Download 200% to 1100 % Increasing Power Generator

The Online Journal on Power and Energy Engineering (OJPEE)
Vol. (3) – No. (1)
200% to 1100 % Increasing Power Generator
Rawash Hamza
Communications Department, Cairo University Egyptian Relativity Group (ERG)
36 Abd Alhameid Abd Rabu st, West Mounera, Imbaba, Giza, 12421
[email protected]
Abstract-The paper gives a new method of increasing
generator’s power through application o f Finsler
geometry (two approaches on a sample generator (data
reference)). Two times voltage increasing& 1.5 times
current increasing and 3 times power increasing with
efficiency increasing to 200% (normal model) were
recorded in 1st approach, another turbine must be
installed on free stators; stator and rotor turbines must be
rotated at same time in different directions. 4 times
voltage increasing & 3 times current increasing and 12
times power increasing with up efficiency increasing to
1100% (super model) were recorded in 2nd approach,
achieving that can be done by moving three coils inside
each other, inner and outer coils turbines must be rotated
in an opposite direction of medium turbine rotation.
Temperature decreasing was recorded in these
approaches; it can be referred to magnetic field increasing
with current increasing and resistance decreasing.
Key words:-generator, Berwaled-Moor metric, resistance, magnetism.
II. FINSLER GEOMETRY AND MAGDAFE
MAGDA is considered normal extension of MAG
(Maxwell Analogy Gravity) theory (Thierry De Mees in
2003) and mirror of Murad & Bakr approach.
Electromagnetic field in MAGDA will be mirror of a
gyrotation field in MAG theory and spinning field in Murad&
Bakr approach. MAGDA was addressed through FERT
(Cairo- 2008) and PIRT (Moscow -2009) to explain MAGDA
FE and EFE (Einstein field equation) relation [1], then going
to Berwaled – Moor metric which can be reduced to two of
EFE with two orthogonally fields and also, EFE can be
reduced to MAGDAFE, which can be considered relativistic
form of Lorentz force equation or as force with its induction
effect; these relations will be discussed in detail in the
Appendix.
III. ELECTRIC MAGDA GENERATOR (EMAGDAG)
The process will be discussed on theoretical ideas to create
a modified generator.
I. INTRODUCTION
Generator’s power increasing is a big need; many trials
were done for improving actual generator’s fabrication
parameters to gain more power, according to Lorentz force
equation "Force = q × V0 × B" (turbines shape& coil turns&
magnetic flux and rotor velocity), can be reviewed here
q = electron charge& V0 = rotor velocity and B = magnetic
flux density.
The purpose here, is introducing a new idea through an
application of Finsler geometry for producing a friendship
power environment source. Berwaled- Moor metric
(connection type of Finsler geometry) was adjusted to be
general MAGDA (Maxwell Analogy Gravity Different
Aspects) force equation (MAGDAFE), it will be explained in
sec 2. To apply this idea, two dual fields (electric and
magnetic fields) must be moved in an opposite directions
(with each other) using suitable turbines. Stators must be
positioned free with other turbine on it, relative velocity will
be double of original velocity, magnetic field will be
increased, 3 times output power were recorded, comparing
with same generator without such changes, it means 200%
efficiency increasing in electric MAGDA generator
(EMAGDAG), it will be discussed in sec3. Extending such
idea will be applied on 3 coils, 12 times as output power will
be recorded; it means 1100% efficiency increasing in super
electric MAGDA generator (SEMAGDAG), its discussion in
sec4. Critical temperature will be discussed in sec 5.
Reference Number: JO-0010
Figure (1): Electric MAGDA generator (EMAGDAG) =
sample after modification)
In Figure 1, the above invention requires an additional
turbine on free opposite direction stator with rotor motion.
Coil A and its arrow represent rotor and turbine direction, coil
B and its arrow represent free stator and turbine direction,
electric box with required brushes/rings represent transferring
electricity to out. Explanation will be done through 3 views,
in the 1st, MAGDA looks to electric motor motion as
orthogonally result between electric and magnetic fields
(spinning type). Electric power can be produced by moving
one inside other one [2].
  V 2 
  V 2 
(1)
F = A 1 × 1 −  1   + A 2 × 1 −  2  
  c  
  c  




Equation (1) is a generalized MAGDA force equation, If A1=
q x E, A2 = P x H, V1 = V2 = V0, then Eq. (2) will be gained.
  V0  2 
(2)
F = (q × E + P × H )× 1 − 
 
  c  


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The Online Journal on Power and Energy Engineering (OJPEE)
  V0  2 
F = (q × V0 × B(rotor ) + q × V0 × B(stotor ))× 1 − 
 
  c  


(3)
  V0  2 
If B(rotor ) = B(stotor ) F = 2 × q × V0 × B × 1 − 
 
  c  


(4)
 V0 
Actually 

 c 
neglected.
2
will be too small then its value can be
Net electromagnetic force = F = 2 × q × V0 × B
(5)
nd
In the 2 , starting with Lorentz force equation, generator
power can be deduced [3].
F = q × (E + (V0 × B)) → output power
F × r × t = m × V0 × r → angular momntum
(6)
(7)
→ rotation or spinning
E = electric field, t = time, r = distance to force center, m =
rotating (spinning) mass, F = force, Magnetic field existence
is essentially in equations Eq. (8-13), for motor "F = q × E + q
× V0 × B" and for generator "F=q × V0 × B + q × E".
Vol. (3) – No. (1)
In Figure 2, blue curves, (a curve for voltage with value V
and b curve for current with value = I) represent status of
stator /rotor motion (sample generator without modification)
black curves (c curve for voltage with value= 2V and d curve
for current with value= 1.5I) represent status of stator and
rotor movement on generator after modification in equal
speed of both rotor /stator).
3
P(n ) = V(n )× I(n )× p.f = 2 × V(o )× × I(o ) \ 3 × p(o )× p.f (13)
2
(14)
P(n ) = 3 × p(o ) (in case of p.f = 100%)
n = stator and rotor, o = rotor, p = power, V = voltage, I =
electric current, p.f = power factor, experiments were done in
steps (voltage= V & I = current and P = power), 1st we move
rotor with speed = V0, V& I and P as output values were be
recorded, 2nd we move stator (only) with speed = V0, V& I
and P as output values were be recorded, 3rd we move at same
time rotor and stator with the same speed = V0, 2 × V& 1.5 ×
I and 3 × P as output values were be recorded, 4th we move
with different speeds (V1 & V2 ) both of rotor and stator,
leads to 2 × V ≥ voltage ≥V & 1.5_ I ≥ current ≥ I and 3_ p ≥
output power ≥ p.
(8)
E(rotor ) = E(max )× sin (θ)
Due to opposite direction of stator motion w.r.t rotor motion,
a modified generator will be treated as two connected
generators.
E(rotor and stator ) = E(max )× sin (2θ)
E(rotor and stator ) = 2 × E(max )× sin (θ)× cos(θ)
(9)
(10)
Equation (10) expresses about output voltage of both rotor
and stator motion, E (rotor = voltage wave due to rotor
motion, E (max) = max voltage, E(rotor and stator) = voltage
wave due to rotor and stator movement. In the 3rd, starting
with electromagnetic force "F = q × V0 × B” and with
rotating stator turbine and rotor turbine at time in opposite
directions [4].
Net relative velocity = V0 − (− V0 ) = 2 × V0
(11)
Net electromagnetic force = 2 × q × V0 × B
(12)
Voltage difference increasing by 100% & current increasing
by 50% & output electric power increasing by 200% and
intrinsically coil cooling were recorded, output power = coil
edges voltage × current (loads on coil).
Figure (3): Voltage-current relation (samples with different
velocities).
In Figure 3, there are two cases, 1st will be for load case,
voltage current relation is not linear, current change is faster >
voltage change on 1 & 2 and 3 curves, possibility of zero
resistance will be expected. 2nd will be for load case, voltage
current relation is not linear and current change is < voltage
changes, current is ≅ const. at 6.1 m ampere while voltage is
changing on 4 and 5 curves, all curves will be referred to
different samples with different
speeds (gradually).
IV. SUPER ELECTRIC MAGDA GENERATOR
(SEMAGDAG)
Let us have three coils A& B and C; all coils are free (not
fixed). Coil B will be moved between rotated coils A and C,
they will be rotated anti clock wise direction (same direction
of rotating around Kabba (Muslims praying direction)), coil B
will be rotated in an opposite direction of rotating around
Kabba (clock wise direction).
Figure (2): Output sin wave voltage (current) diagram
with θ (angle)
Reference Number: JO-0010
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The Online Journal on Power and Energy Engineering (OJPEE)
Vol. (3) – No. (1)
Figure (4): Super MAGDA generator (SEMAGDAG) 3coils
rotates inside each other.
In Figure 4, invention idea requires that coil A and coil C
rotate in an opposite direction w.r.t coil B rotation direction,
SEMAGDAG consists of coils A and C (inner& outer) & coil
B (medium) represent and electric box with required brushes
and rings (for electricity out), Results were recorded in
following table with comparing of normal generator (case
N0.1).
coil
No A
1
fix
2 mob
3
fix
4 mob
5 mob
coil coil V
I
R
P
P
B
C
V
I
R
P
H
mob
V
I
R
P
H
mob
2×V 1.5×I F(R) 3×P F(H)
mob fix 2×V 2×I F(R) 4×P F(H)
mob fix 3×V 2.5×I F(R) 7.5×P F(H)
mob mob 4×V 3×I F(R) 12×P F(H)
T
T
T
F(T)
F(T)
F(T)
F(T)
Table (1): It describes all the statues of 3 coils (rotating inside
each other).
Case N0.1 represent generator without our changes and case
N0.2 was discussed in the previous section as EMAGDAG,
(mob ≡ mobile). In case N0.3, electric coils will be rotated
between two fixed magnetic coils, it will be considered as two
connected generators with same c/c's, each one has output
voltage = V and output current = I, total output will be 2 × V
in voltage and 2 × I in current, (electric coil ≡ coils for
transferring electricity and magnetic coils for magnetic
creation). In case N0.4, electric coils will be rotated between
one fixed magnetic coil and rotated magnetic coil in opposite
directions, it will be considered as two connected generators
(same c/c's), one will be similar to case N0.2 with an output
voltage = 2 × V and output current = 1.5 × I, the other one
will be similar to case N0.1, total output power will be = 3 ×
V in voltage and =2.5 × I in current. In case N0.5, between
two rotated magnetic coils an electric coil will be rotated with
opposite directions, it will be considered as two connected
generators (the same c/c’s), both of them will be considered
as case N0.2 with output voltage= 2×V and output current =
1.5 × I for each one, total output will be 4 × V in voltage and
3× I in current. In above table magnitude of F(R) will be < R
& magnitude of F (H) will be > H and magnitude of F (T)
will be T, F(R) & F (H) and F (t) are nonlinear functions of R
& H and T in sequence.
Reference Number: JO-0010
Figure (5): 5 modes of coils A&B and C according
previous Table
Figure 5 expresses about H (magnetism) changing of H
where volume change leads to electric current creation by
induction effects (A → B coils) and (C →B coils), volumes
of magnetic field will be observed from up down up down [5,
6]. In Figure 5, each point on curves will be mirror of case in
previous Table from No.1toNo. 5, (V-I) or (P-I) curves
change from case to other will be edge of understanding
effect of magnetic volume change.
V. DISCUSSION
MAGDA explains motor and generator from field criteria,
space magnetic field change ≡ space distortion, by rotor
motion (generator) will create electric field (time distortion),
it will force free electrons in rotor’s coil to be moved in a
specific direction, while change in magnetic field was
increased, created electric field will be increase by induction,
vice versa of this process will be for motor (F =
electromagnetic force). To increase output generator's power,
rotor speed must be increased, but rotor coils will suffer from
high temperature with damage possibility. In EMAGDAG,
output power increased, while rotor’s temperature was
decreasing, why [7]?
V.1 H-R explanation
Stator’s motion will lead to gain induction current which
will be added to original one (with ratio), resistance will have
gotten illusion increasing with ratio because magnetic field
will be cut through two ways from rotor’s motion and from
stator’s motion. Increasing of voltage difference on coil edges
will be explained on decreasing of resistance which means
that magnetic field movement during passive electric field
motion will lead to some actions, more free electrons were
rearranged in specific direction, free new electrons by
breaking its bond with nuclei will be done in sequence, after
that clearing of kinetic energy from bonded electron, stopping
of electron's rotation then its spinning [8].
Next clearing will be in its potential energy with nuclei will
be done; this will be cause of increasing electrons per second
i.e. increasing in current due to difference in voltage.
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The Online Journal on Power and Energy Engineering (OJPEE)
V.2 A. D. Sakharov (volume change)
A. D. Sakharov generator idea application [9] current
increasing /resistance decreasing will be explained on
magnetic field movement, magnetism will be increased
gradually with time at specific space point [10], A . D.
Sakharov (Soviet Union nuclear physicist, in 1951 he
invented and tested the 1st explosively pumped flux
compression generator, compressing magnetic fields by
Explosive material).
H(s, t )1 = H(s, t ) 0 + δH(s, t )
(15)
H = magnetic field intensity, (s, t) = space – time, (s,t)
distortion will takes some time to be released (mirror of
capacitors recharging), then new distortion will be added…
and so on, it was recorded in Eq. (15), it will be observed by
specific generator‘s parameter and " relative velocity ≡
V(rotor) – (– V(stator))". Another view, volume changes
between stator and rotor during relative motion will create
induction current; automatically it will be appeared as an
increasing in magnetic field. Simultaneously, obstacles of free
electrons will be decreased, current increasing with resistance
decreasing.
Vol. (3) – No. (1)
energy for electrons moving. This will be a case until edge
point (b) where T = Tc & R = 0 and I = maximum value in
ranges b-c-d in H-I curve and in ranges b-e-i in H-R curve.
V.4 H-T explanation
BCS (is a complete microscopic theory of superconductivity by Bardeen & Cooper and Schrieffer) theory can
be used in explanation of decreasing resistance until R = zero
and T = Tc, temperature decreasing leads to superconductors
materials. During that process, magnetism disappearing was
recorded, (Meissner effect view) [11], scientist discovered, H
on superconductor phase transition was not disappeared, it
was hidden, others discovered that more and more of H will
return superconductor phase to conductor phase. From above
notes, increasing in H due to volume change in
SEMAGDAG, at Hc electric coil resistance will be = zero,
case of more and more H, the transition phase will back again
and so on.
5.3 H-T-I-R relation
Figure (7): Change of H and I (superconductor view)
Figure (6): Relation between current -resistancetemperature-magnetism
Magnetism changing will be playmaker, because H
increasing will lead to dual change in resistance and on
specific point, coil resistance= zero& current = ∞ (max value)
and T = Tc. In Figure 6, R= coil resistance, I = electric
current, T = temperature, H = magnetism (mili Henry), T=
temperature, Tc = critical temperature, curve a-b-c-d-j
represents H-I magnetism with current, curve h-b-e-i-f
represents H-R magnetism with resistance; k-b-g curve will
be for H-T current with temperature. In period h-b & a-b and
k-b, resistance will be decreased during increasing of
magnetism; the magnetism increasing will be the reason of
decreasing kinetic energy electrons of coil atoms, temperature
of coil will be decreased.
Another view, increasing magnetism will be a reason of
producing different direction magnetic field (anti-magnetism)
then more electrons will be free, change in voltage equals
double value of normal generator will be used for needed
Reference Number: JO-0010
In Figure 7, increasing of H due to volume changes in
SEMAGDAG with value = ∆H, will give meaning of more
than value of Hc, with more H, net H will be returned to
original H of normal generator (this can be considered as a
cycle), again with more H and so on …., existence of original
H on coil and variable H value of SEMAGDAG at the same
time will be seem as hidden[12], where net H will be express
the magnetism result values with phase transition on Hc.
Current will takes maximum value on front of Hc points on
Hc line.
V.5 Non linear relation (V-I)
Applying Ohm’s law on rotor movement (only), resistance
decreasing will be viewed.
V = I × r + I × ω× L
(16)
V = voltage, I = current, r = coil resistance plus load
resistance, ω = angular velocity, L = coil inductance.
According our results with applying Ohm’s law on rotor and
stator case, voltage current relation will be put in Eq. (17).
3
3
× I × r (n ) + × I × 2 × ω × L
(17)
2
2
In case of r (load) = 2.3 Ω, r (coil) = 5.1Ω & output voltage =
4.1 volt and output current = 230 m amp & ω × L = 10.42608
Ω, r (new) = 2.95 Ω, resistance (in ohm) will be decreased
2V =
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The Online Journal on Power and Energy Engineering (OJPEE)
below7.4 Ω, It means that non linear relation between V/I in
EMAGDAG will be hold and inductance will be increased in
non linear graduating.
V = I × function (r ) + I × function (ω × L )
(18)
In Figure 7, dashed curves will be diagram of same status
magnetism change with I & R and T, but with new values
from 160 – 280(2 × 10–1 mh) and accompanied by a new T
value of Tc new (closest to the 1st one Tc), for Δ H (20 – 140
& 160 – 280 and so on…...), all curves will be repeated with
small Tc change.
V.6 Sudden change of free stator
Sudden change, if stator position changed suddenly to rotor
motion (no stator’s motion), it will address results exactly as
case No.2, which means that continuous regular change to
space leads to gradually output increasing (V,I,P). Sudden
change leads to the same values according to time change
equals maximum values of change in s where sudden change
of space stator means time stator change. There is maximum
limit in any of two cases, rotor or stator movement only &
rotor and stator motion in velocity gradually increasing or
sudden change with a definite angle (volume change) and
different types of stator and rotor shapes.
VI. CONCLUSION
Huge gain of generator's power by above methods will be a
concrete of power source, there are many choices for high
quality generators production, relative motion between free
stator and rotor & sudden change of free stator inside moved
rotor & 3 rotated coils in each other . From 200% up to
1100% incredible power gain from original power can be
hold.
APPENDIX: MAGDA to EFE to Berwald -Moor metric
The required relation will be
Schwarzschild metric solution of EFE.
1
8πG
Rµv − g µv R + g µv Λ =
Tµv
2
c4
proved
through
(1)
Rv is Ricci curvature tensor, R is the Scalar curvature, gv is
the metric tensor (general relativity), Λ is Cosmological
constant, G is Gravitational constant, c is light speed, and Tv
is energy- momentum tensor.
Figure (1): Space time within tangent space over trajectory
path in EFE
Reference Number: JO-0010
Vol. (3) – No. (1)
In Figure (1), representation of EFE two vectors of (gμν) μ and
ν can be represented in form "μ = a(s) and c(t)" & "ν = b(s)
and d (t)" same manifold where s = space and t = time
Trajectory path will be referred to effect of two vectors (μ &
ν) and it will be represented by vector (x) at a specific point
on trajectory path on tangent at this point, in EFE (μ & ν) are
vectors of one field (gravitational field). Then enquiry, how
time part of gravitational field, Eq. (2) will be gained?
1
Rµv − R g µv + = K × Tµv
(2)
2
Many solutions of EFE were introduced; Schwarzschild
metric which corresponds to gravitational field of an
uncharged, non- rotating, spherically symmetric body of mass
M. Schwarzschild solution can be in Eq. (3).
 r 
dr 2
c 2 dr 2 = 1 − s c 2 dt 2 −
− r 2 dθ 2 − r 2 sin 2 θdϕ 2 (3)
rs
r 

1−
r
Where τ is the proper time (time measured by a clock moving
with particle) in seconds, c is light speed in meters per
second, t is the time coordinate (by stationary clock at
infinity) in seconds, r is the radial coordinate (circumference
of a circle centered on the star divided by 2π) in meters, G is
gravitational constant, θ is colatitude (angle from North) in
radians, φ is longitude in radians, and rs is Schwarzschild
radius (in meter) of massive body, which is related to its mass
2GM
M by ” rs =
”, geodesic equation will be in Eq. (4).
c2
d 2 xµ
+ Γvµλ
dx v dx λ
=0
dq dq
(4)
dq 2
Where Γ represents Christoffel symbol and the variable q
parameterizes the particle's path through space-time (called
world line). Γ depends only on metric tensor gμν, / rather on
how it changes with position. Simplification form will be in
Eq. (5).
 r 
dr 2
(5)
c 2 dr 2 = 1 − s c 2 dt 2 −
− r 2 dϕ 2
r
r
s


1−
r
Above equations (new) will be considered as a safe hole of
GTR to be accommodated with logical and physical channel
(induced effect and GTR (general theory of relativity)), Eq.(1)
and Eq.(2) were called solutions of EFE will be used through
Schwarzschild metric, (other solutions are down to
Schwarzschild metric)which corresponds to gravitational field
of an uncharged, spherically symmetric non- rotating, body of
mass M, Schwarzschild solution will be in Eq. (6).
 r 
dr 2
c 2 dr 2 = 1 − s c 2 dt 2 −
− r 2 dθ 2 − r 2 sin 2 θdϕ 2 (6)
rs
r 

1−
r
Above equation in the force approach seems in Eq. (7).
V(r ) = K.E + P.E + induction effect
(7)
Haw? Where V(r) = effective potential & K.E = kinetic
energy& P.E = potential energy.
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The Online Journal on Power and Energy Engineering (OJPEE)
V(r ) =
− GMm
L2
GML2
+
+
r
2mr 2 C12 mr 2
−GMm
= Newtonian gravitational potential energy
r
L2
= repulsive centrifugal potential energy
2mr 2
GML2
C12 mr 2
energy added system (EM effect
=
as induced value (body' s motion))
(8)
of relativity theory (GTR) [13], by recalling MAGDAFE
(em = electromagnetic field) Eq. (1).
(9)
  v2 2
F = A1× 1 − 
  c12
 
If A2 = 0, then
(10)
(11)
− GMm
L2
GML2
+
+
r
2mr 2 C12 mr 2
V(r ) =
1  dr 
m 
2  dτ 
2
1  dr 
V(r ) = m 
2  dτ 
2
(12)
(13)
+ GMm
L
GML
V(r ) =
−
−
2
r
2mr
C12 mr 2
+ GMm
L
+ GMm  v 2
V(r ) =
−
−
×
2
 c12
r
r
2mr

2
+ GMm   v 2 2
V(r ) =
1−
  c12
r
 




2
  2
L2
 c1 +
 
2mr 2




 r
c1 dτ = 1 − s
r

2
2
2GM
2
(19)
(21)
− r dθ
2
(23
Where r = distance in meter, m, M = mass in kg, L = angular
momentum, C1 = C = speed of light and dτ = proper time.
Then, induction effect is back bone of physical interpretation
Reference Number: JO-0010
(26)
(16)








(29)
Force due to induced field =
GM
r2
m
(
v12
c12
− GM m v12 r 2 m
2
2 2
(30)
)
(31)
r c1 r m
Force due to induced field = −
 − GML2
F(em ) = 
 C12 mr 4

 − GML2
ζ (em ) = 
 C12 mr 3

GM m 2 v12 r 2
c12




 − GML2
Energy = ζ (em ) = 
 C12 mr 4

(23) ≡ (5)
2







 v12
F = −Gm1 −
 c12

(22)
C12
 2 2
dr 2
 c1 dt −
 rs

1 −
r

G × M × m   v 2 2
× 1−
  c12
r2
 
Adding induced field
F=
(15)
(20)
c12 dτ 2 = c12 dt 2 − dr 2 − r 2 dθ 2 − r 2 sin θ 2 dφ 2
Put θ = zero rs =
, then
(28)
2
E2
L2
L2
 dr 
2 rs
2
+ rd
  = 2 2 − c1 + − c1 −
r
 dτ 
m c1
2mr 2
mr 2
2
(25)
(17)
2
 rs
E2
 dr 
  = 2 2 − 1 −
d
τ
r
 

m c1




Force due to induced field = −
2

 − L
  2mr 2

(24)

 v12
F = − Gm − Gm
 c12



 E
 GMm
1  dr 
1
L
GML
m  = 
− mc12  +
−
+
2
2
2  dτ 
2
r
2mr
C12 mr 2
 2mc1

(18)
2
r2




(27)
2
2
G×M×m
  2

  + A 2 ×  1 −  v3

  c12

 
 G×M×m

F = 
+ induced F(em )
2
r


(14)
2
  v2 2
F = A1× 1 − 
  c12
 
If A1 =
So, effective potential =
V(r ) =
Vol. (3) – No. (1)




mr 4
(32)
(33)

r


(34)
(35)
(36)
Recall Eq. (8-23), → Eq. (37), EFE leads to Eq. (5) and
MAGDAFE leads to the same equation, EFE contains three
parts, Rμν means curvature & gμν means metric tensor & Tμν
means energy momentum change or two parts, Gμν means
Einstein tensor (s – t distortion due to field existence) &Tμν
means energy momentum change in s-t. MAGDAFE
(effective potential energy form) contains inverse law
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The Online Journal on Power and Energy Engineering (OJPEE)
(Newtonian gravitational law) & induction effect & change of
energy momentum or Lorentz force equation; it means space
distortion plus (t) distortion & change of energy momentum.
EFE depends on four dimensions (s-t), MAGDA depends on
field distortion in (s) with distortion of time of same field
(space distortion of dual field), also four dimensions but with
physical meaning [14].
 r 
dr 2
c12 dτ 2 = 1 − s  c12 dt 2 −
r 
 rs

1 −
r

c12 dτ 2 = ds 2



− r 2 dθ 2
(37)
arrow will be for a contact point with a manifold and short
green in an opposite direction will be dual field with time, it
means that space distortion of a field will be accompanied by
a space distortion of a dual field. EFE and Berwald-Moor
metric (new view), Berwald-Moor metric can be down to 2
EFE through Finsler geometry, norm vector expresses dual
field in MAGDA. Eq. (45) is one form of Berwald-Moor
metric.
ds4 = dx1 dx2 dx3 dx4
(45)
ds 4 = ds 2 ds 2
ds 2 = dx12 + dx 2 2 + dx 3 2 + dx 4 2
If
(48)
(39)
ds 4 = dx14 + dx 2 4 + dx 3 4 + dx 4 4
(zero cross points due to orthogonal)
dx 2 = a dx1 & dx 3 = b dx1 and dx 4 = c dx1
(49)
ds 4 = dx14 (1 + a 4 + b 4 + c4 )
(50)
In general relativity
ds = g ab dx a dx b
(40)
g = g ab dx a ⊗ dx b
(41)
G ab = K 0 Tab
(42)
2
(46)
(38)
with Cartesian coordinates,
dx 2 + dy 2 + dz 2 − c 2 t 2
Vol. (3) – No. (1)
1
R g ab
(43)
2
EFE≡ Eq. (5)= Eq. (38), MAGDAFE ≡ effective potential
equation ≡ Eq.(43) ≡ EFE, in MAGDA, EFE contains
induction effect, and space- time as 4 dimensions, for creation
any equation with space - time, it means existence of 2 fields,
one and its dual. MAGDA have two fields, one is called
gravity field, 2nd is dual of gravity field (electro-magnetic
field), dual field is gravity field norm Finally, where 4
dimensions of MAGDA will be detected by adding a space
distortion of one field to a time distortion of same field (it
will be created by space distortion of dual field of 1st one),
Need of dual field will be core of 4 dimensions application
[15], impossibility of motion without dual field (velocity of
dual field or not) is clear. Dual field can be recognized by
actual dual field (s/st/t) or same field with s-t as a package,
(EFE has already unification between gravity and
electromagnetic fields).
G ab = R ab −
ds 4 = dx1 dx 2 dx 3 dx 4
If
(1 + a
4
(1 + a
4
)
+ b4 + c4
abc
(47)
)
(51)
+ b4 + c4
= 1 then
abc
ds 4 = dx1 dx 2 dx 3 dx 4
(52)
Other form of Berwald-Moor metric is,
total G = ds12 + ds 2 2
(53)
From MAGDA ds(total ) = ds12 + ds 2 2
(54)
Action ds may be in form,"ds= change in dxi (1dimension)×
(invariant or other three dimension homogeneous change)",
i = 1..4, invariant or homogeneous change in other three
means qualitative.
ds 4 = (dx1 dx 2 dx 3 dx 4 ) gij
So, ds 4 = dx1 dx 2 dx 3 dx 4
(55)
(56)
It will be in Finsler geometry, multiplication will be missed
(Riemannian geometry), Recalling equations from Eq. (26) to
Eq. (44) will be extended.
With respect F (due to A1) we have
Figure (2): Expressing about dual of a field in space by
original one in time
In Figure 2, any field can be represented with a long arrow on
a tangent space with its 3 (x,y,z) coordinates & the tangent
Reference Number: JO-0010
ds12 = dx 2 + dy 2 + dz 2 − c 2 t = G1
(57)
With respect F (due to A2) we have
ds 2 2 = dx 2 + dy 2 + dz 2 − c 2 t = G 2
(58)
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The Online Journal on Power and Energy Engineering (OJPEE)
Total G of a system = G1 + G2 = G3
G3 = g ij (x, y ) dxi ⊗ dxj + h ab (x, y ) δya ⊗ δyt
(59)
(60)
Berwald-Moor metric (h, ν) can be formed in one of its
shapes (2 groups of EFE) [16].
R ab −
1
R g ab = K Tab
2
G ab 1 = K T ab
(61)
(62)
With specific Connection type of Finsler geometry [17], then
1
S ab − S h ab = K R Tab
2
(63)
G ab 2 = K T ab
(64)
The above equations are same as which was gained by
MAGDA, then Berwald-Moor metric can be reduced to EFE
simultaneously, it equals to MAGDAFE [18].
Figure (3): Diagram gab & hab of Berwald-moor metric
In Figure 3, complete diagram of two fields, field with s-t unit
and its dual field with st unit where gab can be formulated in
EFE and hab can be formulated in orthogonal positionEFE of
the 1st.
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