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DISCOVERING THE NATURE
OF THE DARK MATTER
Vu Huy Toan
- Vietnam Academy of science and technology
- Construction Machinery and Industrial Works CONINCO Joint Stock Company (CONINCO-MI)
No.4 Ton That Tung, Hanoi, Vietnam.
Email: [email protected]
CONTENTS
• I - INTRODUCTION
• 1- What is the dark matter?
• 2- The accepted postulates
• 3- The total energy of physical objects in the potential force field
• II - NATURE OF THE DARK MATTER
• 1- What is the photon?
• 2- Photon is the reason for the fast rotary of a galaxy
• III - CONCLUSIONS
• V - ACKNOWLEDGMENTS
I- INTRODUCTION
I-1. WHAT IS THE DARK MATTER?
Rotary speed
• When observing the movement of the stars in the galaxy, Mr.
Jan Oort [1] discovered that the stars are far from the centre of
galaxy do not rotate slowdown as the calculation of Newton’s
mechanics but nearly do not change, and this phenomenon is
observed in all galaxies. See the Fig. 1 and Fig. 2
B – The observation
B-
AA - The calculation
without dark matter
Distance
Figure 1
Figure 2
I-1. WHAT IS THE DARK MATTER?
Figure 3. Some
body assume that
galaxies Abell 222
and Abell 223
are connected by
the dark matter
fibre. However, it is
wrong!
In own report, the author would like to proof that the existance
of the abnormal rotate of galaxies are not caused by any “dark”
matter but only the “visible” matter in the universe,
it is just photons.
I-2. THE ACCEPTED POSTULATES
• Postulate 1: All physical objects interdependently exist.
• Until now, the physics only consider every thing according to the
opposite concept that "existence itself" accordingly, allowing the
existence of a physical object (PO) isolating completely, unique
in the universe, with mass m and then from there to consider its
movement under action of a force by the laws of dynamics.
F = ma
Y
m
m – isolated body
Figure 7.
Free space
Z
0
X
I-2. THE ACCEPTED POSTULATIONS
• “The interdependent existence” is shown for 3 aspects:
•
•
Thus,
it can beofsaid
that the universe
1a. Aspect
a form:
"within
every
PO"PO
is not wrong andField
Formally,
every
that
is alsoof
true
for any- other
object
consists
2 parts:
A
and
for this
they are
“body”
partreason,
with the
limited size (r)Both
which
interdependent.
thewe
two the
can “see”
“body”
and and
“field” parts related to
• each
Theother
“field”dialectical:
part with The
the more the
energy
of this
part
unlimited
size
(Rincreases,
 ∞) the
which
cannot
“see”.one
more
thewe
energy
of other
reduces and vice versa
Field
R
Body
r
∞
Field
Field
Figure 8. “Physical object” = “Body” + “Field”
I-2. THE ACCEPTED POSTULATES
1b. Aspect of the content: “Interaction”
- Every PO can mutual
interact with other PO
– it is simple because
“You are in me and I
am also in you”.
-This interdependent
existence” has the
internal cause, it is the
“interaction”;
M2
M1
M3
M4
Figure 9. Interaction of Physical object
I-2. THE ACCEPTED POSTULATES
• 1c. Aspect of a manifestation mode:
• Both the above form and contents lead to a most common
manifestation mode for every PO that, by our subjective
awareness, we call a “mass” with two types:
• - “Gravitational mass” (we will symbol by Mi) characterize for an
interaction ability of each PO and
• - “Inertial mass” (we will symbol by mik) characterize for an inertia
of movement of a PO having a gravitational mass Mi in a potential
force field of other PO having the gravitational mass Mk.
• For example, if we only pay attention to two PO with the
gravitational masses M1 and M2, their inertial mass m concerns to
that gravitational mass as per the formula which have been
proofed by the author in the book “The New way For Physics” [3]:
I-2. THE ACCEPTED POSTULATES
• In here, F12 and F21 – are the gravitational forces of M1 and M2
acting on each other correspondingly; a12 and a21 – are the
relative movement accelerations of M2 and M1 with respect to
each other correspondingly. Shortly:
(1)
I-2. THE ACCEPTED POSTULATES
•
From (1), we can see clearly that the interdependent existence has
been shown how to quantity: Only one of two gravitational masses
is a truth:
equals zero and that POThere
is considered
as the isolation, i.e, the inertial
mass is also Non-Interaction
equals zero. Or in the other
words, when one PO moves
≡ Non-Inertia
without interaction with other PO, its inertial mass will be zero (m ≡ 0).
Y
Potential
Free space
force filed
M2
a = F/m = ∞
Z
M1
M0.1 M2
m=0
M10 + M2
X
Figure 10. The interdependent existence
I-2. THE ACCEPTED POSTULATES
• Postulate 2: The fundamental particles
•
The fundamental particles are the particles cannot be broken further
into anything other, so all physical objects are composed of them.
The author assumed a following postulate:
• “Electron and positron are two
fundamental particles; they have only
electric interaction rather than
gravitational interaction”.
I-3. THE TOTAL ENERGY PHYSICAL
OBJECT IN THE POTENTIAL FORCE FIELD
• As we know, “total energy” of a body is
determined by Einstein as per the famous
expression [3]:
•
(2)
• However, people have forgot the important
detail the expression (2), is not total energy of
the PO, because it only consists of kinetic
and internal energies, in which it does not
completely contain a potential energy.
I-3. THE TOTAL ENERGY PHYSICAL
OBJECT IN THE POTENTIAL FORCE FIELD
• In the book “The New Way for Physics” [3], the author has proofed
an expression of total energy of the PO corresponding to a most
characteristic state – a freely falling state, or resting in a force field:
•
(3)
• where Uk – the critical potential energy of the PO in the force field,
i.e, the biggest potential energy that one PO can have in that force
field, still maintain its structure; exceeding this value, the “body part”
of the PO will be crushed by the force field. Also starting from that
critical condition, the formula (3) can be written in the more simple
form:
•
(4)
• Compare (4) with the formula (2) received by Einstein for a body
freely moved, we see that when calculating to potential energy in a
force field, its total energy is bigger than twice.
I-3. THE TOTAL ENERGY PHYSICAL
OBJECT IN THE POTENTIAL FORCE
FIELD
• On the other hand, according to the postulate “1a”, photon must
have its “field” part far  ∞ so, according to the postulate “1b”, it
must have an interaction with other PO in this “field”, this
interaction can be only the gravitational. In other words, photon
have the gravitational interaction as any other PO that we know.
While, according to the postulate “1c”, it must have gravitational
mass Mph and inertial mass mph in gravitational field. We can
approximately determine this minimum gravitational mass of
photon based on the total energy of electron and positron to
create it as per the expression (4):
(5)
• As per (4), we can write for photon:
(6)
• From here, we can calculate the inertial mass of photon when
balancing (5) and (6):
(kg) (7)
II- NATURE OF THE DARK
MATTER
II-1. WHAT IS THE PHOTON?
• In the "Photon structure" Report published in the Proceedings:
“Advances in Optics, Photonics, Spectroscopy & Applications VI,
2011” [4], the author showed that there are some experiments,
for example, phenomena of photon decay and photon emission,
evidences us the structure of photon, including two fundamental
particles: electron and positron; these particles in some way, the
combination of two particles with opposite charge may result in
the electric neutralization from a certain distance, like atom,
molecule.
e-
p+
RT
+
F=0
From certain distance RT, atom become the neutral object
II-1. WHAT IS THE PHOTON?
E
In the near distance,
creates electromagnetic field with the
Ethis
= 0; Hphoton
=0
X
c)
vector
of electric-field
intensity
and magnetic-field
intensity
H putting
“Photon”
is the particle
whichEhave
the structure from
electron
and
H
as positron
per the description
the Maxwell
equations.
both turningofaround
the center
of the common inertia and
moving withE the light speed cElectromagnetic
(see Fig. 4a)
At the limited distanceERT far from the wave
movement axis X,
Orbitfrom
of eOrbit of e+ with other electric charges and
photon
do not interact
e
RT
the distance R ≥ RT, it does not have the inertial mass in theX X
b)
a)
e+
electromagnetic
be zero.
H c
H field, i.e, its inertial mass must
eR
e+
λ
Figure 4. Motion of a photon created the “electromagnetic wave”.
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
•
•
•
Up to now, the modern physics still assume that photon do not have
the rest mass, its relative mass is too small and calculated as per the
formula of Einstein:
where h ≈ 6,63x10-34 Js – Planck constant; c ≈ 3x108 m/s – the speed
of light in the vacuum; v – frequency of photon. They estimate that
there are about 500 microwave photons in each cm3 in the space
among galaxies or N = 5x108 photon/m3 [8]. While, the density of
photon as per the mass is only by:
(8)
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• If the frequency of microwave photon is average about 1010 Hz,
in each m3 have ~4x10–32 kg photons. While, the average
matter density of universe is ~10–27kg/m3 [8], ie, is bigger
than thousand times. May be because of that reason, photons
have been ignored?
• However, if we draw mph from (7) and place it into (9) with the
numerical value we obtain a density of photons ρp0 ~ 10–22 kg,
that means, it is bigger than the matter density of thousand
times.
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• We will evaluate concretely: Assuming
that the matter distribution in the galaxy
with the simple form is the black hole in
the center with the mass of M0, the stars
and interstellar dust with the density ρs
= const up to the radius Rs (see the Fig.
3).
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
Z
Rs
Ri
M0
Y
r
Ri+1
X
Figure 5. The model of matter distribution in a galaxy
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• In the fig. 6, the density distribution of matter and photons in
galaxy is demonstrated.
7E-22
Density (kg/m3)
6E-22
5E-22
4E-22
Density of matter
Density of photons
3E-22
2E-22
1E-22
0
0.2 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
Relative distance to the galaxy center (Rx/Ro)
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• While, the gravitational mass of the matter quantity
contain in the globe with the radius r < Rs will be:
(9)
4
M m  M 0  Rs3  s
3
• From this radius (R > Rs), assuming that the matter
density reduce as per the formula:
(10)
• where a – any constant.
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• Simply, we can divide the galaxy into the globe thin-layers with
the thickness of (Ri+1 – Ri) and assuming that the matter density
in the scope of each thin-layer ρsi+1 ≈ const, so we can calculate
the matter mass contain in each thin-layer as per the normal
way but cannot to use a complex integral:
(11)
• Thus, the total mass in the globe with the radius R > Rs will be:
(12)
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• On the other hand, we also assume that the density of photon
ρps = const in the radius Rs, and outside this radius it also reduce
as per the exponential function rule as per the distance to the
center of galaxy from the value ρps ≈ 2x10–22 kg/m3 as above
mentioned:
(13)
• where
• with
– is the density of photons in the space among
galaxies; b – constant.
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• In the scope of galaxy (<Rs) where the stars and interstellar dust
concentrate essentially, photon density is higher in comparison
with its density in the space among galaxies because photons
always produced from the stars and reduce their density as per
the distance. While, similar to the matter form as above
mentioned, we also have the gravitational mass of photon
contain the globe with the r < Rs:
• I
(14)
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• In the scope of outside radius Rs, we also do similar to the type
of other matter and so the mass of photon in the globe with the
radius R will be:
(15)
• While, we can calculate the total matter quantity of matter and
photons in the globe with the radius R as well as centripetal
force due to that total quantity effects to a star with the mass M.
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• a) In a distance r < Rs
• - From (9) and (14), we have the total mass Mr∑:
(16)
• From a balance condition between centripetal and centrifugal
forces, we take out a rotary speed Vr of the star in the radius r:
(17)
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• b) At Rs
• - From (4) and (10), we have the total mass Ms∑:
(18)
• - From a balance condition between centripetal and centrifugal
forces, we take out a rotary speed Vs of star in the radius Rs:
(19)
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• c) In a distance R > Rs:
• - From (7) and (11), we have the total mass Ms∑:
(20)
• And the rotary speed:
(21)
• The calculation of rotary speed of galaxy is realized by Excel
program on a computer for the cases which count not mass of
photons (VA) out and count that mass but with a different density
distribution level of matter and photons, we have VB
corresponded to the case when a = 3; b = 0,038 and VC
corresponded to the case when a = 1,5 ; b = 0,02 while all other
parameters are the same.
II.2 - PHOTON IS THE REASON FOR
THE FAST ROTARY OF A GALAXY
• I one case, We have Vb (correspondence to the case when a = 7; b
= 0,05) and in other case, it is Vc (correspondence to the case
when a = 1,5 ; b = 0,035) while the other dimensions are the same.
400
350
Rotary speed of stars (km/s)
From here, we know that
the calculation of
gravitational mass of
photon as per this new
way is completely suitable
to the observation result of
astronomy: The shape of
Vb is coincided with the
shape of B on the Fig. 1a,
the shape of Vc coincided
with the shape of B on the
Fig. 1b.
Figue 1a
300
250
Va
Vb
Vc
200
150
100
50
0
1
2
3
4 5 6 7 8 9 10 11 12 13 14 15 16
The distance to galaxy center (5 kps)
Figue 1b
CONCLUSIONS
IV - CONCLUSIONS
• 1- It is necessary to accept the postulates:
• - Every physical object interdependently exist and that existence
is shown through the form “body – field”, the content
“interaction” and the dynamic characteristics “mass” with two
different types, but it has the causality relation together:
“gravitational mass” (M), or “interaction mass”, and “inertial
mass” (m).
• - Electron and positron are the fundamental particles and only
appear in the electric interaction but without the gravitational
interaction…
IV - CONCLUSIONS
• 2- It is clear that, the so-called “dark
matter” has been shown one’s face: It is
just the photons flooding in the Universe
made the galaxies rotating much more
extraordinarily with the different modes
depend to the distribution characteristic
of matter as well as photons in that
galaxies.
V - ACKNOWLEDGMENT
• The author is grateful to Professor Nguyen Dai Hung, Director of
Institute of Physics (Academy of Sciences and Technology of
Vietnam) for his highly valuable assistance and honest
encouragement to finish this work.
REFERENCES
•
•
[1] Goddard universe flight center (NASA). Hidden mass.
http://imagine.gsfc.nasa.gov/docs/teachers/galaxies/imagine/hidden_mass.html
•
•
[2] Discovering the dark matter fibre. Khoahoc.com online.
http://www.khoahoc.com.vn/khampha/vu-tru/40433_Phat-hien-soi-vat-chattoi.aspx
•
[3] Vũ Huy Toàn. Con đường mới của vật lý học. NXB Khoa học và Kỹ thuật. Hà
Nội, 2007.
•
[4] Vu Huy Toan. Structure of photon. Proceedings: “Advances in Optics,
Photonics, Spectroscopy & Applications VI, 2011”.
http://vuhuytoan.wordpress.com/2010/12/25/c%E1%BA%A5u-trucc%E1%BB%A7a-photon/cau_truc_photon_bc_hnvl_en_18-6_final/
•
•
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[5] Vũ Huy Toàn. Khối lượng của photon. 2012.
http://vuhuytoan.files.wordpress.com/2012/09/27_khoi-luong-cua-photon.pdf
•
[6] Новиков И.Д. Эволюция вселенной. Москва. “Науки”. 1990.