Nacchr. Math. Phys. 4, 90 (1903)
[41] Bucherer , A.H. Phys. Z, 9,755 (1908) ; Ann. Phys. 28, 513 (1909)
[42] Einstein A 1948 Letter to Lincoln Barnett, quoted in `The concept of mass' by Lev
Okum Physics Today (June 1989)
[43]
A. Einstein,
Annalen der Physik 17, 891-921 (1905).
[44] Robert Resnick, Introduction to Special Theory of Relativity (John Wiley and Sons, New
York, 1968), p. 120. (1968)
[45] A. Pais, Subtle Is the Lord (Oxford University Press, Oxford, 1983), p. 149 (1983)
[46] R. Resnick and D. Halliday, Physics Part I, Forty Second Reprints (Wiley Eastern
Limited, New Delhi, 1987), pp. 2, 45, 81 (1987)
[47] Einstein, A Ann. der Phys. 18 639-641 (1905).
Beyond Einstein and E =mc2
Science is infinite
Ajay Sharma
Chapter 3
Derivation Of Generalized Form Of Mass Energy
Equation, ∆E =Ac2∆m
First Glimpse
 It is justified by many persons, philosophers, scientists etc. that higher the mass annihilated, more
energy is emitted; even in daily life observation.
 Such observations existed before Einstein. Einstein gave the conversion factor c 2 ( 9×1016 m2/s2) by
method which is not consistent in many cases.
 Here the generalized equation ∆E
=Ac2∆m of mass energy inter-conversion is derived and
conversion factor is regarded as other than c2 ( 9×1016 m2/s2).

Thus generalized mass energy equation is defined as
61
“The mass can be converted into energy or vice-versa under some characteristic
conditions of the process, but conversion factor may or may not always be c 2 (9 
1016 m2/s2) or c-2 (1.1110-17).’’
1.0 Mass Energy inter-conversions
Many philosophers and scientists have put forth that more the mass annihilated more energy
is emitted. Thus mass energy equation is expressed in proportionality form or qualitative
form. Even an illiterate villager knew that more the wood or grass he burns more heat energy would be
produced. Expecting longer winter, the heap of wood is thicker and higher. He may not be knowing the work of
luminaries but conclusion is obvious, more the mass of wood consumed, more energy is emitted. This aspect
was stated by many directly or indirectly.
Now it is discussed that higher the mass annihilated, higher would be energy emitted. Then
from the relevant equation the coefficient of proportionality can be experimentally calculated.
(i) Newton [1] has stated that
‘Light and gross bodies are convertible to each other’
in his book ‘Optiks’ in 1704.
Newton’s perception can be put in proportionality form,
L=km
(3. 1)
where k is conversion factor between mass and light energy. But Newton did not even give
qualitative equation to his perception.
Einstein [2] tried to give mathematical derivation for Newton’s perception in 1905. On the
basis of Doppler principle for any velocity whatever i.e.
 v

1  c cos  

   
2
v
1 2
c
(3.2)
where  is light energy emitted by body in frame (x,y,z) and  * is light energy measured in
system (ξ, η, ζ ), and v is velocity with which the frame or system (ξ, η, ζ ) is moving. This
equation was given in Einstein’s June 1905 paper in Section 7 and is called Doppler principle
62
for any velocity whatever. But there is no specific derivation to the equation in paper. Then
this equation is used in derivation which is basically equation of conservation of energy.
Einstein derived L = ∆mc2 from this equation and speculated E = ∆mc2. Thus we find that E
= ∆mc2 is speculated from L = ∆mc2 which is based upon eq.(3.2) and eq.(3.2) is not derived
as in Einstein’s June 1905 paper. It is really a strange situation about origin of E=∆mc2 and
from equations it is derived.
Under the special or handpicked conditions Einstein derived
or L = ∆mc2
(3.3)
Under the general conditions
L  ∆mc2
is also possible.
From here Einstein speculated whatever is true for ‘light energy’ is true for ‘every energy’ or
energy content [ energy in Joules , m in kg. ] E i.e.
E  ∆mc2
Practically it is used to explain every energy as Einstein stated that
The mass of a body is a measure of its energy-content.
Einstein himself coined E as every energy or energy-content . In the derivation Einstein has
only considered that body emits light energy, but the luminous body can also emanate the
heat energy or other forms of energy simultaneously. Why other forms of energies emitted
along with light energy by body are neglected . All forms of energies must be taken in
account by eq.( 3.2) takes only light energy in account. Thus for wider acceptability the
approach must be general not special and based upon theoretically consistent equation and
derivable equation[3].
The other energies are NOT considered by Einstein at all in mathematical calculations of L
= ∆mc2 . In the derivation equation Mb =Ma , is also possible . Thus higher the mass
annihilated, higher the energy emitted
dE  dm
Undoubtedly it is indicated that the perception of Einstein’s derivation
2
of ∆E=∆mc is dubious and confirm that Einstein speculated ∆E=∆mc2 . The equation does
not arise in the derivation at all. However, Einstein derived light energy mass interconversion equation, ∆L=∆mc2. Then Einstein wrote
63
If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact
that the energy withdrawn from the body becomes energy of radiation evidently makes no
difference, so that we are led to the more general conclusion that
The mass of a body is a measure of its energy-content; if the energy changes by L, the mass
changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in
grammes.
From here Einstein arbitrarily concluded ∆E=∆mc2 , which is not justified there is
tremendous difference between light energy and every energy. It is not logical and
scientific at all.
Why did not Einstein write ∆E=∆mc2 in Sep. 1905 paper? This issue was raised by Fadner
in American Journal of Physics [4]. Apparently, Einstein was not certain about the content of
the paper which has title
Does The Inertia Of A Body Depend Upon Its Energy-Content?
Thus all aspects of Einstein’s Sep. 1905 paper are not completely understood.
(ii) Einstein has derived under super special conditions that the mass energy conversion
factor between mass and energy is c2. It is justified that under general condition the mass
energy conversion equation in proportionality form is
L  ∆mc2
or E  ∆mc2 .
The value of conversion factor, other than c2 can also be justified in many other cases in
which E = ∆mc2 is not confirmed yet. The mass energy inter-conversion phenomena are
weird in nature, and all are not studied yet. It is pertinent to mention that Einstein’s derivation
which leads to E = ∆mc2 , also implies Mb =Ma .
(iii) The chemical reactions are the most abundant reactions in nature and were main sources
of energy even in Einstein’s days. But neither Einstein nor any other scientist tried to confirm
E = ∆mc2 in chemical reactions [5]. However they extended its applications E = ∆mc2 to
the sun which is 150 millions of kilometers away from the earth and evidences are indirect.
Why applications of E = ∆mc2
are not extended to chemical reaction where direct
evidences are possible? Well experiments may be complicated in this case also. Are
scientists doubtful about confirmation of E = ∆mc2 in such cases? Till date E=∆mc2 is not
confirmed in chemical reactions, but E = ∆mc2 is regarded as true in such cases, which is
not justified [5].
64
If 10-9 kg of matter is annihilated then energy equal to 9×107J will be produced.
E = ∆mc2 = 10-9 ×9×1016 kg m2/s2 = 9×107 J
(3.4
This energy can derive a truck of mass 1,000 kg to distance of 90 km. So such experiments
based upon E = ∆mc2 serves as alternative energy source. Thus such sources must be
exploited . Just possible scientists or technocrats may have proceeded in this regard (the
annihilation of 10-9 kg may lead to creation of energy which may take the truck of mass
1,000 kg to distance of 90km) . But failure to get this much amount of energy may have
compelled to abandon the experiments that E = ∆mc2 is being exposed. Thus sensitive and
specific experiments are absolutely necessary. Such or similar predictions are not
experimentally confirmed in specific experimentation. If we burn 1kg, hay/straw or wood or
petrol some ashes and gases are produced. The mass of ashes and gases can be measured in
sensitive instruments. Then energy corresponding to mass annihilated can be calculated by
using E = ∆mc2. Then experimentally energy emitted can be checked whether it is
quantitatively consistent with theoretical estimates or not.
In terms of heat energy,
1 calorie = 4.18 J
or 9×107 J = 2.153×107 calories
(3.5)
It will raise the temperature of mass of water 21,530 kg from 14.5°C to 15.5°C.
The energy emitted can be found less than predictions of E = ∆mc2. It is preliminary
conclusion from observations, as even very little energy (comparatively) is emitted when
huge amount of wood , paper, straw etc. burn. Further reason for this conclusion is that
conceptually the chemical reactions (atoms are exchanged, making and breaking of bonds)
are entirely different from nuclear reactions (new atoms are formed, nuclei are broken or
fused). The conditions under which nuclear reactions proceed are entirely different from
chemical reactions. It would mean that the conversion factor between mass and energy is
other than c2. So in every type of reaction E=mc2 must be confirmed specifically.
The reason given by scientists for non-confirmation of E=∆mc2 in chemical
reactions is that in chemical reactions energy emitted is too less to be measured. Also in the
existing literature there are no evidences that ever serious attempts have been made for the
confirmation. Just possible in some experimental results may have not been inconsistent with
E=∆mc2, hence such experiments were discontinued due to lack of viable alternative. Also in
65
nuclear phenomena exceptionally expensive and sophisticated experiments have been
conducted. But now such data can be accommodated in ∆E =Ac2∆m.
Now sophisticated instruments are being prepared to study various scientific phenomena, but
no headway is made in confirmation of E=∆mc2 in chemical reactions. Such experiments
may definitely change the perception of E = mc2 in science.
(iv) In the laboratory[6-9] it is confirmed that using thermal neutron the Total Kinetic
Energy (TKE) of fission fragments that results from U235 and Pu239 is 20-60MeV is less
than predicted by E = mc2. This prediction is nearly 40 years old in the existing physics.
Unfortunately no significant work is being done in nuclear fission. At that time there was no
alternate equation such as E=Ac2m. It further implies that
dE  c2dm
(iv) Similarly mass of particle Ds(2317) has been found more than current estimates [10]
based upon E = mc2. Thus again
dE  c2dm
(v) Robert Serber (member of first American team entered Hiroshima and Nagasaki in
September 1945 to assess losses) had pointed out that efficiency of the atom bomb [U235,
49kg ] ‘Little Boy’ that was used against Hiroshima was about 2% only [11]. The remaining
98% energy is not accounted for. It is assumed that all atoms don’t undergo fission, thus
material is wasted. But the wasted material is not measured, nor are such experiments in
controlled way conducted. How much energy is emitted in form of heat energy, light energy
or energy in form of invisible radiations is not measured? Further
Einstein has derived equation (under super special conditions) for light energy only, but here
energies in various forms are emitted. Einstein did not derive equation for such energies.
But it is not calculated that how much ‘material is wasted’ and how
much ‘energy is emitted’? Einstein has simply considered emission of the light energy by
luminous body, but in nuclear explosion, heat energy, light energy, energy in form of
invisible radiations etc. is also emitted. Under ground nuclear explosions also justify dE 
c2dm [as E = mc2 is not confirmed]. How E = mc2 is regarded as true for those energies
for which it is not derived. Until such predictions are not precisely confirmed it is equally
possible that conversion factor other than c2 is feasible i.e.
dE  c2dm
Thus it is absolutely incorrect to state that E = mc2 is confirmed in uncontrolled nuclear
66
explosions. The energy may co-exist in various forms. In nuclear fusion or fission explosions
various types of energies are emitted, and L = mc2 is derived for light energy under super
special cases. So this derivation is not meant for other energies than light energies. So it is
illogical to assume that E = mc2 is correct for all energies even without experiments. Also
derivation of E = mc2, as given by Einstein is mathematically inconsistent. Thus it
should be specifically mentioned in such cases.
E = mc2 is not experimentally confirmed, but regarded as true.
(vi) Also in laboratory the mass of the secondary (product) neutrons is underestimated , it
affects the mass defect and hence energy released.
The neutron emitted in fission of U235 have energy nearly 2MeV . Thus mass of emitted
neutron must be relativistic. Whereas in calculation of energy with help of equation E =
mc2 the mass of neutron is regarded as equal to rest mass. If the relativistic mass is used
then obviously equation should be
dE  c2dm
(vii) The Big Bang Theory (the biggest energy releasing process in universe), is the most
successful theory of understanding of the origin of universe.
This theory assumes that whole mass of the universe (1055 kg, say) was in form of ‘primeval
atom ‘ and then suddenly exploded [12]. According to E = mc2, this mass (1055 kg )
would have been created from energy 9×1071 J.
E= 1055 kg × 9×1016 m2/s2 = 9×1071 J
(3.6)
But from where this energy had come? How this energy changed to mass? This huge amount
of energy can not be regarded as to exist as such automatically. The answer to one question
is other question.
How whole the mass is condensed to a single point?
From where energy was created for explosion?
Which is the source of energy, causing universe to expand?
How mass equal to 1055 kg (generally agreed) was created?
How it changed into singular state (state of infinitely large density and high temperature) ?
How the ‘primeval atom’ exploded (what is the source of this energy) ?
What is the reason of gravitation within the constituents of universe?
How infinitely large amount of energy is created which is responsible for these processes?
67
But we reach at logical conclusions (justified in applications) if the conversion factor
between mass and energy is considered other than c2, as conversion factor c2 does not
explain those.
It means that
dE  c2dm
(viii) Webb [13] has reported results for time variability of the fine structure constant or
Summerfield fine structure constant (  ) using absorption systems in the spectra of distant
quasars. It means the variations in the values of c are being discussed, if variation in value of
c is confirmed then energy emitted is less. Hence,
dE  c2dm
General Remarks: In addition it can be justified that Einstein derived L=∆mc2 or
speculated E=∆mc2 in 1905 and nuclear reactions were discovered in 1920s. Thus E=∆mc2
was applied after gap of 15 years in nuclear reactions. Then this equation is used as basis i.e.
defined 1Atomic Mass Unit (1amu) in terms of E=∆mc2. Then all data was standardized in
terms of 1amu (based upon E=∆mc2). Had Einstein discussed his derivation fully then ∆E
=Ac2∆m would have been available for discussion in 1905 and afterwards along with
E=∆mc2. Any data which was found inconsistent with E=∆mc2 was neglected, as there was
no alternative.
Also neither Einstein nor other scientists applied it for chemical reactions.
[Further an indirect or unrelated or analogous example may be given here regarding
transformation of energy from one form to other.
Energy in one form = k (energy in the other form)
(3.7)
where ‘ k ’ is conversion factor just like J (4.2 107 erg cal-1) in equation
W  JH
(3.8)
But the same transformation factor does not exist if ‘electrical energy’ is changed to ‘sound
energy’ or ‘light energy is changed to ‘electrical energy’ etc. Thus transformation factor
between ‘one form of energy’ to ‘other form of energy’ is not constant. Thus in science in
many cases, other phenomenon is a new phenomenon. However in E=∆mc2 , the conversion
factor between mass and energy is regarded as constant, equal to c2.]
Thus from various deductions (including that of Einstein’s Sep. 1905 paper) it is logically
concluded that
dE  c2dm
68
The above proportionality, dE  c2dm can be changed into equation by introducing a coefficient of proportionality. The appearance of coefficient of proportionality here is consistent
with centuries old perception of coefficient of proportionality in physics since days of
Aristotle and Newton.
According to Aristotle (384-322)
’Speed is proportional to motive force, and inversely proportional to resistance.’
v
F
F
or v = C
r
r
(3.9)
where is C is co-efficient of proportionality and determined experimentally. It is like
establishing relation between quantities by method of dimensions and value of co-efficient
of proportionality is experimentally determined.
According to Newton’s Second Law of motion as stated in The Principia
The alteration of motion is ever proportional to the motive force impressed; and is made in
the direction of the right line in which that force is impressed.
Alternation in motion  motive force
Motive Force  Alternation in motion
or F  change in momentum
or F  ma
F=K ma
(3.10)
The value of K is regarded as unity to define unit of force in systems of units e.g. FPS, SI and
CGS etc. However the values of coefficients of proportionality are experimentally
determined. In Newton’s Law of Gravitation the coefficient of proportionality G is
determined experimentally (as like other co-efficients), but in F=Kma, K is regarded as unity
in systems all of units just to simplify system of units, which is anomalous. The value of k is
always regarded as unity. It is not established way to determine the constant of
proportionality, which is determined experimentally as it varies from one situation to other.
2.0 Various Coefficients Of Proportionality
In case constant of proportionality varies from one situation to other then it is known
as co-efficient of proportionality e.g. co-efficient of thermal conductivity or viscosity etc.
When more and more complex phenomena were studied or values of coefficients of
proportionality were determined then it showed dependence on the inherent characteristics of
the phenomena. So it varies from one situation to other.
69
Thus removing the proportionality between dE and c2dm we get:
dE =Ac2dm
(3.11)
where A is a coefficient used to remove that sign of proportionality; it depends upon inherent
characteristics of the processes in which conversion of mass to energy takes place and it is
dimensionless. There are many existing derivations of this type.
The ‘constant of proportionality’ varies from one situation to other depending upon
inherent experimental conditions of the process. If it varies from one situation to other, then
constant of proportionality is called ‘coefficient of proportionality’. There are many
examples about it. In ΔE = Ac2Δm, A is a coefficient not a constant depending upon inherent
characteristics of mass energy inter-conversion processes. The mass energy inter-conversion
processes are numerous in nature, and each is independent to other. The concept of coefficient of proportionality is applicable to many equations in the existing literature. For
example,
(i) Hubble’s Law
Edwin Hubble (1889–1953), American astronomer, who has made a very significant discovery in
understanding of expanding universe, enunciated a law known after by his name. Hubble stated
a linear
relationship between the distance S of heavenly body and velocity of recession, V i.e.
VS
To remove the sign of proportionality the century old tradition in physics is to introduce a constant.
Hubble also followed the same,
V = HS
(3.12)
where V is velocity of recession of heavenly body, S is the distance of a heavenly body and H is Hubble’s
constant (popularly known). However, the value of H is never constant, it is experimentally determined
(knowing velocity V and distance S) as H =V/S. In
1929, Hubble found that farther the galaxy, faster
it moves away from us. Thus H must be called Hubble’s co-efficient scientifically.
The general range for value of H is 50
to 80 kilometers per second-Mega parsec (Mpc). Thus, there
is difference of 60 percent between upper and lower limits of value of Hubble’s constant. The
inherent characteristics of cosmological phenomena and astrophysical phenomena are so diverse that H can not
be regarded as universal constant in any way. The different values of H are being obtained experimentally. The
inverse of Hubble’s constant gives age of universe, thus as the value of Hubble’s constant varies, the estimates
for the age of the universe also vary. Hubble’s law justifies experimentally the Big Bang Theory.
70
ΔE = Ac2Δm has similar nature like V=HS
The mass-energy inter conversion reactions (chemical, nuclear, cosmological, astrophysical reactions etc) so
diverse that it is not possible to set A as universal constant, as in F = kma. The values
of A may be A=1,
A<1 or A>1 in different reactions or processes depending upon inherent characteristics of the
mass energy inter conversion reactions. Till date scientists have only one equation ΔE =
Δmc2 available, hence used the same for all explanations. Now an alternate equation ΔE =
Ac2Δm is also available the same can be used in such weird phenomena. The value of H is
different for different heavenly bodies. The value of A can be different for different weird
mass energy inter-conversion phenomena.
(ii) Coulomb’s Law
Charles-August Coulomb in (1736-1806) between 1777-1785 stated and developed the
famous law regarding interactions between the charges. If the bodies are oppositely charged,
one positive and one negative, they are attracted toward one another. If the bodies are
similarly charged, both positive and both negative, the force between them is repulsive.
The force of attraction or repulsion between two charges q and Q separated by distance r is
Fc = KqQ/r2
This law has similar nature like Hubble’s law. The value of K varies from one situation to other, hence further
like A. The value of K is 1/4π ε0 εr
F = KqQ/r2 = qQ/4π ε0 εr
value of
(3.13)
ε0 = 8.85410-12C2N-1m-2 and is constant. Further the value of εr varies from one situation to other. For
example values of
εr are for air 1.0006, for glass 4.9 to 7.5, for distilled water 80.0, for barium-
strontium-titanite 7500, hence values of K varies from one situation to other.
(iii)
The Equation for Half Life
Antoine Henri Becquerel (1852-1908) discovered the radioactivity and half-life of
the sample is very important property. The radioactive half-life for a given radioactive sample
is the
Time for half the radioactive nuclei in any sample to undergo radioactive decay.
The original numbers of atoms of radioactive substance keep on decreasing with time and
equation for half-life is
71
The equation for T1/2 = 0.693/ λ
Or λ = 0.693/T1/2
(3.14)
where λ is decay constant and its general trend is 1015 s-1 –10 -10 s-1.
The value of T1/2 ( half life time) elementary particles vary from 10-6 s to 10-23 s and
for uranium-238 is 4.5 billion years, depending upon their inherent characteristics and
accordingly decay constants vary. Similar is nature and characteristics of A, the value of A is
determined like that of λ i.e. experimentally.
(iv)
Equation for Resistance, R
George Simon Ohm (1787-1854), in 1827 experimentally established the law known
after his name known as Ohm’s Law. According to this law resistance R in an electric
conductor is defined as the ratio of the potential difference V, across the conductor and the
current I, flowing through it (if physical conditions of the system remain the same).
Mathematically we have
V  I or V = I R
R = V/I
(3.15)
The SI unit of resistance is ohm (), and it is defined as the resistance of a conductor
that has current of one Ampere flowing through it and a potential difference of one Volt
across it.
1  = 1Volt / 1Ampere
The resistance of a conductor is directly proportional to its length (L) and inversely
proportional to its cross-sectional area (a). The proportionality constant is known as the
resistivity () of the material of the conductor. Mathematically the concepts can be
represented by the following equations
R = ρL /a
(3.16)
where ρ is resistivity of the conductor having area a and L is length of the conductor. Further
the value of resistivity, ρ for
72
(a) metals and alloys varies from 1.610-8 to 4910-8 Ωm,
(b) for semi conductors it is 3.510-5 to 2300 Ωm
(c) for insulators 1010-1016 Ωm.
It further varies with temperature. The value of resistance R changes with experimental
conditions thus may be regarded as a co-efficient. Similar is the nature and characteristics of
A in ΔE = Ac2Δm.
(v) The Equation for co-efficient of Viscosity
The viscosity of a fluid can be defined as the measure of resistance of fluid to flow. It is
analogous to the friction of solid bodies. All fluids i.e. all liquids and gases, exhibit viscosity
to some degree. The viscous force F, is related with co-efficient of viscosity, η
F = η Adv/dx
(3.17)
Higher the co-efficient of viscosity, more viscous the fluid is. In general the co-efficient of
viscosity η varies from 1.0510-3 poise to 19.210-6 poise. Similar is nature and
characteristics of A.
(vi) Equation for Modulii of Elasticity (general)
This law was stated by Robert Hook (1635 -1703) in 1660. Robert Hook claimed he has
discovered that light when passes through prism is split in colours. When in 1674 Newton
declared the discovery as his own, there was constant clash or warfare between two, which
lasted till death of Hook in 1703. And then Newton published the ‘Optiks’ in 1704.
In addition, Robert Hook has discovered [24] the essence of inverse square law of
gravitation before Newton. Thus, when Newton published the Principia in 1685 then again a
controversy started. Eventually Newton was credited with discoveries of Theory of Light and
the Law of Gravitation. Anyhow, Hook’s law of elasticity in general form can be understood
as below.
The modulus of elasticity is ratio of stress to corresponding strain of body.
73
Y = stress [force per unit area] / strain
The general trend of Coefficient of elasticity is
3  109 N/m2 to 200  109 N/m2
Similar is the nature and characteristics of A in ΔE = Ac2Δm.
(vii) Faraday’s laws of electrolysis
Michael Faraday (1791-1867), the genius English Chemist and Physicist, has also the
discovered the significant law of electromagnetic induction. The Law of electromagnetic
induction is the most significant discovery ever made, as the generation of electricity is based
upon it. Faraday’s this law may be more useful than Newton’s Second law of motion
practically for humanity.
Faraday had many discoveries to his credit. Faraday was deprived of formal education
in the childhood and he learnt science while working at bookbinder’s shop. Then with the
simplest instruments, he made the most complex and useful discoveries for humanity.
Faraday’s First Law of electrolysis is defined as
“The mass of substance liberated or deposited at an electrode during electrolysis is directly
proportional to the quantity of charge passed.”
m  q or m = z q
(3.18)
where z is constant of proportionality known as Electrochemical Equivalent, m is mass
deposited and q is charge. The value of z varies from one experimental situation to other like
A. Similarly there is co-efficient of proportionality in Faradays second law of electrolysis,
“It states that when the same amount of electricity is passed through different electrolytes, the
amount of different substances deposited or liberated are directly proportional to the
equivalent weight of the substances.”
(viii) Equation for Co-Efficient of Thermal Conductivity
The coefficient of thermal conductivity is expressed as the quantity of heat that passes
through a unit cube of the substance in a given unit of time when the difference in
temperature of the two faces is 1°.
74
Q = KA [T1-T2]t/d
(3.19)
The general range of variation of co-efficient of thermal conductivity K for various
conductors is
0.02 Wm-1K-1 to 400 Wm-1K-1
Thus, the value of the co-efficient of thermal conductivity varies from one body to other.
Similar in nature and characteristics of A in ΔE = Ac2Δm.
Some co-efficient of viscosity are shown in Table I for comparison.
Table I: The various values of constant of proportionality in existing physics
Sr. No 1
Equation
Co-efficient of
Value
proportionality
1
V=HS
H, Hubble’s
Co-efficient
50 to 80 kilometers per
second-Mega parsec
(Mpc).
( popularly
known as
Hubble’s
constant )
εr
2
KqQ
qQ
F=
=
2
4 0  R
r
Relative
permeability of
medium
εr are for air 1.0006, to
for barium-strontiumtitanite 7500,
3
T1/2 = =
0.693

λ
Decay constant
general trend is 1015 s-1
–10 -10 s-1.
75
4
ρ
V  I or V = I R
R=
R=
(a) metals and alloys
varies from 1.610-8 to
V
I
Resitivity
L
4910-8 Ωm,
(b) for semi conductors
a
it is 3.510-5 to 2300
Ωm
(c) for insulators 10101016 Ωm.
η
5
F =
Co-efficient of
Adv
viscosity
dx
6
Q=
KAT2  T1 t
d
1.0510-3 poise to
19.210-6 poise.
K
0.02 Wm-1K-1 to 400
Coefficient of
Wm-1K-1
thermal
conductivity
7
Aristotle’s speed v = C
F
r
C is coefficient
of
C to be determined for
different media
Proportionality
8
Semi empirical binding
ai’s
Different values to co-
76
energy formula
efficients are assigned
E  Ac 2 m
9
A, conversion
Coefficient
Numerous values
in bizarre phenomena
of mass energy interconversion.
Thus, the value of the co-efficient of thermal conductivity varies from one body to
other. Similar is nature and characteristics of A in ΔE = Ac2Δm.
equation for modulus of elasticity,
equations of Faraday’s laws of electrolysis
equation for critical velocity in fluid dynamics,
equation for Newton’s law of cooling,
equation for induced dipole moment,
equations for co-efficient for linear expansion, superficial
expansion, cubic expansion,
equation for specific heat etc. etc.
3.0 Derivation of
∆E =Ac2∆m
Now consider the case that when mass is converted into energy. Let in some conversion
process mass decreases from M i (initial mass) to M f (final mass), correspondingly energy
increases from E i (initial energy) to E f (final energy). The eq. (3.11) gives infinitesimally
small amount of energy dE created on annihilation of mass dm . To get the net effect the eq.
(3.11) can be integrated
 dE  A c  dm
2
(3.20)
Initial limit of mass = M i
Initial limit of Energy = E i
Final limit of mass = M f
Final limit of Energy = E f
Initially when mass of body is M i , then E i is the initial energy of the system. When mass
(initial mass, M i ) is converted into energy by any process under suitable circumstances the
final mass of system reduces to M f . Consequently, the energy of system increases to E f the
77
final energy. Thus M f and E f are the quantities after the conversion. Hence, eq. (3.20)
becomes
or E f – Ei = Ac 2 [ M f − M i ]
(3.21)
or E  Ac 2 m
(3.22)
Energy evolved = Ac 2 (decrease in mass)
(3.23)
Special cases
Now the following cases can be discussed for further understanding of the equation.
E f – Ei = Ac 2 [ M f − M i ]
(3.27)
(i) If the initial and final masses remain the same, then Mi = Mf then from eq. (3.27)
Ei = Ef
(3.28)
i.e. under this condition when no mass is converted into energy, the energy remains the same.
It implies that energy is emitted at expense of mass. Energy cannot be created out of nothing.
It is consistent, whereas predictions from Einstein’s derivation are inconsistent in many cases.
(ii) If the characteristic conditions of the process permit then whole mass is converted into
energy i.e. after the reaction no mass remains (Mf = 0)
E f – Ei =  E = − Ac2Mi
(3.29)
Since Ei is the initial energy can be regarded as zero, then
Ef = − Ac2 Mi
(3.30)
If the characteristic conditions of the process permit then whole mass is converted into energy
i.e. after the reaction no mass remains ( M f = 0)
E   Ac 2 M i
(3.31)
In this case energy evolved is negative implies that energy is created at the cost of
annihilation of mass and the process is exo-energic nature (energy is emitted which may be in
any form). In other words it is exothermic process. Energy is scalar quantity having
78
magnitude only, thus no direction is associated with it. The negative sign is neglected in case
of exothermic reaction also.
It indicates that when mass is converted to energy the reaction is exothermic process.
Such processes are discussed in the existing literature frequently.
Now it is natural to calculate the difference in mass by subtracting the final mass from
initial mass as taken as in equation
E f – Ei = Ac 2 [ M f − M i ]
(3.24)
For example, a child is born and has weight 5 kg (in general sense). After few years, his
weight becomes 40 kg, and then we say his weight is increased by 35 kg i.e.
Increase in weight = Final weight –Initial weight = 40–5 = 35 kg.
We never say that increase in weight of child is –35 kg
(3.25)
i.e.
Increase in weight = Initial weight – Final weight =5–40 = –35 kg.
(3.26)
Further energy is scalar quantity, it has only magnitude. The velocity is vector quantity for
example, consider two buses are moving with velocity 40 km /hr.
(a) Both are moving in the same direction then
Net velocity = (40-40)km/hr =0
(b) Both are moving in opposite directions with same velocity
Net Velocity = [(40-(-40)]km/hr = 80km/hr
Similarly mass is scalar quantity , thus direction is not associated with it. The buses may
move either way the mass remains the same.
Thus the generalized mass-energy equivalence may be stated as
“The mass can be converted into energy or vice-versa under some characteristic conditions
of the process, but conversion factor may or may not always be c 2 (9  1016 m2/s2) or c-2
(1.11 10-17)
The generalized mass energy equation E  Ac 2 m or Energy evolved = Ac 2 (decrease in
mass) can be obtained by the method of dimensions. It is consistent with existing literature.
4.2. E=Ac2m can be Obtained by Method of Dimensions
The method of dimensions is one of the oldest methods for deriving relations between various
physical quantities, but under some conditions only. For example, the numbers of physical
79
quantities involved are not more than three and no trigonometric or special quantities are
involved. Further the constant of proportionality involved in the derivation by method of
dimensions, is determined experimentally. Thus, experimental verification is supreme in all
cases.
Let the energy emitted (E) on annihilation of mass or energy materialized to mass
(m). The energy E, depends upon annihilated mass (m) as dimensions a, depends upon
speed of light c, as dimensions b and depends upon time t as dimensions c. Thus as in other
cases in existing physics, E can be expressed as
E  (m)a cb tc
E = A (m)a cb tc
(3.32)
where A is constant of proportionality and its value is experimentally measured like other
constants, which arise in method of dimensions. According to principle of dimensional
homogeneity, the dimensions of both the sides must be the same. Hence eq.(3.32) can be
written as
ML2T-2 = A Ma (LT-1)b Tc = A Ma Lb T–b+c
Comparing the dimensions of mass, length and time of the both sides we get
Or a = 1, b = 2 and –2 = –2 +c or c =0
Or E = A mc2 to = Ac2 m
(3.33)
Hence, the same result is obtained by the method of dimensions also. The constant of
proportionality A varies from one situation to other and determined experimentally, which is
established method since many centuries under such circumstances. In this case, it may be
called a conversion co-efficient.
4.0
Conclusions
It is well known that higher the mass annihilated, higher is the energy emitted. As Einstein’s
derivation leads to inconsistent results (contradiction of law of conservation of matter). Thus
relation between mass annihilated and energy emitted is established by simple calculus
method. Thus generalized equation
E  Ac 2 m
Energy evolved = Ac 2 (decrease in mass)
80
is obtained by method of integration.
Both the equation E  Ac 2 m and E=∆mc2 imply that when mass is annihilated , energy is
emitted.
(i) According to E=∆mc2 , energy emitted is always fixed.
(ii) Whereas according to E  Ac 2 m the energy emitted can be less or more than
predicted by E=∆mc2.
The mass energy inter-conversion equations (chemical reaction, volcanic reactions, nuclear
reactions, cosmological reactions, astrophysical reaction) are weird in nature and generalized
equation E  Ac 2 m can be experimentally justified in such reactions. It implies that
conversion factor other than c2 can be confirmed in such reactions.
Reference
[1] Sir Isaac Newton, Opticks, pp. CVX (1704; reprinted by Dover Publications, Inc., New
York, (1952).
[2] Einstein, A Ann. der Phys. 18 639-641 (1905).
[3] Sharma, A American Journal of Scientific Research Issue 12 , pp.67-112 (2010),
[5] Arthur Beiser, Concepts of Modern Physics, 4th edition (McGraw-Hill International
Edition, New York, 1987), pp. 25, 27, (1987)
[6] E.G. Bakhoum, Physics Essays 15 (1) 2002 (Preprint archive: physics/0206061)
[7] E.G. Bakhoum, Physics Essays 15 (4) 2002
[8] Hambsch, F.J. et al. Nucl. Phys.A, 491,p.56 (1989)
[9] Thiereus, H. et al., Phys. Rev. C, 23 P 2104 (1981)
[10] Palano, A. et al., Phys.Rev.Lett. 90 (2003) 242001
[11] Serber , R The Los Alamos Primer (U.S. Govt. first published as LA1, April 1946),
declassified 1965 , annotated book, 1992. also R . Serber (editor) , The Los Alamos
Primer pp. 38 , Univ. of California Press, (1992)
[12] S. Hawking, A Brief History of Time (Bantam Books, New York, 1988), p. 121. (1988),
[13] Webb , J. K. Webb et al., Phys. Rev. Lett. 82, 884 (1999).
81
Beyond Einstein and E =mc2
Science is infinite
Ajay Sharma
Chapter 4
Applications Of Equation ∆E =Ac2∆m In Understanding The Origin
Of Universe.
First Glimpse
 It has been dream of the man since stone age to understand the cause of origin
stars, moon, sun etc. Gradually as science developed, man became curious to
know about mysterious universe. Many theories grew and fell in the process
but riddle is not fully solved.
 The Big Bang Theory or Big Explosion Theory of formation of universe assumes
mass of universe (1055kg) had size less than that of atom i.e. known as ‘primeval
atom’. Suddenly it exploded and heavenly bodies are accelerating outwards.
 How mass of universe was created? How mass of universe changed to ‘primeval
atom’ ? How and why it exploded? How energy was created for explosion? All
these questions are not answered by existing theories as they don’t exist. The Big
Bang Theory is theory of explanation to an observation , not that of ‘origin’ of
observation’.
 E =mc2 implies mass equal to 1055 kg was created from energy 9×1071 J. But from
where this energy was created. Was it created from mass? Then how mass is
created? So circular arguments continue.
 According to ∆E =Ac2∆m mass 1055 kg can arise from infinitesimally small
energy, hence life started from zeroans (simply waves of mass tending to zero or
equal to zero). This energy changed into mass according to ∆E =Ac2∆m . It may be
called ‘Primeval Theory ‘ of universe.
82
 It is believed that Higgs Boson has its hypothetical field and imparts mass to
particles of the universe. But it is not discussed that how Higgs Boson (125 times
bigger than proton) attained mass and hypothetical field. According to law of
conservation of matter, mass is converted to energy as E=mc2. What about this
equation when mass is imparted to particle? How energy is created? Does this
hypothetical field gives mass to antiparticles as well ? E=mc2 is applicable here
also.
 This theory justifies that the gravitational energy is due to conversion of mass to
energy and given by Ug = k Ac 2 m . Due to exceptionally high value of A and k,
high amount of gravitational energy is produced, corresponding to annihilation of
small mass.
 The gravitational energy compressed the mass beyond limits then ‘primeval atom’
exploded which is called The Big Bang Explosion.
 The creation of mass and big bang can be explained with these perceptions. Also
black holes, dark matter, gamma ray burst etc. can be explained with these
equations.
 In brief origin and development of universe is nothing but transformation of mass
and energy , as indicated by ∆E =Ac2∆m.
1.0 Introduction
The understanding of origin of universe is the most complex thing as there are no earliest
experimental evidences. The various theories have been put forth to understand it by
mathematicians, scientists, intellectuals and clerics, but concrete conclusions are yet to be
drawn [1]. If universe has started from the state of cipher, then will it change to state of
cipher ? The conservation law requires, may be after infinite time the mass of universe will
change to cipher. The current stage of universe is simply intermediate stage. It is different
from ordinary reaction, and may have life time tending to infinity. Consider a hot frying pan
placed over the burning oven. It is empty. Now put few cubes of ice on it, it will change to
water, then to vapors and eventually the frying pan will be empty. It is simply a passing
remark to be substantiated logical scientific background.
If Einstein’s derivation of E =∆mc2 is critically analyzed taking all values of
variables elusive in the derivation [2-28], the same derivation indicates ∆E =Ac2∆m , where
A is conversion coefficient. The reason is that both the equations involve creation of mass
83
from energy or vice-versa. Both mass and energy constitute universe.
The equation ∆E =Ac2∆m is helpful in understanding the pre-big bang origin
of universe. The big bang theory assumes that about 13-14 billion years ago whole mass of
the universe (1055 kg or assessed mass of universe) was in the most compact, dense and hot
form having atomic dimensions. This infinitely dense mass of the universe is known as
‘primeval atom’. Then it exploded automatically and universe is expanding ever since. But
this theory is silent about some of the obvious questions.
2.0
Origin of pre-big bang or pre-singular cosmology
Or
How singular or primeval atom is formed?
Main aim:
Here aim is to explain or understand how the ‘singular atom’ or ‘primeval
atom’ (state of volume tending to zero and infinitely large density)was formed? What was the
state of affairs in universe before formation of singular or primeval atom? If singular atom is
formed then how it is exploded?
The understanding of the formation of universe is tedious and
speculative process as no direct experimental evidences are present. The big bang theory
assumes that automatically primeval or singular atom (state of volume tending to zero and
infinitely large density) existed as such in space of atomic dimensions. The physical laws did
not exist at time of big bang, as the time started after Planck’s time i.e. 5.39×10-44 s after
big bang . In pre-singular theory mass is not regarded as 1055 kg existed automatically, but
attempt is made to explain how primeval atom is formed?
The pre-singular theory assumes that universe started its life from
zeroans i.e. particles of zero masses. The waves of zeroans automatically and spontaneously
moved with infinitely large velocities. It is logical deduction. According to E=mc2 the mass
1055 kg must have come from energy 9×1071 J, but how this energy is created? Thus it is
postulated that wave(s) of energy accumulated itself as infinitesimally small of energy(ies).
Thus newly created waves of energy converted into mass(es), according to equation E =k
mass annihilated = k ∆m , k is coefficient of proportionality .
The particles of mass so produced were in super active state, thus a
part of mass converted to gravitational energy and other energies. Consequently the various
particles condensed and led to formation of singular atom. Due to conversion of mass to
84
energy in primeval atom size of the atom decreased. When size became smaller than
optimum size, the explosion known as big bang took place. Thus it is not assumed that mass
of universe 1055 kg existed as such , but it created from zeroans and central equation is E= k
∆m.
2.1
Mass and Energy of Universe
The understanding of origin of universe is the most complex thing as there are no earliest
experimental evidences. Consequently all such theories are based upon hypothesises and
postulates. The existing theories don’t quantitatively address following questions.
(a) How mass of universe equal to 1055 kg (generally assumed) is produced ?
(b) What is the reason of gravitation within the constituents of universe? How heavenly
bodies are formed? How heavenly bodies attract each other?
(c) Which is the real source of energy, causing universe to expand in spite of gravitation?
The various theories have been put forth to understand it by mathematicians, scientists,
intellectuals and clerics, but concrete conclusions are yet to be drawn [1]. Many theories have
been put forth to explain the same e.g. steady state theory, (in expanding universe mass is
continuously created) and big bang theory (mass of universe existed as such in singular state).
But some questions are unanswered. Thus the current discussion presents a new theory on the
topic. Also equation E=mc2 predicts mass is converted to energy or energy is converted to
mass. Then mass of universe 1055kg (estimates vary), is created out of energy9×1071 J. How
this energy is created? One answer gives rise to other question. Thus no valid answer is
obtained.The various studies regarding origin of the universe have not discussed anything
about the formation of first particle on universe [29-31].
Total Mass of Universe: The limits of universe extend beyond observable or detectable
distances. The total mass of universe is sum of various parts. The total mass includes visible
mass of universe, antimatter, dark matter, mass existing in inaccessible space , mass which is
converted to energy etc. Here mass of universe in totality is considered right since beginning
of universe. The mass of heavenly bodies receding with speed approaching to that of light is
exceptionally high.
Normally in calculations mass equal to 1055 kg is taken, for realistic calculations the mass in
totality must be considered. Also considerable mass may have been converted to energy.
Thus actual mass of universe is far higher than general estimates of mass of universe. Thus
the theoretical possibility of existence of unimaginably large amount of mass in universe (
85
accessible and inaccessible ) cannot be denied.
Total Energy of universe. If energy of the universe is expressed in totality then it is far more
than normal estimates. The total energy includes the visibly measureable energy, energy
emitted in inaccessible space, dark energy, energy which is converted to mass, gravitational
energy and kinetic energy within constituents of the universe energy responsible for outward
acceleration of universe, energy emitted in universe etc. Hence universe contains gigantic
amount of mass and energy which may be beyond current estimation. Thus since inception of
universe unimaginably large amount of energy may have been exchanged in the universe
(accessible and non-accessible). These are the most mysterious and bizarre phenomena of
universe.
Thus universe may consist of infinitely large amount of mass and energy. Logically such
huge magnitudes cannot exist as such. How this infinitely large mass and energy is produced
in the universe? The big bang theory of universe assumes automatic and spontaneous
presence of the primeval atom ( 1055 kg , infinitely large density and size tending to zero).
This is the core issue which is discussed in various existing theories.
2.2 Postulate of pre-singular or primeval Theory of Universe
The Primeval Theory is based upon following postulate (genuine perception).
This theory postulates that infinitely large number of zeroans ( mass less particles ), moving
with infinitely large velocities changed or transformed into small pulses of infinitesimally
small energies.
Even current physical laws permit the perception of zeroans ( mass less particles) move with
infinitely large velocities without external force (F=ma). So it can be regarded as a reality
postulate. It can be safely concluded that if nothing were present in the universe then
constituents of zero mass called ZEROANS or waves of mass less particles (zeroans) were
present. The numerous waves of zeroans consisted of particles of mass exactly zero moved
with infinitely large velocities in infinitely vast existing space. Zeroans may be present even
now. As laws of physics were not valid before Big Bang, so such perception is valid. The
laws of physics became valid after 5.39×10-44 s ( Planck’s time) after Big Bang.
These waves of energy are distributed in all over the space. In the universe there
may be infinitely large waves of energy. It is only the postulate in this theory. As the creation
of mass is the most bizarre process, so similar would be the perception.
86
Einstein’s Mass energy inter-conversion equation ∆E =mc2 and mass of universe.
In one estimate mass of universe is regarded as 1055 kg in calculations. The laws of physics
were not valid at time of big bang (or before). Even time came into existence after
5.39×10-44 s of big bang. The dark matter, antimatter and mass of inaccessible universe etc.
are not taken in account. The creation of mass 1055 kg (generally accepted value of mass of
universe), requires mammoth amount of energy i.e.
E = 1055 kg × 9×1016 m2/s2 = 9×1071 J
(4.1)
How energy equal to 9×1071 J is originated? But it is another question. This energy should
have been produced from mass 1055 kg. Then how this mass is produced? Thus endless
questions and answers continue without any conclusion. Thus E=mc2 is not applicable as at
that stage, it is also justified by the fact that at that stage none of the existing laws is
applicable. Even time was defined after big bang. Hence a new perception of mass energy
inter-conversion is perceived here for understanding of pre-singular universe.
2.3 Pre-singular Mass Energy Inter-conversion, and formation of primeval or singular
atom.
Before big bang of ‘primeval atom’ the time did not exist at all. It was measured 5.39×10-44 s
after the big bang. The physical law also did not exist before big bang. Hence the upper limit
of speed of light was not 3×108 m/s2, as speed of light was not defined or measured. Thus
instead of Einstein’s E=∆mc2, pre-singular mass energy inter-conversion equation
E =k mass annihilated = k ∆m
(4.2)
is regarded as applicable, where value of k is like co-efficient of proportionality. Its value
depends upon various inherent characteristics, like other co-efficients. Eq.(4.2) is consistent
with the law of conservation of matter given by Lavoisier in 18th century i.e. matter can
neither created nor be destroyed but can be transformed from one form to other. This law is
qualitative does not point out ‘how much energy’ will be created on annihilation of specific
mass quantitatively.
Here aim is to explain or understand how the ‘singular atom’ or
‘primeval atom’ was formed? What was the state of affairs in universe before formation of
singular or primeval atom? If singular atom is formed then how it is exploded?
The formation of primeval or singular atom.
It is assumed that the existing the laws of science did not exist before big bang so the
formation of primeval atom (state of volume tending to zero and infinitely large density) is
87
understood in different way. The particles of zero masses can be visualised in every situation
in the infinitely large vast space, moving with infinitely large velocity and no law is
contradicted.
‘Thus infinitely large number waves known as zeroans (having exactly masses equal
to zero), moved with infinitely large velocities in infinitely vast existing space.’
It is the consistent deduction. Also particles of zero mass can be perceived. No external force
is required to set such constituents in motion.
Mathematical Equations
The fast moving wave of numerous zeroans constituted a wave or pulse of energy known as
primeval wave of energy. It may have resulted due to combination of various waves of
zeroans. Then magnitude of this primeval wave of energy increased gradually and became
nearly 10-6 J.
Now eq.(4.1) becomes
E =k mass annihilated = k ∆m
(4.2)
10-6 = k 1055
Thus corresponding to small energy (10-6 J) gigantic amount of mass (1055) is emitted.
or k = 10-61
(4.3)
54
If it is assumed that primeval wave of energy has value 10 J and converted into mass
1055 kg , then
k =0.1
(4.4)
The co-efficient of proportionality varies from one situation to other. Thus from eq.(4.2) mass
is produced. However actual process of creation of mass may be quite mysterious, tedious
and time consuming process. The universe may have been created in small fragments or
parts. In free space the motion of wave of Zeroans hence process of creation of mass is
continuous processes. This is one way of understanding the origin of universe on the basis of
inter-conversion of mass and energy, which is independent of significant theories. The mass
of universe is generally regarded as 1055 kg, however different estimates can be there.
.
2.4 The origin of gravitation.
The cause of origin of gravitational energy is mass i.e. mass is converted to gravitational
energy as like other energies.
Mass is converted into Gravitational Energy: The mass may be regarded as primary form
of energy in nature. The one form of energy can be transformed to other forms. If mass
changes to other forms of energy then it can also be changed to Gravitational Energy. In
88
nuclear explosion or chemical reactions mass is converted to heat energy, light energy,
energy in invisible form etc. In nucleus, the nucleons weigh less in nucleus thus mass is
converted to binding energy. Mass is also changed to heat energy, sound energy or light
energy etc. In uncontrolled nuclear fission or in nuclear reactors mass is converted to light
energy, heat energy, sound energy and energy in form of invisible radiations is emitted or
energy may co-exist in various forms.
In nucleus the mass is converted or transformed into the binding
energy (attractive like gravitational energy). The attractive binding energy exists within
nucleus and attractive gravitational energy exists on large scale. It is confirmed that binding
energy is result of annihilation of mass, likewise gravitational energy may be regarded as
result of annihilation of mass, but both arise from the annihilation of mass. Thus law of
conservation of matter is obeyed. Electrons move around the nucleus and heavenly bodies
move around the sun due to attraction. As mass is created in space, a suitable fraction of that
mass is simultaneously and automatically converted to gravitational energy and other forms
of energy. As mass was created it was in super active state, so a part of it also annihilated to
various forms of energies.
If mass can be changed to other forms of energy, then it can also be changed to attractive
gravitational energy. It is already justified that mass of universe created is more than
generally accepted mass 1055 kg ( used in calculations as standard for simplicity) , the excess
mass ( actual mass created – 1055kg ) is converted into various forms of energy.
Excess Mass = [Actual mass created – 1055kg]
(4.5)
This mass is converted to various forms of energy including gravitational energy. The energy
cannot be created out of nothing.
2.5
Basis of mathematical equation
The energy is transformed from one form to other. In electric bulb
electrical energy changes to light energy, in heater electrical energy is converted to heat
energy, in radio electrical energy is converted into sound energy, in cell chemical energy is
changed to electrical energy, in photocell light energy changes to electrical energy, in a.c.
dynamo mechanical energy is converted or transformed to electrical energy there are many
such examples. The inter-conversion of energy from one form of mass to other may be
written as
Energy in newly converted or transformed form =Z (energy in the first form)
(4.6)
89
where ‘Z’ is conversion co-efficient just like Joule’s Mechanical Equivalent of Heat J (4.2
107 erg cal-1) in
W  JH
(4.7)
Gravitational energy ( U g ) = Z Energy emitted in annihilation of mass (∆m)
= Zk ∆m = K∆m
(4.8)
where Z is conversion coefficient which determines the extent of transformation of energy to
gravitational energy. Thus higher the value of K more gravitational energy will be produced.
The values of K depend upon inherent characteristics of the process. Their nature is like other
existing coefficients in science. So,
” creation of mass of universe and origin of gravitation are both simultaneous processes”.
The inter conversion of energy to mass is continuous process. The fraction of mass (so
produced) also changed into gravitational energy as described by eq.(4.8). This gravitational
energy held together the created mass, if the gravitational energy simultaneously produced in
one particular case is considerable then that matter remained in cohesive state. The formation
of mass and appearance of gravitational energy are the simultaneous processes. The
gravitational energy is universally prevalent and is inherent property of bodies; it unites the
bodies as these are produced. If gravitational energy produced is less in some cases then
mass remained in un-cohesive or comparatively free state. Thus continuum of particles is
possible.
2.6
The formation of singular or primeval atom
The infinitely large number of waves of zeroans moving with infinitely large velocities in
random directions manifested as primeval pulse(s) of vanishing small energy(ies). Thus the
energy is converted into mass, according to eq.(4.2). At this stage mass was in super active
state which transformed easily to various forms of energies. Thus numerous small particles
were formed, a part of mass so produced changed into various form of energies i.e. heat,
gravitational energies etc. The particles having large amount of gravitational and heat
energies etc. (whose mass converted to energy as per E=km, large value of k) were
compressed. In case particles having large magnitudes of gravitational and heat energies
stuck together to form bigger particles. Then it has to be assumed (for perception of primeval
atom) that for smaller annihilation of mass , large amount of heat and gravitational energies
are produced. It means higher the value of k .Thus masses attained condensed and state of
exceptionally higher density. This led formation of primeval atom. Thus gravitational energy
90
is further increased due to annihilation of mass then and mass was further compressed.
2.7
Explosion of singular atom
The process of annihilation of mass to energy continued. The energy may be in various
forms such as heat energy and gravitational energy. When primeval atom compressed
beyond limits (as large amount of gravitational energy is produced due to annihilation of
mass), then size of primeval atom decreased beyond optimum size. Consequently big bang
took place and all the matter is expanding ever since. It is like variation of intermolecular
force with distance. The force is neither attractive nor repulsive at equilibrium distance but it
suddenly becomes repulsive when distances between molecules decreases. Just possible at
this stage some sort of reaction equivalent to nuclear reaction but far more violent took place
in primeval atom. Thus big bang took place. The extent of conversion of mass to energy
depends upon k which is co-efficient of proportionality.
Smaller particles: At the same time it is just possible that some particles which were created
from wave of zeroans, energy wave of zeroans may have not developed considerable amount
of gravitational energy, hence not condensed to bigger units. Thus matter may be present
here in continuous amount. These particles are present in universe in continuous form and
largely may be undetectable. Thus possibility of quarks, sub-quarks, axions etc. or further
lighter particles are completely feasible. Further smaller particles are existing which may be
immeasurable by current precision. These may have mass trillion-trillion times smaller than
axions hypothetical particles proposed by Peccei [32] or their mass is so smaller to be
compared with axions. These particles may constitute dark matter in category of Weakly
Interacting Massive Particle. Thus mass in primeval era has been continuous not discrete (not
whole number multiple of some ‘minimum mass.’)
These particles developed charge due to friction while in motion (the
particles are charged by this method even now). The different charges can be understood due
to friction of particles in different directions. Thus charges of the order of fraction of
electronic charges are possible i.e. so smaller to be detected by current instruments. Thus
charges are continuously distributed. As particles are in state of continuous motion so they
attain considerable charge while moving. The build up of particles of similar charge, like
electron and proton was formed in due course of time.
When electrons, protons and neutrons combined an atom is formed, hence
molecules in due course of time. Due to exceptionally large amounts of heat, gravitational
91
energy etc the various molecules condensed to form mass. Thus origin and development of
mass took place in state of motion. All the three theories are compared on the Table I.
Table I Comparison of Pre-singular Theory, Big Bang Theory and Steady State Theory
Sr. No
Characteristic Pre-singular or
Big Bang Theory
Steady State Theory
Primeval atom
Whole universe as such
(m=1055kg)
(m=1055kg)
Primeval Theory
1
2
3
4
First particle
Zeroan (m=0)
Reason for
Natural and
Speculation
Speculation
existence
logical
existed as such
existed as such
Conservation
Laws
Obeyed
Zeroans are
perceived
Not obeyed
mass=1055kg
existed as such
Not obeyed
mass=1055kg
existed as such.
State
Moving before
Motion due to
Origin not discussed
formation
explosion
5
Origin
Discussed
Not discussed
Not discussed
6
Origin of
gravitation
Mass is converted
to gravitational
energy
Not discussed.
Not discussed
3.0
Supplementary topics /Additional topics
3.1 Findings based upon NASA’s Wilkinson Microwave Anisotropy Probe (WMAP).
Erickcek and colleagues [33] deduced on the basis of NASA’s Wilkinson Microwave
Anisotropy Probe (WMAP) that existence of time is possible before Big Bang and universe
may be created in empty space. Normally microwave background radiations are mostly
smooth but Cobe satellite discovered some fluctuations. Erickcek and colleagues believed
92
that these fluctuations contain hints that our universe ‘bubbled off’ from previous one. Thus
time and space, hence universe existed before Big bang.
It is consistent with explanation of ∆E =Ac2∆m and provided natural explanation
for formation of universe (creation of mass, creation of primeval atom, its explosion and
outward acceleration). As we are simply discussing the formation of primeval atom (which is
not discussed yet), hence there is no contradiction of any existing fact. The big bang theory
starts with explosion of primeval atom without any query or explanation how it is formed?
3.2
Annihilation of antimatter
At the time of big bang equal amount of matter (1055 kg, generally accepted) and antimatter
were produced. This antimatter was annihilated during hadron epoch (10 -35 – 10 -4 s) as now
antimatter is not found at all [34]. It would have released energy equal to 9×1071 J i.e.
E = 1055×9×1016 = 9×1071 J
(4.9)
Due to this energy temperature would have risen. However in this epoch temperature fell
down from 10 27K to 10 12 K in usual way. In Planck’s time the distance travelled is equal to
Planck’s length i.e. 1.61×0−35 meters. Thus it is contradiction, as energy is released and
temperature falls.
It can be explained with help of E  Ac 2 m . It can be explained if we assume that
negligibly small amount of energy has been produced during hadron epoch, in
equation E  Ac 2 m . The generalized equation implies that energy emitted due to
characteristics of reactions can be less than predicted by E =mc2. Let this energy be only 1
J. Now the value of A must be 1.11×10-72 i.e.
1= A 9×1071
Or A = 1.11×10-72
(4.10)
Thus,
E  1.11 10 72 c 2 m
(4.11)
Hence antimatter is not observable as it is annihilated during hadron epoch without raising
the temperature. Thus this perception justifies big bang theory.
3.3 Black Holes.
The black holes are results of exploding stars. The black hole is regarded as end stage of stars
93
whose mass is roughly 20-25 times (estimates may vary) the mass of the Sun. In such cases
huge amount of energy is produced. Stars explode when they are in super active state.
If the gravitational pull of a heavenly body is exceptionally-2 higher even
then visible light does not escape from it and remains invisible. According to this perception
the pre-requisite for formation of the black hole is that it must have unimaginably high value
of gravitational energy. On the basis of E  Ac 2 m the reason for formation of black hole
( density of the order of 1018kg/m3 ) is that due to small annihilation of mass, enormous
amounts of heat and gravitational energies are produced. According to eq. (4.6) it is only
possible if the value of A and k must be exceptionally high. Thus even smaller bodies can
become black hole, the condition is that the gravitational pull must be such that even light can
not escape from the body. Such bodies may be understood as constituents of dark matter.
This perception implies that for annihilation of small mass, huge amount of
gravitational energy is gained by body, consequently does not allow light to escape. Such
processes may be categorized as ‘super special annihilation’ i.e. in which for smaller mass
exceptionally large amount of energy is emitted. Thus exceptionally huge amount of
gravitational energy is produced. If this condition is satisfied then even bodies of smaller
mass may become black holes. In view of this the lightest black holes are also possible, and
some of them are observed to reside in the youngest galaxies. Even small heavenly bodies
may form black holes. The micro or mini black holes have mass of the order of Planck Mass
(1.2209×1019 GeV/c2 = 2.17644×10−8 kg).
3.4 Dark Matter
About 80 % of the matter of the universe is regarded as dark matter (supposed to exist but
invisible). The dark matter can be understood in two in categories:
(i) MACHOs (Massive Astrophysical Compact Halo Objects). MACHOs are the big, strong
dark matter objects ranging in size from small stars to super massive black holes. MACHOs
are made of 'ordinary' matter, which is called baryonic matter. Astronomers search for
MACHOs.
(ii) WIMPs (Weakly Interacting Massive Particles). WIMPs, are the little weak subatomic
dark matter candidates e.g. yet undetected gravitinos and photinos, undetected axions
particles with extremely small masses etc. which are thought to be made of stuff other than
ordinary matter, called non-baryonic matter. Particle physicists look for WIMPs.
3.5 Explanation for WIMPS on the basis of ΔE = Ac2Δm
ΔE = Ac2Δm favours that the dark matter in form of the lightest neutrinos, axions etc.
(a) The reason is that the heavier particles are annihilated to energy with value of A
extremely less than one say, A =10-10 or less
ΔE = 10-10 c2Δm or less
(4.12)
94
Thus the bulk of the mass of antecedents according to ΔE = Ac2Δm (value of A less than
unity) is annihilated and small energy is emitted, thus they reduce to the lightest descendants
e.g. neutrinos, axions etc. which is consistent with existing perceptions. Or primeval theory
assumes that zeroans are the earliest constituents of the universe which may be regarded as
predecessors of WIMPS.
(b) In the Primeval Theory of the Universe, it is assumed that the universe started its life
from the Zeroans and changed to Primeval pulse of energy. Thus particles like gravitons ,
photino’s , neutrinos etc were created. This process is even now continuing in the empty
space. Thus, lighter particles are possible which may be contributing to the Dark Matter.
Thus lighter particles i.e. WIMPS are naturally preferred candidates for dark matter according
to Primordial Theory of origin of universe.
3.6 Explanation for MACHOS on the Basis of ΔE = Ac2Δm
The MACHOS may have size from small stars to massive black holes. They may remain
invisible due to two reasons.
(c) Firstly, they may have so strong gravitational field that even light energy may not be
emitted. Thus, they remain invisible. It is already explained.
(d) Secondly, the visible energy they emit is instantly converted to some form of invisible
energy. As the inter-conversion of energy from one form to other are feasible processes i.e.
visible radiations may change into infrared radiations. Hence such objects are invisible.
3.7 Gamma ray bursts.
Gamma ray bursts (GRBs) are intense and short (approximately 0.1-100 seconds long) bursts
of gamma-ray radiations and originate at very distant galaxies (several billion light years
away). GRBs are the most energetic events after the Big Bang in the universe and emit
energy up to 1047 J in exceptionally short time.
The origin of GRB can be understood on the basis of this perception
also. If for black hole (formation described above) the values of A and k are higher, then it
contracts beyond a optimum limit due extreme conditions of gravitation and temperature.
Thus it may further result in a detonation known as black bang emitting exceptionally high
amount of energy in form of GRBs, due to high value of A . It is just like big bang. Thus the
explosion like big bang are continuing even now but at much smaller scale emitting energy
in form of GRBs and corresponding to annihilation of small mass huge energy is emitted with
high value of A . This discussion permits that GRBs may be emitted from black holes of
smaller bodies comparatively.
95
According to E  mc 2 if energy emitted is 1047 J, then mass annihilated will be
1.111030kg, that too in few seconds. This annihilated mass is comparable with mass of Sun
1.991030 kg. In fact in GRBs then energy emitted is experimentally estimated but the mass
annihilated is not, thus exact value of A cannot be precisely determined. In GRB, the energy
equal to 1047 J can be emitted from annihilation of mass of 10 kg. The annihilation of mass
may take place in any way. In this case the value of Agrb is 1.111029 i.e.
Agrb =
E
= 1.111029
2
c m
(4.13)
ΔE = 1.111029 c2Δm
(4.14)
Likewise explanation for other cosmological phenomena and bodies can be given on the basis
of the generalized mass energy inter-conversion equation.
Like this energy emitted by QUASARS and other heavenly bodies can
be explained. Solar storm (100 million hydrogen bomb strength) can be associated with
∆E
=Ac2∆m with high value of A. It is other examples of super special annihilation processes. It
implies conversion of mass to energy on the surface of sun is not at constant rate, hence
variable value of A is justified. Thus it is justified that A is co-efficient. During such
activities for smaller mass more energy is being emitted.
4.0 The dawn of Higgs Bosons
Existing facts
English scientist Peter Higgs a predicted particle on the basis of calculations based on
Standard Model in 1964. This particles is known as Higgs Boson. The Bosons were coined in
respect of Indian physicist Dr S N Bose who worked with Einstein on the topic. These
particles are about 125 times heavier than proton (125GeV/c2 -127GeV/c2). These particles
are believed to be associated with hypothetical field. It has no spin, electric charge, or color
charge. It is also very unstable, decaying into other particles almost immediately.
On 4 July, 2012 scientists at CERN in Geneva declared that they had
discovered a new particle 'consistent' with the long-sought Higgs Boson, also known as the
'God particle.' In science no concrete conclusions can be drawn on the basis of one set of
observations, so such experiments are required to be repeated in future for final
96
confirmation.
On 23 September 2011, scientists have announced the neutrino moving with
speed more than that of light. But claim did not last long. In this experiments the neutrinos
were pushed through the earth, thus their speed was measured. Some scientific reasons based
upon characteristics of neutrinos were given for pushing neutrinos through earth. Whereas
speed of light is measured when it passes through vacuum. So it is like to set two
competitors, in race one through water and other through air. The results would be more
interesting if the neutrinos are sent through vacuum pipes, as light travels in vacuum. In this
case there is no possibility that neutrino will interact with matter.
The Higgs Boson are theorized in understanding the origin of the universe.
(i) At the time of explosion of the singular atom in Big Bang massless particles scattered all
over the universe with speed of light.
(ii) It is believed that these massless particles interacted with Higgs field and attained mass.
Even then there are some unanswered questions about Higgs Boson.
Unanswered Questions
(a) When singular atom exploded in Big Bang then it is assumed that mass less particles
scattered in the universe. They interacted with Higgs field and attained mass. Now if all other
particles appeared massless then how Higgs Boson was heavier i.e. nearly 125 times mass of
proton. Why special status is given to Higgs particle? There is no valid reason. It is not
explained.
If other particles attain mass due to hypothetical field of Higgs Boson, then following
conclusion is obvious. Does Higgs Boson gets mass due to field of other particle may be
termed as Senior Higgs Boson?
(b) The law of conservation of mass and energy is the basic law in all mass energy interconversion process. If a massless particle attains mass through Higgs field, then from where
energy is created to impart mass (m=E/c2)? Mass is created when energy is materialized. Is
E=mc2 not applicable at all? Is there any scientific relation between Higgs Field and energy
annihilated? Higgs field may give energy, and this energy is automatically materialized to
mass when particle interacts with this.But how Higgs field creates energy ?
(c) How Higgs field is persistent, when Higgs Boson has mean life time zeptosecond
(10-21 s) seconds. If Higgs particle decays to other particles and loses its identity then how
97
Higgs field is maintained throughout universe?
If Higgs field extends in the all universe, then how many Higgs Bosons are there in the
universe? How the infinitely large numbers of Higgs Bosons were produced? A Higgs Boson
is produced in the exceptionally sophisticated experiment in Large Hadron Collider at
CERN, Geneva.
(d) Does hypothetical field of Higgs Boson interacts in similar way with antiparticle as in
case of particle. At time of Big Bang (explosion of singular atom) the matter and antimatter
was produced in equal amount. Does the hypothetical Higgs field produces matter and
antimatter with equal ease ? What are the conditions?
Such questions needs to be answered before the existence of hypothetical field of
Higgs Boson is established. As far as discovery of Higgs Boson in technological
advancements is concerned, it is exceptionally extraordinary.
Reference
[1] S. Hawking, A Brief History of Time (Bantam Books, New York, 1988), p. 121. (1988),
[2] Sharma, A American Journal of Scientific Research , Vol. 12 pp.67-112 (2010)
[3] Sharma , A Proceedings of the 4th international conference of IMBIC, pp. 211 (2010).
[4] Sharma, A Proceedings of the Natural Philosophy Alliance , Vol.6 No. 2 pp. 261-263
(2011).
[5] Sharma, A International Journal of Nuclear Science and Technology Vol.
3
No 4
pp. 370-77
(2007)
[6] Sharma, A. Galilean Electrodynamics, Vol. 18, No. 5, pp 99-100 (2007).
[7] Sharma, A. Kurt Godel Society Collegium Logicum Volume IX pp. 67-71 (2007)
[8]
Sharma, A Progress in Physics, Vol. 3 pp. 76-83 (2008)
[9] Sharma, A. Concepts of Physics, Vol. III, No. 4, pp.345–373 (2006),
http://merlin.fic.uni.lodz.pl/concepts/2006_4/2006_4_351.pdf.
[10] Sharma, A. Abstract Book: 38th European Group of Atomic Systems (Euro physics
Conference), Isachia (Naples), Italy, p.53 (2006) .
[11]
Sharma, A. Abstract Book: A Century After Einstein Physics 2005, (Organiser
Institute of Physics, Bristol) University of Warwick, UK, 10–14 April. (2005)
98
[12]
Sharma, A. Presented in 19th International Conference on the Applications of
Accelerators in Research and Industry, Fort Worth, Texas, USA, 20–25 August. 2005
[13] Sharma, A. Abstract Book , Oral presentation (lecture) on 21st September 2005, in The
5th British Gravity Meeting , Oxford, England.
[14] Sharma, A. Physics Essays, Vol. 17, pp.195–222 (2004)
[15] Sharma, A. Proc. Int. Conf. on Number, Time, Relativity, United Physical Society of
Russian Federation, Moscow, p.81 (2004)
[16] Sharma, A Acta Ciencia Indica Vol. XXIV P No. 4 pp.153-158 (1998).
[17] Sharma, A to be published in Galilean Electrodynamics, Massachusetts in , USA
[18] Sharma, A submitted for publication.
[19] Sharma, A Acta Ciencia Indica Vol. XXVI P. No. 1 pp.013-016 (1998).
[20] Sharma, A International Conference on World Year of Physics, University of Rajasthan ,
Jaipur pp.14 (2005)
[21] Sharma, A. III international Young Scientists Conference, Kyiv National University ,
Scientific works pp. 19 ( 2002).
[22] Sharma, A Journal of Theoretics Vol.6-5 2004
[23] Sharma, A Einstein’s E=mc2 Generalized Raider Publishing International (2007) New
York , USA
[24] Sharma, A Einstein’s Mass Energy Equation, Lambert Academic Publishers (2009)
,Saarbrucken , Germany
[25] Sharma, A. Journal of Vectorial Relativity . JRV (4) 1-28 (2009)
[26] Sharma, A. Concepts of Physics, Vol. V, No. 3, pp.553–558 (2006)
[ 27 ] Sharma, A. Apeiron Vol. 18 No 3 (2011)
[28] Sharma, A. Apeiron Vol. 18 No 4 (2011)
[29] Fox, K.C ., The Big Bang: What it is,Where It Came From and Why It Works , (New York
:Wiley) 224 (2002)
[30] Luminet, J.P., The Rise of Big Bang Models, from Myth to Theory and Observations ,
Arxiv preprint arXiv:0704.3579, 2007
[31] Joseph L R, Journal of Cosmology 6 1548 ( 2010 )
[32] R. Peccei, R, Quinn, H Phys. Rev. Lett. 38 1440 (1977)
[33] A.L.Erickcek , M Kamionkowski and Sean Carroll ,Phys. Rev D 78 123520 2008
[28] R. Peccei, R , Quinn, H Phys. Rev. Lett. 38 1440 (1977)
[34] Taubes, G, Theorists nix distant antimatter galaxies, Science, 278:226, (1997).
99
Beyond Einstein and E =mc2
Science is infinite
Ajay Sharma
Chapter 5
Applications of generalized mass energy inter-conversion equation in
Nuclear Physics and Nuclear Reactors
First Glimpse
 The chemical reactions are the most ancient reactions in science but E =∆mc2 is not
confirmed in such cases. If out of 90 kg, mass 10-9 kg is converted into energy, then
according to E=∆mc2 energy equal to 9×107J will be produced. This can push a
truck of mass 1000 kg to a distance of 90 km.
 There are some observations nearly 40 years old , that energy emitted in fission of
U235 and Pu239 is 20-40 MeV, less than Q-value predicted by E=∆mc2. These can
be explained with help of ∆E =Ac2∆m with value of A equal to 0.875. Similar other
observations can be explained.
 E = Δmc2 fails to explain the ‘universal equality of proton and neutron’ and the
binding of the deuteron simultaneously. Under these conditions atom is unstable. It
is serious limitation of E = Δmc2. E = Ac2 m is able to explain it and in this
case
co-efficient of proportionality is 1010 .
 The nuclear fission is caused by slow neutrons (2185m/s), after fission again 3
neutrons are emitted. But these are fast (relativistic) neutrons (1.954×107 m/s)
which have mass 0.215% more than slow ( classical ) neutrons.
 But in calculations the mass of neutrons (classical velocity) and neutron (relativistic
velocity) is regarded as same. Thus energy estimated from E = Δmc2 is more. If
the exact masses of neutrons are used in calculations then energy emitted is less.
 If the exact relativistic masses of other fission products e.g. barium and krypton are
taken then exact amount of energy can be calculated.
100
1.0 Introduction
It is already mentioned that Einstein derived equation [1] for light energy –mass interconversion as
∆L =∆mc2
(5.1)
under super-special conditions [2-6] in his Sep. 1905 derivation. It is also mentioned in the
first chapter that from the derivation two equations i.e. L=∆mc2 and Ma = Mb are equally
feasible. But Einstein did not discuss the equation , Ma = Mb at all. If various parameters are
properly taken in account then Einstein’s derivation also yields
∆L =
mc 2
2
or ∆L = 518∆mc2
Hence ∆L α ∆mc2
or ∆L=0.002∆mc2,
or ∆L = Ac2∆m
It implies that conversion factor can be different from c2 . On the basis of equation(5.1)
Einstein speculated E=∆mc2. Further the generalized mass energy equation is
∆E =Ac2∆m
(5.2)
In early 1920s nuclear reactions were discovered and scientists have no other equation at that
time, hence started using E= ∆mc2. Thus E= ∆mc2 was established as standard at that time as
there are 7 days in week not 10 or 12 months in a year not 10. The data which was consistent
with E= ∆mc2 was retained, and observation which were inconsistent with E= ∆mc2 was
neglected. Had Einstein critically analyzed his derivation, he would have given ∆E =Ac2∆m,
then it would have been considered along with E= ∆mc2. Thus theoretical, experimental and
industrial aspect would have been different. The generalized equation can be successfully
applied in various phenomena.
The conversion factor other than c2 is also discussed in cosmological
and astrophysical reactions. If all the interpretation is true, then conversion factor other than
c2 must be observed in nuclear phenomena, which is indeed the case. For example E=∆mc2
cannot explain simultaneously the ‘universal equality of masses of nucleons’ and ‘binding
energy of the deuteron’. Also there are some phenomena which are not explained by E=∆mc2
. These can be explained by generalized equation of mass energy inter-conversion i.e. ∆E
=Ac2∆m. Like this critical analysis of mass of fast neutrons yields interesting results which
have bearings on nuclear physics and support ∆E =Ac2∆m.
2.0 E = Ac2 m in chemical reactions
These reactions existed since ancient time but neither Einstein nor any other scientist
101
confirmed E = ∆mc2 quantitatively in such reactions. Let wood or straw of mass 1kg is burnt
under controlled conditions, consequently ashes and gases are emitted. The magnitude of
ashes and masses are measured. Let the mass equal to 10-9 kg is annihilated , and equivalent
amount of energy is emitted.
If 10-9 kg of matter is annihilated then theoretically energy equal to 9×107J will be produced
i.e.
E = ∆mc2 = 10-9 ×9×1016 kg m2/s2 = 9×107 J
(5.3)
This energy can derive a truck of mass 1,000 kg to distance of 90 km. Such or similar
predictions are not experimentally confirmed in specific experimentation. In daily life it
appears that this prediction may not be justified, as even huge amount of wood is burnt then
energy appears to be emitted too less than that above prediction to be justified [7]. Nearly 2
quintals (200kg) wood is required for burning in a dead body, this observation is seen daily
by thousands of people. It is not justified to regard E = ∆mc2 true without experiments, rather
it should be clearly mentioned that E = ∆mc2 is not confirmed in such cases. Thus results are
wide open unless specific experiments are not conducted and E = ∆mc2 is confirmed.
Let experimentally energy observed is 4.5 ×107 J corresponding to mass annihilated
10-9 kg, then value of A from E = Ac2 m will be 0.5 i.e.
A =
E
= 4.5×107 / 9×1016×10-9 = 0.5
c 2m
(5.4)
Thus in this case mass energy inter-conversion equation becomes
E  0.5c 2 m
(5.5)
In volcanoes gigantic amount of energy is emitted, which has not been confirmed in case of
E =mc2. Thus applications of E = Ac2 m cannot be extended in this regard, apparently
high values of A are expected to justified in volcanic reactions. Apparently it can be justified
experimentally but in indirect experiments.
Similar can be the case of cosmological and astrophysical reactions. Thus
we should not mislead ourselves that everything regarding mass and energy is completely
studied in the universe. Realistically we understand only less than 1% of such weird
phenomena and there is lot of room for newer perceptions.
2.1 The total kinetic energy(TKE) of fission fragments of U235 or Pu239 Is 20-60 Mev
less than predicted by E =mc2.
The familiar fission reaction is
235
+ 0n1 → 56Ba141 +
92U
92
36Kr
+ 3 0n1 + Q
102
In laboratory [8-11] it has been experimentally confirmed that using thermal
neutrons the total kinetic energy of fission fragments that result from U235 or Pu239 is 20-60
MeV less than the Q value of the reaction predicted by E =mc2. These observations are over
40 years old. Earlier lot of work is done on nuclear fission when it was discovered, but now
it is regarded as saturated field more or less. If experiments are again conducted then such
results may be obtained which would confirm E = Ac2 m. Unfortunately little research is
being done in this regard, in existing physics these inconsistent observations are explained in
the following ways.
(i) It is typically assumed that energy is lost in unobservable effects [8-11]. If so then such
unobservable effects may also be applicable to those cases where E =mc2 is regarded as to
hold good.
(ii) Also attempts have been made to explain the total kinetic energy (or essentially total
energy) of fission fragments by extending the successful liquid -drop model of Bohr and
Wheeler [8-11]. It implies the gravity of inadequacy of E =mc2 in this case.
The controlled chain reaction was discovered in 1945 and soon atom bombs were exploded.
Then considerable research was done on topic. Earlier lot of work is done on nuclear fission,
but now it may be regarded as saturated field. If purposeful experiments are again repeated to
experimentally measure energy, then such results may be obtained. Consequently results can
be interpreted in view of the generalized form of mass energy equation E = Ac2 m.
The same can also be explained on the basis of E = Ac2 m. Let
according to E =mc2 the total kinetic energy (or essentially total energy) of fission
fragments of U235 or Pu239 is 200 MeV theoretically and experimentally observed energy is 25
MeV less i.e. 175 MeV. Then according to E = Ac2 m the value of A is 0.875 i.e.
A = E / c2 m = 175 / 200 = 0.875
(5.6)
So in case of fission fragments of U235 or Pu239 the value of A is less than one i.e.
0.875 as in eq.(5.4) , hence the energy emitted is less than predicted by E =mc2. In this case
the value of A other than unity is justified.
2.2 Did Hiroshima and Nagasaki atomic bomb explosions on Japan absolutely confirm
E=Δmc2?
Not at all. The Atomic Bomb explosions on Hiroshima and Nagasaki did not
confirm E=Δmc2 QUANTITATIVELY. These explosions simply confirmed ΔE  c2Δm or ΔE
=Ac2Δm (mass is converted to energy). It is justified from report of the first American team
which visited the affected places in August 1945.
The efficiency of the nuclear weapons as well as nuclear reactors is far less than the
theoretical value predicted by E=Δmc2. Robert Serber (member of first American team
entered Hiroshima and Nagasaki in September 1945 to assess loses), has mentioned [36 ]
103
that the efficiency of “Little Boy” atom bomb [U235, 49kg] that was used against Hiroshima
was about 2% only. It is assumed that all the atoms do not undergo fission, thus material is
wasted. However, no such waste material is specifically measured quantitatively. Thus the
waste material (nuclear reactor or weapon) must be measured and corresponding energy is
calculated, and it must quantitatively explain that why efficiency is less. It may require the
measurements of all types of energies (may co-exist in various forms) emitted in nuclear
reactions or in the processes and experimental errors. Only then quantitative conclusions
must be drawn that up to which extent E = Δmc2 is obeyed in such cases.
Until such calculations are not precisely confirmed experimentally; it is equally
feasible to assume that the energy emitted may be less than E = Δmc2 (or E  Δmc2), when
reactants are in bulk amount and various types of energies are simultaneously emitted (or
energies co-exist in the various forms). Thus, both the possibilities are equally probable until
one is not specifically ruled out.
2.3 Anomalous observation
The anomalous observation of excess mass of Ds(2317) can be understood with help of
E  Ac 2 m , as mass of the observed particle is found more [12] than predictions of
E  mc 2 . In this case value of A will be less than one. For understanding consider energy
10 10
equal to 10 J is converted into mass, then corresponding mass must be
kg. i.e.
9
6
m =
E
c2
=
10 10
10 6
=
9 1016
9
(5.7)
We are considering the case that mass is found more than this. Let the mass be
10 10  10
kg.
99
The value of A in this case is 0.9 as calculated from E  Ac 2 m i.e.
106 =
A9  1016  10  10 10 9 A  10 7
=
81
81
(5.8)
A= 0.9
(5.9)
E = 0.9c2 m
Thus corresponding to same energy more mass is observed.
(5.10)
3.0 E = Δmc2 in case of deuteron contradicts universal equality of masses of nucleons
There are two inherent observations;
(i) firstly masses of nucleons ( neutrons and protons) are fundamental constants i.e. same
universally (inside and outside the nucleus in all cases)
(ii) and secondly nuclei possess BE (mc2) due to mass defect.
To explain these observations of deuteron (BE = 2.2244MeV), the difference
in masses of nucleons must be 0.002388 u or about 0.11854% of masses of nucleons outside
nucleus. Thus theoretically, according to E = Δmc2 masses of nucleons must be less in
104
nucleus, which is not justified as all data is based upon equality of masses of protons and
neutrons in all cases. The masses of nucleons are constants in category of atomic and nuclear
constants. Conceptually according to E = Δmc2 the binding energy and mass defect cannot
exist simultaneously.
If the applications of the generalized equation E = Ac2 m are invoked in
this regard, then it is capable of explaining BOTH the observations simultaneously i.e.
equality of masses of nucleons (assuming infinitesimally small mass defect) and binding
energy. As according to E = Ac2 m even due to infinitesimally small mass defect
(2.388×10-14 u , say) the binding energy of deuteron can be 2.2244MeV due to presence of
conversion factor A. The mass defect according to E = Δmc2 is 2.388×10-3 u. Thus E =
Ac2 m, explains both the intrigues simultaneously i.e. equality of masses of nucleons and
binding energy of deuteron. Theoretically it is clear that conversion factor c2 is forced in
equation E = Δmc2, in mathematical derivation. It has bearings on experimental observations
also.
3.1 Decrease in masses of proton and neutron in deuteron nucleus
In the experimental and theoretical nuclear physics the masses of nucleons (protons and
neutrons) are fundamental physical constants in category of atomic and nuclear constants,
and binding energy (energy required to break the nucleus) is an inherent property of all
nuclei. Also it is equally true that all the mass energy inter conversions are universally
explained on the basis of E=∆mc2, where ∆mc2 is mass defect.
Mass defect =
Mass of nucleons out side nucleus – Mass of nucleons inside nucleus
(5.11)
Binding Energy =
[Mass of nucleons out side nucleus – Mass of nucleons inside nucleus ]c2
(5.12)
This aspect is critically discussed in view of deuteron, which contains just one neutron and
proton.
(a) The mass of proton is experimentally measured equal to 1.672621×10-27 kg, (1.007276u
or 938.272029 MeV) and is same in all cases. Also the mass of neutron is 1.674927×10-27 kg
(1.008664u or 939.565360 MeV) in all cases.
(b) Experimentally binding energy (BE) of deuteron is measured by various methods [13-15]
has been found to be 2.2244MeV (1amu = 931.494MeV, 1amu =1.660 5381×10-27 kg), which
is equivalent to 0.002388u (3.984×10-30 kg ) on the basis of ∆E=∆mc2 i.e. masses of
nucleons are converted into energy. The conversion factor is c2 same for all masses.
In analogous way for public understanding the let us compare the
binding energy and mass defect with two electric bulbs. According to ∆E=∆mc2 only one
bulb glows at a time and other blows off, whereas experimentally both the bulbs must glow
simultaneously. For example the binding energy and mass defect both must be explained
105
simultaneously. ∆E=∆mc2 explains either mass defect or binding energy. Whereas
E = Ac2 m explains both binding energy and mass defect simultaneously.
3.2 Decrease in mass of nucleons in nucleus is not justified.
The phenomena of universal equality of masses of nucleons and origin of binding energy of
nuclei have been studied critically and quantitatively [13-15]. The binding energy of the
deuteron is experimentally observed as 2.2244MeV [14.94×10-11J], according to ∆E=∆mc2 it
is equal to mass defect 0.002388amu. It means in the nucleus of deuterium, mass 0.002388u
(of proton and neutron) is converted into binding energy[16].
The mass defect i.e. 0.002388u is comparable with sum of masses of the neutron
and proton (2.01594 u), masses must decrease in nucleus considerably i.e. 0.11845 %
(compared to mass in free state). In deuteron there are only protons and neutrons, hence
theoretically decrease in mass or mass defect 0.002388u is only at the cost of mass of proton
(Mp) and mass of neutron (Mn). There is no third entity whose mass may decrease. The mass
of proton is 1.007276u and let decrease in mass of proton is half the mass defect (0.002388 u)
i.e. 0.001194 u (which contributes towards the binding energy of deuterium). Then
theoretically mass of proton in nucleus must be 1.006082u (1.67064×10-27 kg) and then
decrease in mass of proton must be 0.1185 %. Also mass of neutron is 1.008664u and let
decrease in mass of neutron is half the mass defect i.e. 0.001194u. Then mass of neutron in
nucleus must be 1.00747 u (1.67294×10-27 kg). Similarly is the decrease in mass of neutron in
nucleus is 0.1185%.
Like this theoretically decrease in mass of nucleons in other nuclei
can be estimated taking all relevant factors in account. More the value of binding energy
more would be the decrease in mass of nucleons in the nucleus. The decrease in masses of
neutron and proton in deuteron, to explain the values of BE on the basis of E = mc2, are
shown in Table I
3.3 E = Δmc2 , binding energy and mass of nucleons in deuteron.
If mass of nucleon remains the same universally (fundamental fact used in existing physics
in all aspects of experimental and theoretical nuclear physics) i.e. mass defect (Δm =0).
Then according to ΔE = Δmc2 , binding energy is also zero.
Binding Energy (BE) = Mass Defect (Δm)c2
=0
(5.13)
Thus universal equality of masses of protons and neutrons (means Δm =0) implies that mass
defect must be zero theoretically, hence binding energy is also zero (Δm =0, . E =0.c2). If
binding energy (energy required to break the nucleus) is zero then nucleus will be unstable.
Hence it is not experimentally justified. The eq.(5.12) cannot explain two observations.
The masses of proton and neutron are same inside and outside the nucleus, it is
experimentally confirmed [7].
106
(i) When a gamma ray photon of energy 2.2244MeV hits the deuteron (binding
energy of deuteron is 2.2244MeV), then deuteron is split up and proton and neutron are
emitted. The mass of the released proton and neutron from nucleus is the same as usual mass
i.e. 1.007276 u and 1.008662 u.
The masses of proton and neutron are never less in nucleus i.e. 1.006082u and 1.00747u as
theoretically predicted by E = mc2 to explain binding energy. No external energy is
provided by the gamma ray photon to increase mass of proton and neutron inside the nucleus.
If the masses of proton and neutron are less in nucleus, then lighter protons and neutrons
must be emitted. But masses of emitted proton and neutron are usual masses. Whatever is the
energy of gamma ray photon that is provided to dissociate the binding energy of deuteron as
both are exactly equal i.e. 2.2244MeV each. Gamma ray photon does not provide any energy
to increase masses of proton and neutron [16].
Consequences of equality of masses of nucleons: Thus mass defect and binding energy both
must be zero,
Mass defect =
Mass of nucleons out side nucleus – Mass of nucleons inside nucleus
(5.14)
Binding Energy =
[Mass of nucleons out side nucleus – Mass of nucleons inside nucleus]c2
(5.15)
The masses of protons and neutrons are equal both outside and inside the nucleus.
Instability of deuteron
According to E = mc binding energy of nucleus can never originate without annihilation
of adequate mass of nucleons, which is not justified. If mass defect Δm =0 (masses of
nucleons are same inside and outside the nucleus) then binding energy is also zero; implying
instability of nuclei which is never justified. Then what is the source for binding energy on
the basis of E = mc2 ? E = mc2 implies instability of deuteron, as binding energy
(energy required to break the nucleus) is zero (m=0).
Importance of E = Ac2 m:
E = Ac2 m is applied even (on adhoc basis) in this regard i.e. to simultaneously explain
the binding energy and mass of nucleons in nucleus.
Consequently the generalized mass energy equation implies that for even
annihilation of INCALCULABLE mass defect (this assumption is for obeying universal
equality of protons and neutrons), binding energy equal to 2.2244MeV (3.965×10-13 J ) is
feasible due to presence of conversion factor A.
Let us assume that in this case mass defect is 2.388×10-14 u or 3.965×10-41
kg and due to higher value of proportionality or conversion coefficient the binding energy can
be 2.2244MeV. Thus there is consistency between experimentally observed facts (binding
energy and equality of masses of nucleons) and theoretical predictions based upon E =
Ac2m. Thus conversion factor may not be regarded as c2 in all cases.
The E = Ac2m implies universal equality of masses of nucleons ( as mass defect is
negligible ) and binding energy is 2.2244MeV ( as conversion factor A is very high). Thus
2
107
E = Ac2m explains both phenomena of equality of masses of nucleons and binding
energy simultaneously which is not so in case of L = mc2 .
3.4 Explanation on the basis of E = Ac2 m
Einstein’s Sep. 1905 derivation of mass energy inter conversion equation has been critically
analyzed by the author [2-6] and found that this derivation is true under special conditions
(only for certain values of parameters, not for all values of involved parameters). In this paper
firstly Einstein [1] derived under super-special conditions the light energy-mass inter
conversion equation i.e.
L = mc2
(5.1)
The eq.(5.1) is based upon relativistic variation of light energy, which was given by Einstein
[1] in his June 1905 paper as
 v

1  c cos  

   
2
v
1 2
c
(5.15)
where  is light energy emitted by body in frame (x,y,z) and  * is light energy measured in
system (ξ, η, ζ ), and v is velocity with which the frame or system (ξ, η, ζ ) is moving. This
equation was given in Einstein’s June 1905 paper in Section 7 and is called Doppler principle
for any velocity whatever. But there is no specific derivation to the equation in paper. Then
this equation is used in derivation which is basically equation of conservation of energy.
Einstein derived L = ∆mc2 from this equation and speculated E = ∆mc2. Thus we find that E
= ∆mc2 is speculated from L = ∆mc2 which is based upon eq.(2.2) and eq.(2.2) is not derived
as in Einstein’s June 1905 paper. It is really a strange situation about origin of E=∆mc2 and
from equations it is derived.
The eq.(5.15) is purposely mentioned here as Einstein derived eq.(5.1) using it
for light energy only. Neither eq.(5.15) nor eq.(5.1) is meant for attractive binding energy of
nucleus. Also Einstein did not mention anything about it in the derivation. In L = mc2
Einstein arbitrarily replaced light energy L by energy E (every type of energy) and
speculated eq.(5.1) i.e.
E = mc2
(5.16)
Further Einstein maintained that E = mc2 holds good for all perceivable energies e.g.
heat energy, attractive binding energy of nucleons in nucleus, chemical energy, nuclear
108
energy, magnetic energy, electrical energy, sound energy, energy emitted in form of invisible
radiations, energy emitted in cosmological and astrophysical energy etc. However in
Einstein’s derivation there is no mathematical basis which accounts for all the energies for
which equation is applied.
How an equation meant for calculation of ‘decrease in mass of body on emission of light
energy’ can be applied to attractive binding energy of deuteron?
In view of theoretical situation the author [2-6] has derived the generalized mass energy
inter conversion equation i.e.
E = Ac2 m
(5.17)
specifically for all energies by an independent method, here A is coefficient of
proportionality. Like many other co-efficients of proportionality in the existing literature the
value of A depends upon the inherent characteristic conditions of the process. It can be equal,
less or more than one. Thus according to E = Ac2m like Einstein’s equation mass is
converted to energy but unlike Einstein’s equation conversion factor is not always c2. Thus
according to E = Ac2 m, the energy emitted can be less, equal or more than E = mc2,
also experimentally inter-conversion of mass and energy are bizarre processes right from
chemical reactions to heavenly phenomena governing origin and development of universe.
3.5 E = Ac2 m implies smaller mass defect can give binding energy 2.2244Mev.
(i) The equality of masses of proton and neutron inside and outside the nucleus implies that
mass defect is too less to be measured by all means. Only then masses of neutron and proton
are fundamental physical constants. Let us speculate that the mass defect in this regard is
2.388×10-14 u or 3.965×10-41 kg ( in previous case it was 2.388×10-3 u or 3.965×10-30 kg ),
if it is the case then masses of nucleons inside and outside the nucleus are equal or difference
is too less to be measured. According to the generalized form of mass-energy interconversion equation, for annihilation of infinitesimally small mass, large amount of energy
can be emitted i.e. conversion factor is much higher than c2. Now applying equation E =
Ac2 m under this condition, the value of A can be determined as [16]
BE = 0.03563752×10-11 J, m = 0.003965274×10-37 , c2 = 8.9874044×1016
(5.18)
E
0.03563752  10 11
A= 2
=
= 1010
37
16
0.003965274  10  8.9874044  10
c m
E = Ac2 m = 1010 c2 m
(5.19)
109
The value of conversion co-efficient ( ‘A’) is similar to co-efficients of proportionality in C.
F. von Weizsacker’s semi-empirical formula [7] for binding energy (associated with Bohr’s
Liquid Drop Model).
(ii) The masses of neutron and proton are same inside and outside the nucleus as mass defect
is 2.388×10-14 u or 3.965×10-41 kg which is incalculable. Corresponding to this mass defect
mass of proton is 1.007274 u will decrease by incalculable amount 1.195×10-14 u. Similar is
the case of neutron. Thus masses of nucleons are same inside and outside the nucleus , and in
this particular case for annihilation of negligible mass defect more energy is emitted
compared to predicted by E = mc2.
According to E = Ac2 m the mass defect 3.984×10-41 kg can explain
binding energy equal to 2.2244MeV if A is 1010 . Thus generalized equation simultaneously
explains both intrigues e.g. universal equality of masses of nucleons and binding energy of
nucleus 2.2244MeV. The decrease in masses of neutron and proton in deuteron, to explain
the values of BE on the basis of E = Ac2 m are shown in Table II.
Hence according to the generalized form of mass-energy inter
conversion equation i.e. E = Ac2 m masses of protons and neutrons are the same inside
and outside the nucleus; and binding energy for deuteron is same as experimentally observed
i.e. 2.2244MeV. In this case conversion factor A is exceptionally more than one, thus results
are consistent with observations. As newer and newer phenomena in such cases are being
discovered, then in such phenomena the E = Ac2 m can be discussed critically.
Table I. The universal equality of masses of protons and neutrons is not justified when
binding energy is calculated on the basis of E =mc2.
Sr. Characteristi
No. c
1
1H
2
1H
e=1
p=1
e=1
p=1
n=1
1
Binding
Energy
(MeV)
0
2.2244
2
Mass defect
(BE/c2) in
amu
0
2.388×10-3
or
3.965364×10-30 kg
3
Decrease in
0
1.194×10-3
110
mass per
nucleon
(amu)
Or
1.982682×10-30 kg
4
Mp and Mn in Mp=
nucleus
1.00727
6
Mp=1.006082
or
1.670637×10-27 kg
Mn =1.00747
or
1.672942×10-27 kg
5
%age
Decrease in
Mp
0
0.1185
%age
Decrease in
Mn
0
0.1183
6
7
Universal
obeyed
equality of
masses of Mp
and Mn
Not obeyed
Table II The universal equality of masses of protons and neutrons is justified when
binding energy is calculated on the basis of E = Ac2 m ( A=1010 ).
Sr. Characteristi
No. c
1
1H
2
1H
e=1
p=1
e=1
p=1
n=1
1
0
2.2244
Binding
Energy
(MeV)
111
2
2.388×10-13
Mass defect
(BE/Ac2) in
amu
0
3
Decrease in
mass per
nucleon
(amu)
0
4
Mp and Mn in Mp=
nucleus
1.00727
6
5
%age
Decrease in
Mp
0
1.185×10-11
%age
Decrease in
Mn
0
1.183×10-11
6
7
Or
3.965364×1040
kg
Universal
Obeyed
equality of
as
masses of Mp masses
and Mn
are
precisel
y same.
1.194×10-13
or
1.982×10-40
kg
Virtually
same
Obeyed
as masses
are virtually
same.
Further interesting results are obtained if the masses of neutrons are considered during the
nuclear chain reactions in fission. These are discussed below.
4.0 Relativistic mass of secondary neutrons in fission and fusion.
The fission is initiated by thermal neutron (0.025eV or 2,185m/s). In the fission reactions
neutrons produced are known as fast (secondary) or relativistic neutrons having energy 2MeV
112
(1. 954×107 m/s or ~ 7% speed of light). With help of moderator the velocity is reduced to
thermal neutrons or in classical limits. The relativistic variation of mass of fast neutron has to
be taken in account.
The masses of thermal and fast neutrons are 1.0086649156u and 1.01080879u
respectively from relativistic variation of mass. But in calculations of Q-value (energy of
reactants – energy of products) the masses of fast (secondary) and slow neutrons are taken as
same i.e. 1.0086649156u. Nonetheless, it is not justified to take the relativistic velocity (1.
954×107 m/s) or relativistic mass is taken same as classical velocity (2,185m/s) or classical
mass. Thus in the existing literature, then Q value is calculated as 166.728MeV, the masses
of products in this case is 235.8736037u. If masses of fast neutrons are considered, then
mass of the products must be 235.880035u. The mass of the reactants in both the cases in the
i.e. 236.05255948u.
The masses of fission fragments Ba144 and Kr89 are taken as classical masses due
to non-availability of exact velocities. If the relativistic masses of secondary neutrons are
taken in account correctly, then Q value of the reaction is 160.7373MeV. Thus the accepted
Q-value is 5.99MeV (or 0.00643u) less, which is comparable with energy of gamma ray
emitted in fission. But this decrease in energy is always neglected which is unfair.
There may be numerous such reactions involving fission and fusion. If
velocity is found in relativistic region, then relativistic mass has to be taken in account in
energy considerations. In fusion the energy is emitted is very high and hence velocity of
products is comparable to c. So the conclusions must be drawn with all fission and fusion
events to draw conclusions over wider range. Similar calculations can be done for fusion of
deuterium to helium.
4.1
Initially fast neutrons are emitted in nuclear fission
Neutron was discovered by Chadwick [17] in 1932. O. Hahn and F. Strassmann reported
to Naturwissenschaften the nuclear fission and new element barium was obtained [18]. The
discovery of fission and production of barium from uranium was also confirmed [19-20] by
Lise Meitner and O. R. Frisch. In fission of U235, the various fission fragments with different
isotopes are possible. In first ever nuclear fission one of the fission fragment was barium,
hence this reaction is considered in discussion. In nuclear fission the energy of neutron is
nearly 2MeV (velocity 1.954×107 m/s), such neutrons cannot cause further fission. Thus with
help of moderator its velocity is reduced to 0.025eV (2185m/s). The theme of discussion is
113
that relativistic mass of neutron is not properly taken in account in calculation of Q-value. If
it is taken in account then significantly new results are obtained.
4.2
Q-value in reactions
Q value for the reaction is the amount of energy released in a reaction,
Q Value = E (Reactants) –E (Products)
(5.20)
According to law of conservation of matter,
Matter can neither be created nor be destroyed but can be transformed from one form to
other.
Energy is other form of mass, according to Einstein c2 is the conversion factor, when mass is
converted to energy. Further energy emitted may exhibit in different forms, heat, light or
invisible forms etc. Every energy emitted is at cost of mass. Realistically all the energies
must come from annihilation of mass (m), according to mass energy inter-conversion
equation, E = mc2. Energy or mass cannot be produced out of nothing. According to
Einstein energy emitted can neither be more nor less than E = mc2. For example,
Energy emitted = (mass annihilated)c2
= KE of the fragments + Heat energy + Light energy+ Sound energy +Energy of
various particles and rays + other forms of energy if any
(5.21)
Here origin of all energies is mass. The general reaction for nuclear fission is,
1
0n
+ zXA →
zY
A+1
Now consider fission of
235
92U
→
235
92U
2FF + 0n1’s +  + E
(5.22)
with neutrons
+ 0n1 → [ 92U236]* →
144
56Ba
+
89
36Kr
+ 3 0n1 + 
(5.23)
Normally fission reaction is regarded as complete as far as calculation of Q-value is
considered.
On the basis of mass of reactants (92U235, 0n1 ) and products (56Ba144 ,
89
36Kr
,
3 0n1 ,  )
Q-value is determined. The products are unstable. Further barium and krypton are unstable
and further decay in due course of time.
114
A=144 Ba(11s)  La(41s)  Ce (285d)  Pr(17m)  Nd
A=89
Kr (3m)  Rb(15m)  Sr(51)  Y
Barium has half life 11s and final stable product is Neodymium, whereas Krypton has half
life 3m and final product is Yttrium. The final products i.e. Neodymium and Yttrium are
virtually stable.
4.3
Insights in Q value
The law of conservation of mass-energy is obeyed in the reactions; the energy emitted in
nuclear reactions is due to annihilation of mass. Thus energy released in the process can be
considered in two main parts
(i) When uranium
235
92U
and neutron 0n1 change to compound nucleus by radiative capture
reaction. It gets into excited state U236*, the excitation energy tends to distort the shape
further.
235
92U
+ 0n1 →U236* → U236 +  ray
(5.24)
Then compound nucleus comes to ground state by emitting gamma ray photon of energy
6.54MeV and get split up in fission fragments. The energy required to excite nucleus or
energy emitted when compound nucleus come to ground state.
Excitation Energy = [(235.0439299+1.008665)-(236.045568)] 931.49MeV
= 0.007026 × 931.49 =6.54MeV
(5.25)
When compound nucleus [92U236]* is transformed to
144
56Ba
and
89
36Kr
along with  ray
of energy (6.53MeV or 0.007026u). The energies calculated in eq.(5.13) and eq.(5.19) are
calculated for this stage.
(ii) Then radioactive isotopes of
144
56Ba
and
89
36Kr
decay to stable products. The final
products i.e. Neodymium and Yttrium are virtually stable. At this stage energy is emitted in
form of beta rays, neutrinos emitted in beta rays, gamma rays accompanying beta rays etc.
The energy emitted in each stage is currently explained by E = mc2, as is at the cost of mass.
Thus now the Q value in terms of various three contributions may be summed up as
115
Q-Value = [mass of reactants] c2 – [Actual mass of fission fragments+ mass equivalent to
excitation energy]c2 + Energy due to unstable decay products.
(5.26)
The  ray (6.53MeV or 0.007026u) is also a product.
Now various possibilities can be considered.
1. The energy emitted in decay products is produced after fission, hence this energy may be
neglected if this stage is not considered. However the excitation energy cannot be neglected.
Q-Value = [mass of reactants] c2 – [Actual mass of fission fragments+ mass equivalent to
excitation energy]c2
(5.27)
The mass equivalent to excitation energy is 0.007026u as measured in eq.(5.25)
Further sub-cases are also considered depending upon velocity of fission fragments.
1(a). If the velocity of fission products is in classical region, v<<c, then
Q-Value = [mass of reactants]c2 – [ mass of fission fragments when v<<c + mass equivalent
to excitation energy] c2
(5.28)
1(b). If velocity of fission products is in relativistic region i.e. v~c then,
Q Value = [mass of reactants]c2 – [ mass of fission fragments when v~c + mass equivalent
to excitation energy] c2
4.4
(5.29)
Magnitude of Q value
(a) Thermal Neutrons (0.025eV or 2185m/s): If it is assumed that velocity is in classical
region i.e. v<<c, then according to eq.(5.28) the Q value can be written as
Mass of reactants = (235.0439299 +1.0086649156) u = 236.0525948u
(5.30)
Mass of products = (143.922 953 + 88.917 630 +3.02599473+0.007026) u =235.8736037u
(5.31)
Obviously 0.007026u is mass equivalent to energy of
 ray as in eq.(5.25.)
Mass annihilated = m =236.0525948u-235.8736037u= 0.1789911u
Energy released (Q Value) =166.728MeV
(b) Fast (relativistic) Neutrons (2MeV or 1.954×107 m/s).
(5.32)
(5.33)
116
The neutrons which are emitted in the fission are fast neutrons having energy nearly equal to
2MeV (3.2×10-13 J). With this energy (2MeV) neutron moves with relativistic velocity i.e.
1.954×107 m/s (~7% that of light). The mass of neutron is 1.0086649156u. If velocity is in
relativistic limits then mass of particle increases [22-26], according to equation
Mmotion =
M rest
v2
1 2
c
(5.34)
As velocity is 1.954×107 m/s (2MeV) then relativistic mass has to be taken in account,
otherwise eq.(5.34) will be irrelevant or relativistic effects will be insignificant. The
relativistic effects cannot be neglected otherwise it would mean
Mmotion (1.954×107m/s) = Mrest
(5.35)
which is not justified. Thus when neutrons move with relativistic velocity then relativistic
mass has to be taken in account.
The relativistic mass of neutron can be calculated from equation of relativistic kinetic
energy.
K = [Mm –Mr ]c2
Mm = K /c2 +Mr = 3.204×10-13 / 9×1016 + Mr
(5.36)
Mm = 0.002143883u + 1.0086649156u = 1.010808793u
Thus the mass of fast neutrons must be 1.01080879u (%age increase of 0.2125% ) i.e. more
than rest mass 1.0086649156u. It cannot be neglected. The mass of product neutrons (2MeV,
1.954×107 m/s, ~ 7% that of light) must be different from reactant neutron (0.025eV,
2185m/s). Now substituting various values in eq.(5.29), in this case Q-value further decreases
as mass of products is higher.
Mass of reactants = 236.0525948u
(5.37)
Mass of products = (143.922 953 + 88.917 630 +3.032426394 +0.007026) u
=235.8800354u
(5.38)
m = 0.1725594 u
Q = 160.7373MeV
(5.39)
117
Hence when relativistic mass of neutrons is considered then energy predicted is 5.99 MeV
(2.29×10-13J) less. Now the difference in mass defects in both cases (when relativistic and
classical masses of neutrons are considered) is 0.0064317u. So energy predicted is over
estimated by 3.45%, if relativistic mass of neutrons is neglected and mass of neutron is
regarded as same as rest mass. Such relativistic effects need to be studied for the other fission
fragments.
In this regard experiments involving Relativistic Radioactive Beams utilising
secondary beam facilities as available at GSI are useful [27]. In these experiments the
velocity and total kinetic energy of fission fragments are measured along with other
parameters. With such experiments or specifically improved experiments the relativistic mass
of the fission fragments can be calculated. In the present experiment the relativistic fragments
are Ba144 and Kr89. The exact measurements of relativistic masses are required in
calculations.
The various results when classical and relativistic masses are taken in
account in calculation of Q value are shown in Table I for single fission event.
Table I. Significance of relativistic mass of neutron in mathematical calculations.
Sr
Velocity
Mass (u)
%
age Energy
Difference
No
difference emitted
in energies
.
in
(MeV)
(MeV)
mass(u)
1
2
Classical
1.008664915
2185m/s
6u
Relativisti
1.010808793
c
u
1.954×107
m/s
%age
differenc
e
166.72MeV NA
NA
0.2125
----
160.73MeV 5.99
3.45
118
4.5 Conclusions.
The discussion can be concluded in the followings way.
(i) The variation of mass with velocity is well known and it is experimentally established
fact when velocity of body is comparable to that of light. In nuclear fission there are two
types of neutrons.
Firstly reactant neutrons which have energy 0.025MeV (or velocity v=2185m/s), it is in
classical limits hence mass of neutron is taken as classical mass 1.0086649156u.
Secondly the energy of secondary neutrons which are emitted in fission and have energy is
2MeV (1.954×107 m/s) which is relativistic region. Thus relativistic mass must be
1.010808793u.
(ii) But mass of secondary neutron (relativistic) is regarded as same as rest mass i.e.
1.0086649156u. In the existing literature masses of slow and fast neutrons (having energy
0.025MeV or 2185m/s, and 2MeV or 1.954×107 m/s or ~ 7% speed of light) are regarded as
rest masses (1.0086649156u) in calculations. According to eq.(5.24), the relativistic mass
must be 1.010808793u. This is point of contention here.
Thus Q-value of reaction is
166.72MeV i.e. eq.(5.33).
If the mass of reactants neutrons (0.025MeV or 2185m/s ) is regarded as
classical mass i.e. 1.0086649156u and mass of product (relativistic) neutron (2MeV or
1.954×107 m/s) equal to 1.010808793u. Then Q-value of reaction is 160.73MeV as in
eq.(5.19). Obviously due to relativistic effect mass of neutron becomes heavier, and mass
defect becomes smaller i.e. 0.1725594 u. Thus energy emitted in reaction is 5.99 MeV or
3.45 % less if realistic values of parameters are used or considered.
(iii) According to relativistic variation of mass, if the velocity of particle is in relativistic
region then mass is given by eq.(5.36). This effect is not used in this case even velocity
(2MeV or 1.954×107 m/s or ~ 7% speed of light) is in relativistic region.
(vi) Segre [21] has pointed out that energy emitted in fission of U235 is 175.7MeV , whereas
other scientists give different values for the same. The precise, specific and independent
experimental measurements of energy emitted in single fission event will be helpful in this
119
regard. There are many fissionable nuclei, so experiments should be conducted individually
and specifically.
(vii) The scientists of OPERA group at CERN, has observed the faster than light neutrinos
[28] , but abandoned due to faulty experimental set up. Similar results were obtained at Fermi
Laboratory in MINOS experiments, which are being conducted again at the same laboratory
in the NOVA experiments. The basic postulate of constancy of speed of light is being tested.
Hence this theoretical analysis is meaningful and logical.
ACKNOWLEDGEMENTS
Author is highly indebted to Dr T Ramasami and Stephen Crothers for encouragement and
Anjana Sharma for critical discussions.
References
[1] Einstein, A Ann. der Phys. 18
639-641 (1905).
[2] Sharma, A American Journal of Scientific Research Issue 12 , pp.67-112 (2010)
[3] Sharma, A Einstein’s E=mc2 Generalized Raider Publishing International (2007) New York , USA
[4] Sharma, A Progress in
Physics,
Vol. 3
pp. 76-83 (2008)
[5] Sharma, A. Physics Essays, Vol. 17, pp.195–222 (2004)
[6]
Sharma, A. Concepts of Physics, Vol. III, No. 4, pp.345–373 (2006),
http://merlin.fic.uni.lodz.pl/concepts/2006_4/2006_4_351.pdf.
[7] Arthur Beiser, Concepts of Modern Physics, 4th edition (McGraw-Hill International
Edition, New York, 1987), pp. 25, 27, 420, 428 (1987),
[8]
E.G. Bakhoum, Physics Essays 15 (1) 2002 (Preprint archive: physics/0206061)
[9]
E.G. Bakhoum, Physics Essays 15 (4) 2002
[10]
Hambsch, F.J. et al. Nucl. Phys.A, 491,p.56 (1989)
[11]
Thiereus, H. et al., Phys. Rev. C, 23 P 2104 (1981)
[12]
Palano, A. et al., Phys.Rev.Lett. 90 (2003) 242001
[13] G.L. Greene,
E. G. Kessler, and R. D. Deslattes, , Phys. Rev. Lett. 56 (1986) 819
120
Chupp, W.R. Raymond, and J. Walter, Phys. Rev. 121 (1961) 234
[15] E.G. Kessler, M.S. Dewey, R.D. Deslattes, A. Henins, H.G. Börner, M. Jentschel, C.
Doll, and H. Lehmann, Phys. Lett. A 255, (1999) 221.
[14] E.L.
[16] Sharma, A International Journal of Nuclear Science and Technology Vo. 3 No 4 pp. 370-77 (2007)
[17]
Chadwick
J.
Letters
to
the
editor:
Possible
existence
of
a
neutron
Nature vol. 129 p.312 (1932).
[18] Hahn O. and Strassmann F. On the detection and characteristics of the alkaline earth
metals formed by irradiation of uranium with neutrons, Naturwissenschaften vol. 27.-P. 1115 (1939.)
[19] Meitner L. and Frisch O.R. Disintegration of Uranium by Neutrons: a New Type of
Nuclear Reaction Nature, vol. 143.-P.239–240. (1939).
20 Frisch O.R., Physical Evidence for the Division of Heavy Nuclei under Neutron
Bombardment Nature, vol.143.-P.276. (1939).
[21] Segre, E. Nuclei and Particle. 2nd Edition (Reading MA, W.A. Benjamin) p.591 1977
22]. Lorentz H. A., Proc. Roy.Soc. Amst.vol. 1.-P. 427-442, 1899.
[23] Lorentz H A., Proc. Roy.Soc. Amst. .vol. 6.P. 809-831( 1904).
[24] Kaufmann W., Phys. Z. vol.- 4. P. 55, (1903).
[25] Bucherer , A.H., Phys. Ann. Phys.- Vol.28.-P.513 (1909).
[26] Einstein, A., 1948 Letter to Lincoln Barnett, quoted in `The concept of mass' by Lev
Okum Physics Today (June 1989).
[27] K. -H. Schmidt, S. Steinhäuser, C. Böckstiegel, A. Grewe, A. Heinz , A. R. Junghans, J.
Benlliure, H.-G. Clerc, M. de Jong, J. Müller , M. Pfützner and B. Voss, Nuclear Physics
A Vol. 665 pp. 221-267, (2000).
[28] http://arxiv.org/abs/1109.4897
[29] Serber, R The Los Alamos Primer (U.S. Govt. first published as LA1, April 1943),
declassified 1965 , annotated book , 1992. also R . Serber (editor), The Los Alamos Primer
pp. 38 (Univ. of California Press,1992)
121
Beyond Einstein and E =mc2
Science is infinite
Ajay Sharma
Chapter 6
Rest Mass Energy Erme = Mrmec2 Is Derived From Non- Existent
Equation.
First Glimpse
 It is debated that can equation (9) be interpreted under the condition equation (1) is
zero. Can equation (10) be NON-ZERO such as Erme = Mrme c2, when equation (1) is
zero and intermediate equations are non-existent ?

It is basic principle of the scientific analysis is that an equation is derived under
certain conditions and interpreted under those conditions only. Also if first equation is
zero then final results cannot be non-zero. It is against conservation laws.

In derivation of Einstein’s Rest Mass Energy Equation, the very first equation ( dW
=dK=Fdx ) is based upon the fact that body moves with classical velocity.

Then it is assumed that body moves with relativistic velocity and mass of body
increases to relativistic velocity. Other calculations are done under these conditions.
Thus relativistic form of kinetic energy i.e. K = ( Mmotion − Mrest ) c2 is obtained.

Then equation of relativistic kinetic energy, K = ( Mmotion − Mrest ) c2 is written in
arbitrary way.

Further in penultimate equation, condition is applied that, let body is at rest (v=0,
dx =0 ) i.e. dW =dK=Fdx=0. Thus first equation is zero, and following other
equations are NON-EXISTENT. Then from NON-EXISTENT equation
122
Erme = Mrme c2 is obtained. How non-zero and real results are obtained from NONEXISTENT equation?

But in this case first equation is zero, other equations are non-existent and final
equation is non-zero i.e. Erme = Mrme c2 . It is like getting OUT PUT from INPUT,
hence not justified. It is unrealistic and unphysical result.
1.0 Introduction
Einstein mathematically deduced output without input, which is not justified.
Einstein derived the rest mass energy equation
Erest =Mrest c2
from relativistic kinetic energy equation , KE = Mmotion –Mrestc2
when it is written in typical form, under the condition when body is at rest (v = 0 , dx = 0).
When body is at rest (v = 0 , dx = 0), then first equation of KE is zero, the other equations
are non-existent and no conclusions can be drawn from non-existent equations.
The determination of rest mass energy is inconsistent under this
condition. The reason is that under this condition, the very first equation
dK = dW = Fdx
which leads to relativistic form of kinetic energy VANISHES, and hence other equations are
NON-EXISTENT but final result is NON-ZERO. Thus it is debated that whether an equation
can be interpreted to get non-zero results at final stage under the condition when first
equation vanishes and intermediate equations are non-existent. It is like getting output
without input, which is not justified by conservation laws.
It can be understood in general example also. Consider a building is
constructed and it has 10 floors. It is full of residents. All of sudden first floor of the building
is demolished, and it is not possible that remaining 9 floors float in air with residents. But
analogously it is possible with Einstein’s derivation of rest mass energy i.e. the remaining 9
floors of the building can float in air. Thus floating building in air is possible. As this
derivation implies that when first equation is zero, rest of the equations are non-existent, even
123
then from penultimate equation Erest =Mrest c2 can be obtained.
2.0 The relativistic form of kinetic energy, KErel = (Mmotion - Mrest ) c2.
Einstein has derived five equations relating to mass (rest mass, relativistic mass and mass
annihilated or mass created) and energy e.g. mass- energy inter conversion equation E =
mc2, mass-light energy inter conversion equation L = mc2 , relativistic energy ( Emotion
=Mmotionc2 ) and Rest Mass Energy Erest = Mrestc2. L = mc2 is based upon fact that when
mass (m) is annihilated then light energy L is emitted .
The author [1-5] has critically studied the derivation of Einstein’s mass energy
inter-conversion equation and the study has lead to new findings. Here in discussion origin of
the Rest Mass Energy is studied. Einstein [6] initially derived equation for relativistic form of
kinetic energy and later interpreted the Rest Mass Energy [7-10 ] under condition when body
is at rest (v = 0 , dx = 0) , purposely Einstein wrote equation of relativistic kinetic energy in
special way. In normal form of relativistic kinetic energy even applying the condition (v = 0 ,
dx = 0), the rest mass energy is not obtained.
Calculation of relativistic form of kinetic energy
According to Work–Kinetic Energy equation we have
dK = dW = Fdx
(6.1)
where dK, dW are infinitesimally small amounts of kinetic energy and work done, when
force F displaces the body through distance dx.
dK = dW = Fdx =
d
M motionvdx
dt
(6.2)
dM motion 
dv

v
dx
= M motion
dt
dt 

= [ Mmotion dv + v dMmotion ]v
= [ Mmotion vdv + v2 dMmotion ]
[ v = dx/dt ]
(6.3)
124
The relativistic mass is
Mmotion =
M rest
(6.4)
v2
1 2
c
Eq.(6.4) gives appreciable results when v is comparable with c. Squaring eq.(6.4) we get
Or M2motion c2 – M2motion v2 = c2 Mrest
Differentiating w.r.t . time
2
2
dM 2 motion d M motionv
or c

dt
dt
2
d  c 2 M rest
Here
dt
d  c 2 M rest

dt
 involves differentiation

(6.5)
of two constant quantities i.e. c2 and Mrest ,
hence result is zero. Now eq.(6.5) can be further written as
c2
dM 2 motion d  M 2 motionv 2

dt
dt

dM motion
dt
dM motion 2
dv
 2M motion
v  M 2 motion 2v
dt
dt
c 2 2M motion
c 2 2M motiondM motion  2M motionv 2 dM motion  M 2 motion 2vdv
(6.6)
Dividing both sides of eq.(6.6) by 2Mmotion,
c2 dMmotion = v2 dMmotion + Mmotion vdv
(6.7)
Now eq.(6.3) with help of eq.(6.7) can be written as
dK = dW = c2 dMmotion
(6.8)
125
.
∫dK = ∫dW = c2 ∫dMmotion
(6.9)
K = W= c2 (Mmotion– Mrest)
Or K = W = c2 ( Mmotion − Mrest ) = c2 [
M rest
v2
1 2
c
− Mrest ]
(6.10)
Or K = W = Mmotion c2 − Mrest c2
(6.11)
Applying binomial theorem(v<<c) , the classical form of kinetic energy and work done is
obtained i.e.
K = W = Mrest
v2
3v 4
c [(1+ 2 + 4 +……………-1)
2c
8c
2
v2
As velocity is in classical region so v<<c , hence term
is retained and higher orders are
2c 2
neglected . Thus
K =W =
M restv 2
2
(6.12)
If v =1m/s then
K = W = Mrest c2 [(1+1/ 2. 9×1016 + 3 / 8×81×10-32 +……………-1.)
K = W = Mrest c2 [ 1+ 5.55  10 18 +4.629 x10-35
-1 ]
K = W = Mrest c2 5.55×10-18
If body is at rest v =0 ( dx = 0 ) then
K = W = Mrest c2 [ 1 +0 + 0 -1] = 0
(6.13)
Thus from equation of relativistic kinetic energy, classical form of kinetic energy can be
obtained. If body is at rest ( v=0 , dx=0 ), then both the equation i.e.
dK = dW = Fdx
(6.1)
126
and
K = W = Mrest
v2
3v 4
c [(1+ 2 + 4 +……………-1)
2c
8c
2
kinetic energy is zero.
3.0 Interpretation of eq.(6.11) in terms of kinetic energy and work
The eq.(6.11) i.e. K = W = Mmotionc2 − Mrest c2 is derived under some conditions.
(i) Eq.(6.11) is obtained if the force displaces the body in its own direction.
(ii) Eq.(6.11) is obtained when velocity of body is comparable to speed of light i.e.
v ~ c, only then Eq.(6.11) is derivable or gives significant results.
(iii) The motion must be accelerated; if velocity is uniform then acceleration is
zero. The condition of the derivation is body should move with accelerated
motion.
(iii) In case considerable amount of force acts on body and body does not move (
e.g. subtle amount of force acts on body of mass 10kg ), then eq.(6.11) is not
derivable, as eq.(6.1) is zero (dx=0). For simplicity
dK = dW = Fdx = 0
Now eq.(6.11) can be physically interpreted as below.
The kinetic energy attained by a body due to the influence of external force in accelerated
motion when a body moves with velocity v, which is comparable to c
= c2 ( Mmotion − Mrest ) = c2 [
M rest
v2
1 2
c
− Mrest]
(6.14)
= [Increase in mass of body when due to application of external force in accelerated motion,
when velocity v is comparable to c] c2
(6.15)
Or
The kinetic energy attained by body due to influence of external force in accelerated motion
when velocity v of body is comparable to c +Mrest c2 = Mmotionc2
(6.16 )
127
Further, Einstein termed Mmotionc2 as relativistic kinetic
energy [ 20, 41-43, 2] and wrote,
Emotion = KE + Mrestc2 = Mmotionc2
(6.17)
The eq.(6.17) has two signs of equality, as Emotion is additional term imposed or introduced
by Einstein.
In terms of work
The work done by body due to influence of external force in accelerated motion when
velocity v is comparable to c, the speed of light
= c2 ( Mmotion − Mrest ) = c2 [
M rest
1
2
− Mrest ]
(6.18)
v
c2
Similarly
Work Done + Mrestc2 = Mmotionc2 = Relativistic work done
(6.19)
The eq.(6.17) and eq.(6.19) are exactly similar. Both have identical physical interpretation.
These are relativistic equations i.e. exist when v~c, as only under this condition relativistic
increase in mass is observable.
Rest Mass Energy E = Mrest c2 is not obtained under valid mathematical conditions. Einstein
has derived it in 1907.
Classical form of Kinetic Energy i.e. eq.(6.11).
The relativistic form of KE reduces to classical form of kinetic energy if v<<c and binomial
theorem is applied.
K = Mrest c2 [(1+
v2
3v 4
+
+……………-1)
2c 2 8c 4
(6.12)
Neglecting fourth and higher orders
K=
M restv 2
2
If body is at rest ( v = 0 , dx = 0 )
KE =0
K = W=0
v=0
Momentum =0
(6.12)
128
Einstein obtained rest mass energy Erme under the condition when v =0 i.e..
Erest = Mrest c2
(6.20)
3.2 Rest mass energy not obtained from eq.(10)
Also we have equation for relativistic form of kinetic energy (when v~c ) or work done as
eq.(6.10)
W = K = c2 (Mmotion − Mrest )
(6.10)
Applying the condition that body is at rest, i.e. v = 0, dx = 0, dW = dK = 0,
0 = c2 (Mrest − Mrest )
Or Mrest c2 = Mrest c2
Or 1 =1
(6.21)
2
which is true. Nevertheless, result in no case is rest mass energy (Erest = Mrestc ) in any way
as obtained by Einstein under this condition i.e. v = 0, dx = 0.
3.3 Rest mass energy is not obtained if eq.(6.10) is re-arranged.
The eq.(6.10) can be written as
KE + Mrest c2 = Mmotion c2
(6.17)
When a body is at rest i.e. v = 0, dx = 0, dW = dK = 0, then under this condition eq.(6.17)
becomes,
2
0 + Mrest c =
M rest c 2
1
0
c2
= Mrest c2
Mrest c2 = Mrest c2
Or 1 = 1
(6.21)
which is true. Hence in no way the Rest Mass Energy equation (Erest = Mrestc2) is obtained.
Einstein obtained equation for rest mass energy by arbitrary method. Thus rest mass energy
is only obtained if eq.(6.14) is written in arbitrary way as discussed below. However all
scientific deductions must be based upon logic not on arbitrariness.
4.0 The origin of rest mass energy lies in arbitrariness
129
In 1907, Einstein [7-10] interpreted the eq.(6.17) i.e.
Emotion = KE + Mrestc2 = Mmotionc2
(6.17)
as Rest Mass Energy. Under this condition if body is at rest i.e. v = 0, dx = 0. Now the
eq.(6.17) becomes
Emotion ( when v = 0, dx = 0) = 0 + Mrestc2 = Mrestc2
Then Einstein interpreted or coined that
Emotion ( when v = 0, dx = 0) = Erme
(However when body is at rest, it does not possess any energy due to its motion. So it is
hypothetical to associate energy due to motion with this.)
Hence above equation becomes
Erme = Mrestc2 = Mrestc2
or Erme = Mrestc2
(6.22)
But conceptually and mathematically it is not justified, as when body is at rest i.e. (v = 0, dx
=0) then the very first equation i.e.
dK = dW = Fdx
vanishes or RHS becomes zero.
So there is situation of mathematical void and because rest of the equations are non-existent.
Thus the origin of Rest Mass Energy lies in the equation which itself vanishes, if this
condition (v = 0, dx = 0) is applied. Hence Einstein's deduction is not justified. Also in this
case eq.(6.12) is zero i.e.
K = W = Mrest c2 [ 1 +0 + 0 -1] = 0
(6.13)
(ii) Einstein wrote eq.(6.10-6.11) in arbitrary way to get Rest Mass Energy :
Einstein wrote eq.(6.10) as eq.(6.17) in such way that there are TWO
EQUALITY SIGNS (=) that appear in one equation. Only this form of equation
gives Erme = Mrestc2 under this condition (v = 0 , dx = 0 ).
According to Einstein,
Mmotion c2 = Total Energy due to motion when v~c or Emotion
The eq.(6.23) is also known as Relativistic energy. Thus eq ( 6.17 ) becomes
KE + Mrest c2 = Mmotion c2
= Total Energy due to motion when v~c (6.24)
In eq.(6.10) there is only one sign of equality.
(6.23)
130
When a body is at rest, i.e. v = 0, dx = 0, dW = dK = 0, then under this condition eq.(6.17)
becomes
0 +Mrest c2 = Mrestc2 = Total energy due to motion (v = 0, dx = 0)
(6.25)
Einstein wrote
Total energy ( Mmotion c2 ) due to motion ( when v = 0, dx=0 ) = Erest
(6.26)
(However when body is at rest, it does not possess any energy due to its motion. So it is
hypothetical to associate energy due to motion with this.)
or 0 +Mrest c2 = Mrestc2 = Total energy due to motion when v ~c (v = 0, dx = 0 ) = Erest
Thus,
Erest = Mrestc2 = Mrest c2
Hence in this case when
(a) Velocity v = 0, dx = 0
(b) The momentum of body is zero
(c) Classical kinetic energy is zero
(d) Eq.(6.10) is zero i.e.
K = W = Mrest c2 − Mrest c2 = 0
(6.22)
2
It is not justified to draw or interpret non-zero results (Erest = Mrestc ) at final stage of
derivation when very first equation is zero. It is like getting output without input. Under this
condition first equation is zero and other equations are non-existent, and final equation gives
non-zero results. It is never justified by any means. Thus no conclusions should be drawn
from non-existent equation as in this case. Thus Einstein's conclusion regarding the Rest
Mass Energy from non-existent equation is not scientifically consistent.
Einstein wrote equation, W +Mrest c2 = Mmotion c2 in special way to obtained rest mass
energy , which would be called rest mass work. It will not have any meaning. Thus above
interpretation is again not justified.
If an equation is obtained just after mathematical manipulations,
which is not justified. Scientific logic is the most important. Initially Einstein wrote
equations for relativistic energy, and interpreted results when body is at rest. If results are to
be interpreted under the condition body is at rest, then Einstein should have started from
classical equations. By choosing the origin from relativistic equations, Einstein ensured that
term c2 comes in picture. The hit and trial method should not be used to obtain equations.
The various results are shown in Table I.
131
Table I : The various values of magnitude of rest mass energy Erest = Mrest c2, as
obtained from various equations.
Sr
Equation
1
Condition ,
Result
v ≠ 0, dx ≠ 0
dW≠ 0
v ≠ 0, dx ≠ 0
W≠ 0
v ≠ 0, dx ≠ 0
W≠ 0
v ≠ 0, dx ≠ 0
K≠ 0
v = 0, dx = 0
Erest = Mrest c2
dW = dK =F.dx
2
W=K= [Mmotion -Mrest]c2
3
W +Mrest c2 = Mmotion c2
4
K = W = Mrest
v2
c [(1+ 2
2c
2
3v 4
+ 4 +……………-1)
8c
5
Emotion = W +Mrest c2 = Mmotion
c2
if Emotion ( when
v=0 , dx=0 ) = Erest
5.0 Einstein put forth five types of energies
Einstein derived equations relating to various types of masses i.e. rest mass (Mrest),
relativistic mass (Mmotion), mass annihilated (Δm ) and mass created (Δm) to various types of
energies e.g.
ΔL = Δmc2,
132
Δ E = Δmc2,
KErel = (Mmotion – Mrest)c2 ,
Emotion = Mmotionc2
and Erest = Mrest c2
In addition there are more equations involving rest mass and energy .
KE = Mrest v2 /2
PE = Mrest gh
Now the five energy equations were derived by Einstein are ΔL = Δmc2, Δ E = Δmc2, KErel =
(Mmotion – Mrest)c2 , Erest = Mmotionc2 and Erest = Mrest c2 appear to be similar as have same
forms, units and dimensions but conceptually are entirely different. Also the dimensions and
units of equations of PE and KE are the same.
There is similarity between Erme=Mrest c2 and ∆E=∆mc2 that both equations have inconsistent
origin. Erme=Mrest c2 is derived from non-existent equation and
∆E=∆mc2 speculated not
derived. ΔL = Δmc2 implies when light energy ΔL is emitted by body its mass decreases by
Δm. Thus Erme=Mrest c2 and ∆E=∆mc2 .
5.1 Erest = Mmotionc2 does not imply mass Mrest is converted to energy.
Erest = Mmotionc2 can not regarded as mass annihilated to energy.
We have two more basic equations relating with mass and energy .
M restv 2
KE =
2
PE = Mrestgh
If it can be interpreted that in Erest = Mmotionc2 , Mrest is regarded as mass annihilated to
M restv 2
energy then in KE =
2
and PE = Mrest gh, the mass Mrest can also be regarded as
mass converted to energy. But it is not justified then corresponding to same Mrest , the
different energies will be emitted. Hence only in equations ΔL = Δmc2 [11 ] and ΔE = Δmc2,
Δm can be regarded as mass converted to energy or vice-versa. In the derivation all the
variables are clearly defined and Δm represents the change in mass.
133
M restv 2
If simply the dimensions of equations (ΔL = Δmc , KE =
and
2
2
PE = Mrestgh ) are same then they may not necessarily represent the same phenomena. To
interpret equation characteristic conditions, on which derivation is based, has to be taken in
account. An equation can only be interpreted under the conditions it is derived. The
interpretation of equation depends upon the inherent conditions under which the equation is
defined or derived. There is no special reason that Mrest is only regarded as mass annihilated
in equation
M restv 2
Erest = Mmotionc and Mrest is not regarded as mass annihilated in equations KE =
2
2
and PE = Mrestgh. If there is some preferred reason then it can be discussed logically.
5.2 How Mass Is Annihilated To Energy ?
The annihilation of mass to energy can be understood in the following way. Consider the
fission of uranium by neutrons.
235
92U
+ 0n1 →
141
56Ba
+
92
36Kr
+ 3 0n1 + Q
The Q value of the above reaction can be determined as (E =mc2).
Mass of reactants = (235.0439299 +1.0086649156) u = 236.0525948u
(6. 27 )
Mass of products = (143.922 953 + 88.917 630 +3.02599473) u =235.8665777u (6.28 )
Mass annihilated = m = 0.186017115u
Energy released = 0.186017115 × 931.5MeV = 173.274MeV
(6.29 )
(6.30 )
In equation ΔL = Δmc2 initial and final masses are taken in account when body emits light
energy. Whereas in the derivation of Erest = Mmotionc2, there is no such term. Hence equation
of inter conversion of mass to energy is ΔL = Δmc2 .
7. Logical and alternate way to obtain rest mass energy
The origin of rest mass energy can also be understood from Einstein’s derivation of mass
energy inter-conversion equation. Einstein has derived mass energy inter conversion equation
[14] as
E = ( M b  M a ) c 2 = mc 2
(6.31)
134
or Mass of body after emission ( M a ) = Mass of body before emission ( M b ) –
E
c2
(6.32)
If whole mass is annihilated ( Ma =0 ) i.e. no mass is left after emission , then
Mbc2 = E
(6.33)
In Einstein’s derivation Mb is mass before emission and body is regarded at rest [14] , thus E
=Mbc2 may be regarded as rest mass energy i.e. Erest = Mrest c2 . It is energy equivalent to rest
mass energy. It is logical deduction from Einstein’s this derivation. In Einstein’s this
derivation Erest = Mrest c2 is not obtained from non-existent equation as in previous
derivation, hence this derivation is correct.
Appendix 1
Some interesting conclusions can be drawn here on the basis of relativistic variation
in mass, length contraction and time dilation.
(i) Only one particle can attain speed equal to that of light
We have equation for relativistic variation of mass with velocity as
Mmotion =
M rest
v2
1 2
c
(6.4)
Further according to these deductions only one particle in the universe can attain a
velocity equal to c, as velocity becomes c then mass becomes infinity it will occupy infinite
space. Hence, no space will be left for other particle to attain infinite mass i.e. attaining speed
equal to c. If the mass becomes infinity, then no further expansion of space is possible. What
will happen if few particles attain speed equal to c simultaneously! However, it is a
hypothetical assumption only. Also in this regard discussion on the length contraction would
be interesting.
Thus when a particle of mass billion-billion-billion times smaller than mass of
electron, moves with speed equal to that of light, its mass becomes infinity. Even the mass of
the universe is finite. Thus, how such a huge mass has been created? The mass of the whole
universe is 1055 kg. Even by our calculations, God or nature has been able to put or pile just
1055 kg till date. So how mass will become infinite in fraction of second as predicted by
eq.(6.4) is anyone’s guess and speculation? Will it be scientific, non-scientific, humanly or
godly or ghostly phenomena?
135
The utility of eq.(6.4) is well known in a calculation of relativistic form of kinetic
energy. The relativistic form of kinetic energy reduces to classical form of kinetic energy, as
also relativistic mass reduces to classical mass under the conditions when velocity is very-2
less compared to speed of light.
Further let us consider theoretically that the velocity of body increases and becomes
equal to 1.01 times the speed of light i.e. v = 1.01c then v2 /c2 is 1.0201. Now the eq.(6.4)
become
Mmotion = Mrest / √ (1– 1.0201)
= Mrest √ (– 0.202) = imaginary mass
(6.31)
If the body moves with speed precisely equal to that of light i.e. v=c
Mmotion = Mrest / √ (1– 1) = 
(6.32)
Now the eqs (6.31–6.32) can be interpreted as below.
If any particle, say electron or even lighter than this i.e. 10-444 kg (or less) moves with speed
of light c, then its mass becomes infinity. If we extrapolate then particle of mass 10-4444444 or
less can attain velocity equal to c comparatively easily. Even the mass of the whole universe
is not infinite, as it is regarded as 1051 kg. In realistic terms infinite mass is too large, which
can never be assessed, measured and obtained? Therefore, there is a peculiar transition of
mass from infinite to imaginary magnitudes.
Should an imaginary quantity (which can be only imagined) be regarded as more than that of
infinity? The trends available form eq. (6.4) incline towards this. Is it logical? When body is
at rest (v=0) then according to eq. (6.4) the relativistic and classical masses are equal i.e.
Mmotion = Mrest. As the velocity of body increases then its mass increases. The increase in
mass assumes the significant dimensions if the velocity of body increases or enters in
relativistic limits. Thus, it is general trend of the eq. (6.4), as velocity of body increases then
mass increases.
Einstein [2] has discussed the cases if velocity of body is equal to c or more than c in
his June 1905 paper. When the velocity of a body approaches the velocity of light c, then
mass becomes infinite. Hence, when the velocity of body becomes more than c, then mass
becomes imaginary. Thus the trend of variation of mass with velocity as in eq.(6.4) indicates
136
that ‘imaginary mass’ must be greater than ‘infinite mass.’ However, the final conclusions
should not be drawn on the basis of trends from one equation only; there are many other
factors equally significant. The meaning of “imaginary quantity” is that which only exists in
imagination and “infinite quantity” is one, which can never be achieved.
(ii) Length contraction when body moves with speed of light. To explain the negative results
of Michelson Morley Experiment in 1889, the Irish physicist George Francis FitzGerald
explained that the part of a body that moves along the direction parallel to that of the Earth’s
motion becomes shorter i.e. length contracts. At that time, it was regarded as an adhoc
assumption. This result was further confirmed by Lorentz; as follows from Lorentz
Transformations. Mathematically we have
ℓmotion = ℓrest √ (1– v2/c2)
(3.5)
where ℓmotion is the length of an object observed by the moving observer, ℓrest is the length
measured when at rest, v is the velocity of the observer and c is the speed of light. When
body moves with speed of light then
ℓmotion = 0
(3.6)
It implies that length of the earth reduces to zero in one direction. But its mass is infinity.
(iii) Time Dilation. Under the condition cited the time does not pass. It becomes stationary.
Hence it implies when body moves with speed of light , its mass becomes zero, length
becomes zero in one direction and time does not pass and hence becomes stationary.
References
[1] Sharma, A American Journal of Scientific Research Issue 12 , pp.67-112 (2010)
[2] Sharma, A Einstein’s E=mc2 Generalized Raider Publishing International (2007) New
York , USA
[3] Sharma, A Progress in Physics,
Vol. 3
pp. 76-83 (2008)
[4] Sharma, A. Physics Essays, Vol. 17, pp.195–222 (2004)
[5]
Sharma, A. Concepts of Physics, Vol. III, No. 4, pp.345–373 (2006),
http://merlin.fic.uni.lodz.pl/concepts/2006_4/2006_4_351.pdf.
[6] A. Einstein, Annalen der Physik 17, 891-921 (1905).
137
[7]
Einstein, A
Jahr. Rad. Elektr. 4, 411 (1907).
[8] Robert Resnick, Introduction to Special Theory of Relativity (John Wiley and Sons, New
York, 1968), p. 120. (1968)
[9] A. Pais, Subtle Is the Lord (Oxford University Press, Oxford, 1983), p. 149 (1983)
[10] Arthur Beiser, Concepts of Modern Physics, 4th edition (McGraw-Hill International
Edition, New York, 1987), pp. 25, 27, 420, 428 (1987),
[11] Einstein, A Ann. der Phys. 18 639-641 (1905).
Beyond Einstein and E =mc2
Science is infinite
Ajay Sharma
Chapter 7
Frequently Asked Questions
Based on previous chapters
To understand the original derivation of ∆L=∆mc2 or ∆E=∆mc2 is quiet complex, further to
understand the conceptual and mathematical limitations of ∆L=∆mc2 or ∆E=∆mc2 is more
complex. Thus the phenomena can be better understood in specific question and answer form.
Part A
Arbitrary appearance of c2 in ∆L=∆mc2
(Q.1) Einstein is believed to have derived ∆E=∆mc2 in Sep. 1905 paper, but it is strange
that he neither wrote E nor ∆E=∆mc2 in the paper. Explain why?
Undoubtedly it is indicated that the perception of Einstein’s derivation of ∆E=∆mc2 is
dubious and confirm that Einstein speculated ∆E=∆mc2 . The equation does not arise in the
138
derivation at all. However, Einstein derived light energy mass inter-conversion equation,
∆L=∆mc2. Then Einstein wrote
If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact
that the energy withdrawn from the body becomes energy of radiation evidently makes no
difference, so that we are led to the more general conclusion that
The mass of a body is a measure of its energy-content; if the energy changes by L, the mass
changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in
grammes.
From here Einstein arbitrarily concluded ∆E=∆mc2 , which is not justified there is
tremendous difference between light energy and every energy. It is not logical and
scientific at all.
Why did not Einstein write ∆E=∆mc2 in Sep. 1905 paper? This issue was raised by Fadner
in American Journal of Physics[1]. Apparently, Einstein was not certain about the content of
the paper which has title
Does The Inertia Of A Body Depend Upon Its Energy-Content?
Thus all aspects of Einstein’s Sep. 1905 paper are not completely understood.
(Q.2) Author has concluded that Einstein has arbitrarily brought c2 in picture in
∆L=∆mc2
Is it true? If not then how and why?
Explanation: Yes, it is true.
Einstein has brought c2 forcefully or mechanically or arbitrarily in picture taking only
specific values of variables in account in mathematical calculations. Einstein started from
relativistic equations, did the crucial calculations applying the classical conditions. So it is
manipulative to start from relativistic equation. It would have been better to start from
classical equation, if the results are to be drawn under classical conditions. Einstein started
139
the derivation of L = ∆mc2 from basic equation,
 v

1  c cos  

   
2
v
1 2
c
(7.1)
where  is light energy emitted by body in frame (x,y,z) and  * is light energy measured in
system (ξ, η, ζ ), and v is velocity with which the frame or system (ξ, η, ζ ) is moving. This
equation was given in Einstein’s June 1905 paper in Section 7 and is called Doppler principle
for any velocity whatever. But there is no specific derivation to the equation in paper. Also
there are no references in the paper so that its origin may be quantitatively understood. Then
this equation is used in derivation which is basically equation of conservation of energy.
Einstein derived L = ∆mc2 from this equation under special conditions and speculated E =
∆mc2 under all circumstances. Thus we find that E = ∆mc2 is speculated from L = ∆mc2
which is based upon eq.(2.2) and eq.(2.2) is not derived as in Einstein’s June 1905 paper. It
is really a strange situation about origin of E=∆mc2 and from equations it is derived.
Obviously many possibilities exist.
After mathematical treatment based upon eq.( 7.1), Einstein has considered the classical
conditions of velocity i.e. velocity is far less than c ( v<<c). In Sep. 1905 derivation Einstein
derived equation


v2
v4

K 0 – K1 = L 1  2  3 4  .....................  1
8c
 2c

(7.2)
where K0 is KE before emission, K1 is kinetic energy after emission , v is velocity of the
measuring system and c is speed of light. Further, Einstein quoted
Neglecting magnitudes of fourth
K 0 – K1= L
v4
v6 v8
and
higher
,
……. orders, we may place.
c4
c6 c8
v2
+……..higher powers which are neglected.
2c 2
M bv2 M av2
v2
–
= L 2
2
2
2c
or L = ( M b  M a ) c 2 = mc 2
(7.3)
(7.4)
(7.5)
140
(i) Now ∆L=∆mc2 is obtained if term v2/2c2 is retained (classical region of velocity).
(ii) If term v2/2c2 is neglected (classical conditions).
If v =1cm , then v2/2c2 = 5.55×10-22 it implies that velocity is in classical region but very-2
small, hence can be neglected compared to unity. The result is
M bv2 M av2
–
=0
2
2
ma (mass before emission) = mb (mass after emission)
Thus c2 appears in Einstein’s equation under particular conditions. This equation L = ∆mc2 is
not derivable under relativistic conditions.
(iii) If the measuring system is at rest (v=0), then Einstein’s derivation L = ∆mc2 is not
applicable. v can also zero if system (x,y,z) and system (ξ, η, ζ ) move with same velocity.
However in this case (when v =0) experimentally when light energy is emitted mass decreases. It is
serious limitation of Einstein’s derivation.
When the measuring system (ξ, η, ζ ) is at rest v = 0 then
 * =
(7.6)
Ho = H1 +L/2 +L/2
(7.7)
Eo = E1 + L
(7.8)
(Ho – Eo) – (H1 –E1) = 0
(7.9)
As body is at rest and measuring system (ξ, η, ζ ) is also at rest, then (Ho – Eo) or (H1 –E1) cannot
be interpreted as kinetic energy. Hence Einstein’s derivation is not applicable. Practically, there are
numerous cases when light energy is emitted by body and measuring system remain at rest( v=0).
Practical situation: A luminous body is at rest and emitting light energy.
Theoretical prediction: Einstein’s derivation predicts decrease in mass is not possible in this
case. Or Einstein’s derivation becomes invalid in this case.
Experimental situation: Actually luminous body emits light energy and its mass decreases.
But this decrease in mass cannot be measured by Einstein’s derivation.
Conclusions Thus Einstein’s derivation is not applicable under these conditions, however
mass is decreasing when light energy is being emitted. It is serious limitation of the
derivation as it becomes invalid. But experimentally the derivation is valid.
Part B
Einstein’s derivation and conditions of the derivation
141
(Q.3) Author has concluded that Einstein’s Sep. 1905 paper involve many parameters
and Einstein has taken special values of parameters to derive ∆L=∆mc2. Thus Einstein’s
mathematical derivation of ∆L=∆mc2 is true under SUPER SPECIAL or HAND
PICKED conditions only.
Is it correct? If not then how and why?
Explanation: Yes, it is correct.
Einstein’s derivation is true under special conditions only.
In the derivation of E= mc2 Einstein has considered a body which has the rarest existence
or it is exceptionally difficult to fabricate in actual practice. It is basically a thought
experiment which exists only in imagination not in reality. The mathematical derivation is
made for general cases not for specific one’s. In this thought experiment there are many
variables with infinite number of values. But Einstein has taken just few hand picked values
of parameters.
Einstein’s Sep. 1905 derivation [2] of L = mc2 is true under super special conditions or
handpicked conditions only. For such an equation of paramount significance the derivation must be
completely general. From the general derivation some special cases must follow. It is basic principle
of the mathematical derivation. It is justified below. In the derivation of L = mc2 there are FOUR
variables e.g.
(a) Number of waves emitted by body,
(b) l magnitude of light energy by body,
(c) Angle  at which light energy is emitted
(d) Uniform velocity (relative velocity), v.
The fast neutrons are slowed down and called thermal neutron thus their velocities are not necessarily
uniform as can be variable while they cause fission of other nuclei. Thus Einstein’s assumptions are
contradicted by experiments.
Genuine cases neglected in Einstein’s derivation
Einstein has taken super special or handpicked values of parameters. Thus for
complete analysis the derivation can be repeated with all possible values of parameters. In all cases
the law of conservation of momentum is obeyed.
(i) The body can emit large number of light waves but Einstein has taken only TWO light waves
emitted by luminous body.
Why one or n light energy waves are neglected?
142
(ii) The energy of two emitted light waves may have different magnitudes but Einstein has taken two
light waves of EQUAL magnitudes (0.5L each).
Why are other magnitudes (0.500001L and 0.499999L) neglected by Einstein?
(iii) Body may emit large number of light waves of different magnitudes of energy making different
angles (other than 0º and 180º as assumed by Einstein).
Why other angles (such as 0º and 180.001º, 0.9999 º and 180º etc.) are neglected by Einstein?
Thus body needs to be specially fabricated; other forms of energy such as invisible energy are not
taken in account. Further body should emit light energy only, not other forms of energy.
(iv) Einstein has taken velocity in classical region (v<<c and applied binomial theorem at the end) and
has not at all used velocity in relativistic region. If velocity is regarded as in relativistic region (v is
comparable with c), then equation for relativistic variation of mass with velocity i.e.
Mrel =
M rest
v2
1 2
c
(7.10)
Thus it is obvious that Einstein’s derivation is valid only under handpicked conditions.
(Q.4) It is confirmed that Einstein had speculated ∆E=∆mc2 from ∆L=∆mc2
without mathematical derivation.
Is it correct? If not then how and why?
Explanation. Yes, it is completely true.
Einstein derived ∆L = ∆mc2 light energy mass inter-conversion equation, using equations.
 v

1  c cos  

   
2
v
1 2
c
where  is light energy emitted by body in frame (x,y,z) and  * is light energy measured in
system (ξ, η, ζ ), and v is velocity with which the frame or system (ξ, η, ζ ) is moving. This
equation was given in Einstein’s June 1905 paper in Section 7 and is called Doppler principle
for any velocity whatever. But there is no specific derivation to the equation in paper. Also
there are no references in the paper so that its origin may be quantitatively understood. Then
this equation is used in derivation which is basically equation of conservation of energy.
Einstein derived L = ∆mc2 from this equation under special conditions and speculated E =
∆mc2 under all circumstances. Thus we find that E = ∆mc2 is speculated from L = ∆mc2
143
which is based upon eq.(2.2) and eq.(2.2) is not derived as in Einstein’s June 1905 paper. It
is really a strange situation about origin of E=∆mc2 and from equations it is derived.
Obviously many possibilities exist.
But Einstein speculated the applicability of equation for all possible energies such as
(i) sound energy
In Doppler effect change in frequency of sound is estimated, not variation in mass. Thus eq.(7.1) is
not used. Likewise eq.(7.1) is not associated with any other energy. The speed of sound is 332m/s.
(ii) heat energy
There is no equation like eq.(7.1) which relates variation of heat energy. The similar is the case of
other types of energies.
(iii) chemical energy
(iv) nuclear energy (v) magnetic energy (vi) electrical energy
(vii) energy emitted in form of invisible radiations
(viii) attractive binding energy of nucleus
(xi)
energy emitted in cosmological and astrophysical phenomena
(x) energy emitted in volcanic reactions
(xi) energies co-existing in various forms etc. etc.
Thus replacing L( light energy ) by E (every energy) in ∆L=∆mc2, ∆E=∆mc2 is obtained. No
mathematical derivation for ∆E=∆mc2 is given, hence is speculated.
(Q. 5) Author has concluded that Einstein derived mass energy inter-conversion
equation for ‘light energy’ then generalized it for every energy (stating the mass of body
is measure of its energy content) without scientific logic.
Is it correct? If not then what is correct?
Explanation. Yes, it is correct. It is explained in question (4). It is well established that
Einstein never derived ∆E=∆mc2. Einstein arbitrarily replaced L by E in ∆L=∆mc2 to get
∆E=∆mc2. It is not valid operation scientifically. It is also indicated by Fadner [1] in
American Journal of Physics. Thus Einstein’s this derivation is one and only one derivation
in science of its type. If all parameters are taken in account then result is
∆L α ∆mc2
(Q.6) Author has concluded that Einstein’s Sep 1905 derivation also predicts that
decrease in mass is more or less than L/c2. Thus corresponding to mass ‘m’ , the
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numerous values of energy (L) are possible. Thus L  ∆mc2
Is it correct? If not then how and why ?
Explanation : Yes it is true.
In Einstein’s Sep. 1905 derivation, under different conditions the mathematically different
results is obtained. These equations give different results under different conditions.
(a) If the handpicked values of parameters ( two waves of equal energy are emitted in
opposite directions ) are considered in Einstein’s derivation, the result is ∆L=∆mc2 or
∆m=∆L/c2
(b) If the general typical values of the parameters are taken in account then
mc 2
121
or L  ∆mc2
L=
(7.11)
Similarly under typical conditions we get
mc 2
L=
 119
This equation implies that derivation is invalid in this case.
(7.12)
Thus many such equations are possible. Hence Einstein’s derivation does not give unique
value energy L corresponding to annihilation of mass ∆m. Moreover it is not derived by
proportionality method.
(Q.7) Einstein should have objected when applications of ∆L=∆mc2 (∆E=∆mc2) were
extended to nuclear binding energy as originally ∆L=∆mc2 was derived to light energy
mass inter conversion process.
Einstein’s objection would have been correct. If not then how and why?
Explanation; Yes, scientifically Einstein should have objected the same time. It would been
correct and scientific.
Einstein derived the equation, ∆L=∆mc2 for light energy mass inter-conversion.
Einstein used equation
 v

1  c cos  

   
v2
1 2
c
(7.1)
which is equation for relativistic variation of light energy.
But there is no specific derivation to the equation. Einstein gave this equation in his June
1905 paper in Section 7. Einstein derived L = ∆mc2 from this equation and speculated E =
∆mc2 . It is really a strange situation about origin of E=mc2. Obviously many possibilities
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exist here.
Thus derived equation
2
∆L=∆mc which relates decrease in mass with light energy emitted. Now the same equation
was applied to explain the binding energy of the nucleus with mass defect. Both are entirely
different. Eq.(7.1) in no way is associated with above phenomena i.e. binding energy.
So in view of scientific spirits Einstein should have objected the application of ∆L=∆mc2 to
nuclear binding (∆E=∆mc2) energy and mass defect (∆m).
Author has raised this issue with top class nuclear scientists and answer was that we are
‘reading’ and ‘teaching’ the concepts like this over 100 years. The period of 100 years is less
comparatively. For example for about 1,700 or 1,800 years it was preached that the sun
revolves around the earth, but now this perception is abandoned.
Part C
Velocity of body and observing system.
(Q.8) Einstein assumed that light emitting ( luminous) body remains at rest after
emission of light energy. Thus instead of general cases Einstein deduced results for
exceptionally-2 special case.
Is this deduction of the author true ? If wrong then how and why?
Explanation : Yes, author’s deduction is completely true.
Einstein’s derivation is true for special cases only. In the derivation of E=mc2 Einstein has
considered a body which has the rarest existence or it is exceptionally difficult to fabricate in
actual practice. It is basically a thought experiment which exists only in imagination not in
reality. The mathematical derivation is made for general cases not for specific one’s. It is
justified as below:
(a) Only special values of parameters are taken by Einstein as mentioned in Q.2.
(b) Einstein began derivation with relativistic variation of light energy
 v

1  c cos  

   
2
v
1 2
c
(7.1)
which is effective when velocity of measuring system is comparable with speed of light c.
But there is no specific derivation to the equation. Einstein gave this equation in his June
1905 paper in Section 7. Einstein derived L = ∆mc2 from this equation and speculated E =
∆mc2. It is really a strange situation about origin of E=mc2. Obviously many possibilities
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exist here
(b1) Einstein neglected the above fact , applying the Binomial Theorem in the derivation
and did all calculations when velocity is in classical region i.e. v <<c.
(b2) If classical conditions were to be considered, then why relativistic equation for variation
of light energy with velocity i.e. eq.(7.1) was considered . Initially Einstein should have
started with classical equations, then there would be no necessity of application of Binomial
Theorem.
(b3) Such manipulations only bring c2 in pictures. Many critics argue that
……..well energy is converted to mass or vice –versa. But what is necessity of conversion
constant 9×1016 ?
Einstein has brought constant 9×1016 in picture arbitrarily.This conversion factor comes in
picture in the derivation tailored by Einstein. If the results are drawn under classical
conditions, then derivation must initiate from classical equation not from relativistic equation.
In the existing literature it is not clear how eq.(7.1) is derived by Einstein. Thus Einstein’s
derivation is applicable under special conditions.
(Q.9) Einstein assumed that the observer system moves with uniform velocity, v. Thus
instead of general cases Einstein deduced results for exceptionally-2 special cases.
Is this deduction of the author true? If wrong, then how and why?
Explanation: Yes, it is true.
Thus Einstein himself has admitted or assumed that derivation is only valid for special
condition of the velocity. It is evident from the values of various parameters.
The measuring system in Einstein’s derivation can move with both variable velocity
and uniform velocity. Einstein has considered in his derivation the velocity of the measuring
system is uniform in classical region, thus neglecting numerous cases when velocity is
variable and non-relativistic. Thus it is again confirmed that Einstein’s derivation is true
under special conditions only.
Part D
Consistency with law of conservation of energy/matter.
(Q.10) Author has concluded that under general conditions (energy of light waves is
0.50001L and 0.49999L, wavelengths of each is 5000A) the recoil velocity of body is
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5×10-33 m/s. The law of conservation of momentum, is obeyed.
Is it correct? If not then what is correct value?
Explanation: It is correct. Einstein has considered that two light waves of equal energy ( L
and L ) are considered. If two light waves of different energies (energy of light waves is
0.50001L and 0.49999L, wavelengths of each is 5000A) are considered, even then laws of
conservation of energy are obeyed.
Law of conservation of momentum
Momentum of one system = Momentum of other system
In this case the body may tend to recoil, so the recoil velocity must be 5×10-33 m/s. In some
sense it is analogous to firing a bullet from the gun by a man. By definition and the velocity
5×10-33 m/s may be considered at rest.
(Q.11) Author has concluded that Einstein’s Sep. 1905 derivation also predicts that
‘when light energy is emitted then mass increases.’
It is contradiction of mass and energy.
Is it correct? If not then how and why?
Explanation: Yes, it is correct.
There are the numerous predictions from Einstein’s derivation of L=Δmc2 under general
conditions, which contradict the law of conservation of matter.
Conditions: These predictions follow from the derivation under general conditions of the
variables. These conditions are described in Q.3
Firstly let us discuss the special case considered by Einstein. The final equation is
L = ( Mb  Ma ) c2
Ma = Mb - L/c2
Mass after emission = Mass before emission + L/c2
Thus mass decreases when light energy is emitted. It is correctly stated by Einstein’s
derivation under special conditions.
Secondly consider the general conditions of the parameters considered by Einstein. In this
regard typical final equation is
M a = Mb +
133.3L 1.11L
– 17 = Mb + positive quantity
1017
10
(7.13)
Mass of luminous body increases when light energy is emitted by it.
It is contradiction of Law of Conservation of energy.
(i) How energy is emitted?
(ii) How mass increases?
(iii) How does double increase happen simultaneously?
Thus under general conditions contradictory results are obtained from Einstein’s derivation.
(Q.12) Author has deduced generalized mass energy equation ΔE =Ac2Δm by method of
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proportionality and integration. Many equations are derived by this method.
Is it correct? If not then what is correct?
Explanation : It is correct that author has derived the generalized equation, ΔE =Ac2Δm by
method of proportionality and integration. Many equations have been derived by this method
by other scientists and constants of proportionality are experimentally determined or
measured. So it is consistent with scientific derivations and methods.
Part E
Applications in cosmology
( Q.14) ∆E=∆mc2 is regarded as true in every phenomena. Should ∆E=∆mc2 be used to
explain the origin of mass of universe 1055 kg ?
Is it correct? If not then why?
Explanation: Yes it is correct.
∆E=∆mc2 can be used where inter-conversion of mass energy takes place. The observable
mass of universe is generally regarded equal to 1055kg. Thus mass has been created from
energy. Or how mass can be created? Now equation can be applied to calculate the
equivalent amount of energy (∆E) as ∆m and c are already given. It means that mass is
converted from
∆E=∆mc2 = 1055kg × 9×1016m2/s2 = 9×1071J
Thus the mass of the universe is created from energy 9×1071J. Hence there is no reason that
∆E=∆mc2 not applicable in this case. There is no other equation when converts other
quantities (like time, velocity, space) to mass.
(Q.15) Author has given various applications of the generalized equation in chemical
reactions, volcanic reactions, nuclear reactions, astrophysical and cosmological
reactions and various other phenomena.
Are these correct? If not then explain equation wise what is correct equation?
Explanation: Yes these are correct.
∆E=∆mc2 can be used where inter-conversion of mass energy takes place. In equation in
chemical reactions, volcanic reactions nuclear reactions, astrophysical and cosmological
reactions mass is converted to energy or vice-versa. ∆E=∆mc2 is conceptually applicable to
those cases where mass energy inter-conversion takes place. If ∆E=∆mc2 is not applicable
quantitatively, then generalized equation ΔE =Ac2Δm can be considered. Both the equations
have similar nature except magnitude of conversion factor (c2, Ac2 ) of energy emitted.
(Q.16) So far no pre-big bang origin of the universe is described; author has initiated it
for first time. Is it logical? If not then how and why?
Explanation: Yes, it is correct. Author’s approach is completely logical. Science is lighting
one lamp from the other. No perfect theory can be given in a single day.
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Science is an expanding body not a closed one. One problem can be viewed from many
angles. Further the concepts are more important than mathematics.
Currently the Big Bang Theory assumes that whole mass of universe (generally
accepted as 1055 kg ) was in form of a singular atom or primeval atom. Singular atom means,
the density of atom was tending to infinity and size tending to zero. Now many questions
arise.
(a) How mass equal to 1055 kg ( or actual mass of universe whatever it is ) was formed?
(b) If this mass was created from energy, then how energy is created?
(c) Any how if mass is created then how it is changed to primeval atom or singular atom
having atomic dimensions and infinitely large density? Which external agency created the
singular atom or primeval atom.
(d) How singular atom or primeval atom exploded?
These questions need valid and logical answers. These are not answered by existing theories.
Thus author’s attempt to find out pre-big bang origin of universe is original and useful.
Part F
Nuclear Reactors / Physics.
(Q.16) What is present and future of Higgs Boson?
Existing facts
English scientist Peter Higgs a predicted particle on the basis of calculations based on
Standard Model in 1964. This particles is known as Higgs Boson. The Bosons were coined in
respect of Indian physicist Dr S N Bose who worked with Einstein on the topic. These
particles are about 125 times heavier than proton (125GeV/c2 -127GeV/c2). These particles
are believed to be associated with hypothetical field. It has no spin, electric charge, or color
charge. It is also very unstable, decaying into other particles almost immediately.
On 4 July, 2012 scientists at CERN in Geneva declared that they had
discovered a new particle 'consistent' with the long-sought Higgs Boson, also known as the
'God particle.' In science no concrete conclusions can be drawn on the basis of one set of
observations, so such experiments are required to be repeated in future for final
confirmation.
On 23 September 2011, scientists have announced the neutrino moving with
speed more than that of light. But claim did not last long. In this experiments the neutrinos
were pushed through the earth, thus their speed was measured. Some scientific reasons based
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upon characteristics of neutrinos were given for pushing neutrinos through earth. Whereas
speed of light is measured when it passes through vacuum. So it is like to set two
competitors, in race one through water and other through air. The results would be more
interesting if the neutrinos are sent through vacuum pipes, as light travels in vacuum. In this
case there is no possibility that neutrino will interact with matter.
The Higgs Boson are theorized in understanding the origin of the universe.
(i) At the time of explosion of the singular atom in Big Bang massless particles scattered all
over the universe with speed of light.
(ii) It is believed that these massless particles interacted with Higgs field and attained mass.
Even then there are some unanswered questions about Higgs Boson.
Unanswered Questions
(a) When singular atom exploded in Big Bang then it is assumed that mass less particles
scattered in the universe. They interacted with Higgs field and attained mass. Now if all other
particles appeared massless then how Higgs Boson was heavier i.e. nearly 125 times mass of
proton. Why special status is given to Higgs particle? There is no valid reason. It is not
explained.
If other particles attain mass due to hypothetical field of Higgs Boson, then following
conclusion is obvious. Does Higgs Boson gets mass due to field of other particle may be
termed as Senior Higgs Boson?
(b) The law of conservation of mass and energy is the basic law in all mass energy interconversion process. If a massless particle attains mass through Higgs field, then from where
energy is created to impart mass (m=E/c2)? Mass is created when energy is materialized. Is
E=mc2 not applicable at all? Is there any scientific relation between Higgs Field and energy
annihilated? Higgs field may give energy, and this energy is automatically materialized to
mass when particle interacts with this.But how Higgs field creates energy ?
(c) How Higgs field is persistent, when Higgs Boson has mean life time zeptosecond
(10-21 s) seconds. If Higgs particle decays to other particles and loses its identity then how
Higgs field is maintained throughout universe?
If Higgs field extends in the all universe, then how many Higgs Bosons are there in the
universe? How the infinitely large numbers of Higgs Bosons were produced? A Higgs Boson
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is produced in the exceptionally sophisticated experiment in Large Hadron Collider at
CERN, Geneva.
(d) Does hypothetical field of Higgs Boson interacts in similar way with antiparticle as in
case of particle. At time of Big Bang (explosion of singular atom) the matter and antimatter
was produced in equal amount. Does the hypothetical Higgs field produces matter and
antimatter with equal ease ? What are the conditions?
Such questions needs to be answered before the existence of hypothetical field of
Higgs Boson is established. As far as discovery of Higgs Boson in technological
advancements is concerned, it is exceptionally extraordinary.
(Q.17) The speed of the fast neutrons emitted in nuclear reactors is 2MeV ( velocity
=1.954×107 m/s ) thus relativistic mass of neutron must be considered in calculation of
energy. But in calculation of energy rest mass of neutron is taken in mathematical
calculations.
It is incorrect. If it is correct, explain why?
Explanation: It is completely correct.
When velocity of body is in relativistic region then relativistic mass is considered, which is
more than rest mass. We have relativistic mass energy equation
Mmotion =
M rest
v2
1 2
c
(7.10)
according to which the mass of body increases with velocity. It puts upper limit on the
velocity of body equal to c (3×108m/s), as when v =c the mass of body becomes infinite.
(a) In nuclear reactor two types of neutrons exist. The neutrons which cause fission have low
velocity (2185m/s) and question of relativistic mass does not exist for such neutrons. Further
neutron emitted along with fission fragments, and move with relativistic velocity. Their mass
can be measured or estimated.
(b) Hence in view of relativistic variation of mass the relativistic mass of neutrons has to be
considered if velocity is in relativistic region.
(c) In existing calculations the mass of neutrons moving with relativistic velocity(1.954×107
m/s ), is regarded as classical mass which is not true. It means that eq.(7.10) is held invalid,
which has numerous experimental confirmations.
152
(Q.18) In nuclear fission, the fission fragments of
141
56Ba
and 36Kr92 also move with
relativistic speeds , but their classical masses are considered.
Is it correct? If it is not correct, explain why ?
Explanation: It is not correct. The relativistic masses must be considered.
It is true only classical mass (not relativistic mass) is taken in account.
If the fragments move with relativistic speeds then mass increases. Then relativistic mass has
to be taken in account, which is given by equation
Mmotion =
M rest
1
v2
c2
is not applicable. If the reactants and products of fission or fusion move with relativistic
velocities then relativistic masses have to be taken in account. If velocity is in relativistic
region and classical mass is taken in account, then it is not correct.
(Q.19) According to universal equality of masses of nucleons, the masses of proton and
neutron are the same ( i.e. Mp = 1.007276u, Mn = 1.008664u ) in all cases. But if
∆E=∆mc2 is applied to explain the binding energy of deuteron then masses of proton
and neutron decrease i.e. mp = 1.006082u, mn = 1.00747 u. It is contradiction of
universal equality of masses of nucleons.
Thus in this case Einstein’s ∆E=∆mc2 leads to contradictory results.
Is it correct? If not then what is correct explanation?
Explanation: Yes, it is correct.
But scientists have not raised this issue. Author contacted many scientists of international
repute regarding they replied we ‘reading’ and ‘teaching’ it in this fashion since over 100
years. It is not scientific reply.
The equation ∆E=∆mc2 has one constant c, the speed of light and two variables ,
decrease in mass ∆m and emitted energy, ∆E. The energy (∆E) is known as binding energy
(B.E.) in this case and created in the nucleus. In case of deuteron, mass defect ∆m =
0.002388u and binding energy, BE =2.2244MeV.
(a) If energy (binding energy) is created in the nucleus then it cannot be created out of
nothing. So mass ( of nucleons i.e. neutrons and protons) must decrease.
(b)Now according to ∆E=∆mc2 the binding energy is at the cost of decrease in mass of
nucleons.
(c) The decrease in mass of nucleons means contradiction of ‘Universal Equality of Masses
of Nucleons.’ The masses of nucleons are same in all situations. Thus Einstein’s mass energy
inter-conversion leads to contradictions. This aspect is not discussed by scientists in the
existing literature. It is pointed out for first time.
153
(Q.20) According to generalized mass energy equation ΔE =Ac2Δm the energy emitted
for corresponding to small mass can be more than predicted by ∆E=∆mc2 due to high
value of conversion coefficient, A.
Thus in this case value of A can be as high as 1010. Now both
(a) binding energy of deuteron
(b) and ‘universal equality of masses of nuclei’ can be explained.
Is it correct? If not then what is correct explanation?
Explanation: It is correct. It can be easily justified.
(a) Application of ∆E=∆mc2: The mass energy equation ∆E=∆mc2 implies that if BE of
deuteron is 2.2244MeV, then mass defect must be 0.002388u or 3.984×10-30 kg .
It implies that mass of nucleons decrease by 3.984×10-30 kg or 0.1185 %.
According to universal equality of masses of nucleons the masses of nucleons remain the
same inside nucleus and outside the nucleus. Thus this fact is contradicted when ∆E=∆mc2
(b) Application of ΔE =Ac2Δm:
In equation ΔE =Ac2Δm, A is coefficient of proportionality whose value depend upon
inherent experimental conditions. If the value of A is 1010 then for incalculable mass defect
(3.984×10-40 kg ) the energy could be equal to binding energy (2.2244MeV) of nucleus.
Thus the generalized form explains simultaneously the binding energy of the nucleus and
mass of nucleons are explained. The advantage of ΔE =Ac2Δm is that according to this the
annihilation of mass the energy emitted can be less, more or equal to predicted by ∆E=∆mc2.
In this case mass defect is too less that masses of nucleons in deuterons are same. This
prediction is only possible the generalized equation of mass energy inter-conversion.
Part G
Comparison of Erme=Mrest c2 and ∆E=∆mc2 ?
Q.21 Is Rest Mass Energy, Erme=Mrest c2 and Mass energy inter-conversion equation ,
∆E=∆mc2 are the same ?
Einstein derived five equations relating to various types of masses i.e. rest mass (Mrest),
relativistic mass (Mmotion), mass annihilated (Δm ) and mass created (Δm) to various types of
energies e.g.
ΔL = Δmc2,
Δ E = Δmc2,
KErel = (Mmotion – Mrest)c2 ,
Emotion = Mmotionc2
and Erest = Mrest c2
154
In addition there are more equations involving rest mass and energy .
KE = Mrest v2 /2
PE = Mrest gh
Now the five energy equations were derived by Einstein are ΔL = Δmc2, Δ E = Δmc2, KErel =
(Mmotion – Mrest)c2 , Erest = Mmotionc2 and Erest = Mrest c2 appear to be similar as have same
forms, units and dimensions but conceptually are entirely different. Also the dimensions and
units of equations of PE and KE are the same.
There is similarity between Erme=Mrest c2 and ∆E=∆mc2 that both equations have inconsistent
origin. Erme=Mrest c2 is derived from non-existent equation and ∆E=∆mc2 speculated not
derived. ΔL = Δmc2 implies when light energy ΔL is emitted by body its mass decreases by
Δm. But Erme=Mrest c2 there is no term which indicated that Mrest is the mass which annihilated and
energy Erme is created. In the derivation of ΔL = Δmc2 the conceptual basis is such that energy
is emitted by body and its mass is annihilated correspondingly. The derivation of Erme=Mrest c2
and ∆E=∆mc2 are entirely different. Also natures of ΔL and Erme are entirely different.
Part H
Scientist who discovers the law earlier must be given credit.
Q.22 Einstein discussed some concepts in June 1905 paper as his own, which
were already discussed by other scientists. Is it ethical?
Einstein has quoted some concepts existing from the literature e.g. postulates of relativity,
relativistic variation of mass, time dilation, length contraction etc, without acknowledging the
original contributors. It is not ethical. However Einstein justified and admitted that work he
quoted was partly solved by others [1] prior to him. It implies Einstein was aware of the
existing work while quoting the same without references in June 1905 paper.
Further, Einstein’s June 1905 paper which is known as Special Theory
Relativity does not contain any reference of previous literature. Einstein has discussed in it
various aspects (e.g. postulate of relativity, constancy of velocity of light, relativistic
variation in mass, length contraction and time dilation also) without acknowledging the
original contributors. These phenomena existed earlier, so the credit of discovery must to the
original inventor. The way Einstein published his papers implies that above phenomena are
solely his original work. The various contributions are discussed below.
The postulate of relativity
The first postulate of relativity was given by Galileo [32] in his book Dialogues concerning
the two chief world systems. The following is known as Galilean Principle of Relativity i.e.
“the mechanical laws of physics are the same for every observer moving uniformly with
constant speed in a straight line".
The same postulate Einstein has quoted in his June 1905 paper without acknowledging the
155
original contributor Galileo Galilei [1564-1642].
Constancy of velocity of light
So Henri Poincaré (1898) in his paper The Measure of Time drew some important
consequences of this process and explained that light has a constant speed, and that this speed
is the same in all directions. The constancy of speed of light also follows from Maxwell’s
works. So Einstein simply quoted the postulate of constancy of speed of light from existing
literature.
Relativistic variation in mass,
The relativistic variation of mass implies that the mass increases with velocity especially
when the velocity is comparable to that of light. Mathematically equation is given by
Mmotion =
M rest
(7.10)
v2
1 2
c
Einstein has quoted this equation in June 1905 paper without any reference as it is his original
contribution. But this equation earlier existed before Einstein’s June 1905 paper and can be
credited to J J Thomson. Thomson (1881) noticed that the mass of electrons
in motion is
increased by a constant quantity. According to eq.(7.10) the mass electeron (9.1 × 10-31
kilograms ) becomes equal to mass of the earth ( 5.9742 × 1024 kg) if electron moves with
velocity comparable to that of light.
The Dutch Physicist Hendrik Antoon Lorentz (1853-1928) also suggested that the mass
of body increases with velocity. The peculiar aspect about Lorentz is that perhaps he is only
the physicist who taught at school, at one stage of his career and won Nobel Prize.
Walter Kaufmann (1901–1903) was the first to confirm the velocity
dependence of electromagnetic (relativistic) mass by analyzing the ratio e/m (where e is the
charge and m the mass) of cathode rays. The relativistic variation of mass was theoretically
given and experimentally justified before Einstein’s paper.
The Time Dilation
In simplest words the time dilation (act of expanding) means that if system moves with
velocity comparable equal to that of light , then time passes slowly. In his June 1905 paper
Einstein quoted it the paper without any reference that idea did not exist before. It implies
that his own original work. However the concept of time dilation existed earlier.
Joseph Larmor proposed the time dilation first of all while explaining motion of electrons in
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1897,1900. In 1904, Lorentz added time dilation to his transformations and published what
Poincaré in 1905 named Lorentz transformations. So the discovery of Time Dilation can be
credited to Joseph Larmor and Lorentz.
Let there be twins named Ram and John , both are 10 years old. Let Ram is
sent to long journey in space with speed comparable to that of light for 10 years. In this
period John remain at rest. When Ram returns after 10 years then he would be 15 years old,
as the time of 10 years will be equal to 5 years. Thus Ram will be of 15 years. Whereas the
age of John who remain on the earth, will be of 20 years. There is difference of 5 years in
age of both due to relativity. This is believed to true as a result of Special Theory of
Relativity.
Length contraction
In general the length contraction means when a body moves with velocity comparable to that
of light , then body contracts. Again Einstein quoted in his June 1905 paper that it is his
original work like relativistic variation of mass and time dilation. But it is not the truth like
previous cases.
The discovery of length contraction is credited to Fitzgerald in 1889. While explaining the
null results of Michelson Morley experiments Fitzgerald proposed that moving bodies
contract in the direction of motion. Further the length contraction was derived by Hendrik
Antoon Lorentz in (1892).
Opinion of scientists
The purpose of mentioning the various facts is that Einstein should have given
references of the existing concepts in June 1905 paper. Also the readers have right to get the
balanced, unbiased, logical and truly scientific information. The name and status of scientist
should not eclipse the scientific facts.
Einstein did not give any reference to existing work. This aspect was pointed
out by his fellow citizens Stark and Planck just after publications of the papers. Max Born
(1882-1970) co-originator of Quantum Mechanics [4] in his book Physics in my Generations, stated
"The striking point is that it contains not a single reference to the previous literature.”
Therefore, Born’s remarks confirm beyond any doubt that Einstein should have given existing
references in the papers. The other scientists were giving references at that time.
Einstein [2] in 1907 spelled out his views on plagiarism:
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"It appears to me that it is the nature of the business that what follows has already been partly solved
by other authors. Despite that fact, since the issues of concern are here addressed from a new point of
view, I am entitled to leave out a thoroughly pedantic survey of the literature..."
Einstein can be easily contradicted here. Einstein has commented that
“I am entitled to leave out a thoroughly pedantic survey of the literature..."
Einstein’s statement cannot be justified as the existing work was well known not obscure e.g
Galileo has given the postulate of Relativity in 1632 in his well known book, Dialogues concerning
the two chief world systems.
Albert Einstein has given references his own and others’ works in his papers, one
specific example is of the paper which he published in Annalen der Physik [3]. There are
many more such examples. It is evident that Einstein was aware of existing facts in scientific
literature but did not acknowledged the contributing scientists.
Conclusions
By not giving the references of the existing literature, Einstein maintained that this work did
not exist before him, and all are his innovations.
Thus scientists like Galileo Galilee, Henri Poincaré , J. J. Thomson , Hendrik
Antoon Lorentz, Walter Kaufmann, Joseph Larmor etc. who have discovered the scientific
concepts (e.g. postulate of relativity, constancy of velocity of light, relativistic variation
in mass, length contraction and time dilation also) should be given due credit. It is better
late, than never. These are scientists responsible for laying foundations of special theory of
relativity.
Thus it is concluded that the scientists who have given the laws earlier than Einstein
deserve the credit for the discoveries. Einstein ignored to give references of work of
predecessors but he was well aware of the rules and regulation and had been giving the
references in his scientific works.
References
[1] Fadner, W. L. Am. J. Phys. Vol. 56 No. 2, February 1988
[2] Einstein, A. Annalen der Physik 23(4):371-384, 1907 (quote on p. 373).
[3] Einstein, A.
Annalen der Physik 14 354-362 (1904).
[4] Born , M. Physics in My Generation, Pergamon Press, London, p. 193 (1956)
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