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Towards a New Physics (Based on the variable speed of light on quantum level)
Ioannis Xydous Independent Researcher, Greece
Copyright © 2017-2018 by Ioannis Xydous. All Rights Reserved
Abstract: The Author presents an alternative interpretation to quantum phenomena based on a non-constant
speed of light concept. Besides its enormous significance about the interaction between charged particles, it leads
to a new Mass-Energy equivalence that supplements Einstein’s original one. The technological implications of
this discovery may actually open the “doors” for real inertia control through electromagnetic means.
Keywords: Inertia, Variable Speed of Light, Special Relativity, EM Inertial Drive, Casimir Force, Electric Force
E-Mail: [email protected] Website: http://www.tnp.net.gr/
1. Introduction
i. Variable inertia thrust using a pair of forces
2. Inertia
3. Extending Einstein’s Relativity
i. Deviation from the expected relativistic deflection
4. Variable Speed of Light
i. Inertial Drive (Electromagnetic equivalent)
ii. Relativistic electrons suddenly vanish in the outer radiation belt
5. EM Inertial Drive
6. Electric Force
i. Derivation of the Casimir force
7. Universe Properties
8. Relativistic Hamiltonian
2
1. Introduction
The Schrödinger equation plays the role of
Newton’s laws and conservation of Energy
in classical mechanics. It is essentially
based on a wave function, which is able to
predict the outcome of an interaction in a
probabilistic manner. The present work is
an attempt to share an alternative view
(variable speed of light concept) in regards
to the underlying mechanism of kinetics
and tunneling effects of quantum world, by
reinterpreting existing laws of Physics.
Starting from the differential form of the
general equation of motion (Newton’s 2nd
law), implies:
1MRextRext RuFdt
dMuF
dt
pd
dt
pdFA
2mRextRext RuFdt
dmuF
dt
pd
FA: action force
Fext: external force M: object Mass
RM: rate of Mass ejection (as expelled from object Mass)
Rm: rate of mass displacement (medium displacement) uR: velocity of exhaust/displacement relative to object Mass
An object being at rest can be set in motion
either when an external force is exerted
upon it or an amount of its mass is expelled
from it (1) or an amount of medium mass
is being displaced (2) by it, always in
regards to its unchangeable center of mass.
Assuming the sum of all applying external
Forces is null, (1) and (2) become:
30dt
dMu
dt
pdFF RAext
40dt
dmu
dt
pdFF RAext
A positive relative velocity combined with
a positive mass rate would lead to no mass
ejection or medium mass displacement but
local mass confinement that would result
to object’s (M) inertia gain and eventually
to no motion.
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Consequently, the mass rate must be in
both cases negative and in order to agree
with the momentum conservation, the RHS
of (3) and (4) should have in front of them,
a negative sign:
0
extF
5dt
dMuFF
dt
pdF RTRA
and
6dt
dmuFF
dt
pdF RTRA
FR: reaction force
FT: thrust (reaction force)
The difference between (5) and (6) is that
(5) does not require (e.g. rocket thrust) a
material medium as compared to (6) e.g.
ship thrust. In Fig. 1 is presented a new
method of propulsion that uses internal
forces in order the object to propel itself.
Would Newton’s 2nd and 3rd law be in this
case violated? A short answer would be
“yes” since these laws are assumed to
apply to the center of mass of the object
that does not change while the force is
being exerted upon it.
The center of mass of an object is given by
the following expression:
i
n
i
iCMMCM rmM
rordmrM
r
1
11
The time derivative will give:
7)(1
1
i
n
i
iCM
CM rmdt
d
Mdt
rdu
or
81
1
i
n
i
iCM
CM umMdt
rdu
But:
91
n
i
iCMTOTAL puMp
and
10)(
1
n
i
iCMTOTALA
dt
pd
dt
uMd
dt
3
M
uRΔm
Thrust
Δm
MuR
Thrust
Tint
Fext1
Fext2
The expression (10) is identical to (2)
which is the compact form of the total
derivative. In absence of external forces,
(10) turns into (5) and (6):
111 dt
dMu
dt
pd
dt
pdF R
n
i
iTOTALA
or
121 dt
dmu
dt
pd
dt
pdF R
n
i
iTOTALA
A ship thrust mechanism is based on water
acceleration caused by the torque of the
propeller, where each water particle
acquires a mean momentum that is equal:
n
i
iTOTALA
dt
pd
dt
1
n
n
i
i pppdt
d
dt
pd
...21
1
pn ppppbut
...21
dt
dmnu
dt
pdn
dt
pd p
R
pn
i
i
1
dt
dmuF
dt
pdRA
n
i
i
1
Thus, for blades being at zero angle of
attack:
00
dt
dt
dmu TOTAL
AR
On the other hand, a variable inertia thrust
is created by the internal forces imbalance,
resulting to a redeployment of the center of
mass (blue dot on Fig. 1) that carries away
the entire mass of the object.
The mechanism that moves the center of
mass consists of a translation screw (see
Fig. 1) that transforms (assuming lossless
transformations) the applied moment of
pair forces to coupled mass (two trapezoid
rolling masses) linear motion:
02121
extextextextext FFFandFF
021 extcmextcm FrFrdt
Ld
n
i
iTOTALA
dt
pd
dt
1
nn
n
i
i ppppdt
d
dt
pd
...121
1
00... 121 nn pbutppp
131 dt
dmuF
dt
pd
dt
pdRA
nn
i
i
Reinterpretation of 2nd Law of motion Based on the internal forces imbalance
(Asymmetrical inertia reduction)
14dt
dmuF
dt
pdF RTA
or
15t
muF
t
pF RTA
mMR uuu
or
ba CMCMR uuu
FA: action force
FT: thrust (reaction force)
CM: center of mass CM(a): CM position during the inertia imbalance
CM(b): CM position prior the inertia imbalance
Fig.1 – Left: Ship thrust using a variable pitch propeller. Right: Object thrust using variable inertia (triggered by a pair of forces).
4
2. Inertia
The previous expressions lead to a novel
acceleration mechanism, which uses no
propellants and is applicable in absolute
vacuum.
Postulate (1): The acceleration of an object
is fundamentally created by the internal
forces imbalance (asymmetrical inertia
reduction), resulting to a redeployment of
the center of mass that carries away the
entire mass of the object.
A system of parts that transforms the linear
to rotational motion (coupled with Fext1)
makes Fig. 1 also relevant for external
forces having a non-null sum. Apparently,
(14) and (15) become:
Reinterpretation of 2nd Law of motion Based on the internal forces imbalance caused by external forces
(Asymmetrical inertia reduction)
16dt
dmuFF
dt
pdF RTextA
or
17t
muFF
t
pF RTextA
Postulate (2): The acceleration of an object
is fundamentally created by the internal
forces imbalance (asymmetrical inertia
reduction) while a non-null sum of external
forces is being applied to it.
Taking (17) one-step further and applying
it for charged particles then, the Δm can be
written as the difference between the actual
and the rest inertia:
mmm i
t
mmuF
t
p iRext
181
R
imu
pmm
Setting the relative velocity to a constant
maximum value that is indicative on how
fast the inertia changes are taking place, it
makes inertia depended just on momentum
variance.
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Since there are no mechanical or other
moving parts in quantum world, the
maximum allowed speed is addressed by
the electromagnetic interactions speed c.
The relativistic relative velocity equation
applies just for massive objects, but it
could also be used for the demonstration of
its limit when two objects move in parallel
but with opposite momenta:
cuandcu mM
19
12
cu
c
uu
uuu R
mM
mM
R
Fundamental Law of Inertia Non-Relativistic
201
mc
pmmi
mcpandcuR
Postulate (3): Initiation of motion or
acceleration of an object presupposes the
reduction of its rest inertia; otherwise,
acceleration can never take place.
Considering the construction with the
translation screw (Fig. 1) and the frame of
a charged particle as black boxes, the
question that arises for both is what is
being expelled from each of them while
they are being accelerated.
Postulate (4): The acceleration of an object
in vacuum presupposes the existence of a
medium (vacuum) that can be displaced
proportional to momentum variance.
The non-relativistic kinetic Energy based
on (20) is:
mc
pmuU
p
k 12
2
mmmcpmcpbut i 0/
21
2
22
pp
k
mu
mc
pmuU
5
3. Extending Einstein’s Relativity
The RHS of (20) represents the actual rest
mass of a charged particle that could be
blended with the relativistic expression as
follow:
2111
mc
pmm
mc
pm i
2211
2/1
2
2
c
u
mc
pmm
p
i
Assuming the initial momentum of a
charged particle is nearly zero then, the
momentum ratio of (21) becomes:
swsw pppbutppp 000
232
22
c
u
mc
p
mc
p
mc
p swswsw
Fundamental Law of Inertia Relativistic
2411
2/1
2
2
2
2
c
u
c
umm
psw
i
usw: speed during acceleration
up: speed post acceleration (final speed)
Obviously, the new relativistic expression
is described by two different speeds. The
usw represents the changing speed, which
equals to up while the charge is being
accelerated. On the other hand, the up is the
final speed when the charge in not any
more under the influence of an electrostatic
potential (post acceleration).
Fundamental Law of Inertia General Relativistic Inertial Mass
2511
2/1
2
2
2
2
c
u
c
umm
psw
i
Relativistic Inertial Mass during acceleration
swp uu
261
2/1
2
2
c
umm sw
i
Relativistic Inertial Mass post acceleration
0swu
271
2/1
2
2
c
umm
p
i
Back to Contents
The expression (26) was discovered first
by Ricardo L. Carezani who derived it
using a single reference frame for the
coordinate transformations, in his work
called Autodynamics.
Stemming from (20) and (24), the kinetic
Energy is now given by:
Kinetic Energy General Relativistic Kinetic Energy
28112
22
c
umcU
sw
k
Kinetic Energy during acceleration
swp uu
29112
22
c
umcU
sw
k
Kinetic Energy (Einstein) post acceleration
0swu
3012 mcUk
The Lorentz factor can be expanded into a
Taylor series, obtaining:
n
k
n
n
pp
k
k
c
u
c
u
1
2
0
2/1
2
2
2
121
..8
3
2
111
422/1
2
2
c
u
c
u
c
u ppp
Thus:
24
2
1
8
3
c
u
c
ucu
pp
p
22/1
2
2
2
111
c
u
c
u pp
Hence, the classical limit of the relativistic
kinetic Energy becomes:
11
2
22
c
umcU
sw
k
2
2
22
2
11
c
u
c
umcU
psw
k
3112 2
22
c
umuU
swp
k
6
A classical electrostatic deflection setup
that uses careful scaling and Energy levels
is proposed for the detection of significant
deviations from Einstein’s Relativity:
Electrodynamics Electrostatic deflection
xpeeeiee umVqmmcmVq 2
1
2
12
1
X-Axis: Non-relativistic
x
x
p
c
e
ep
u
ltand
m
Vqu
2/1
12
Y-Axis: Relativistic
ci
eeiee
d
V
m
qammcmVq 22
1 03.0
x
y
p
c
ci
ep
u
l
d
V
m
qatu 2
Inside E2: Acceleration
c
c
i
esw
d
l
V
V
m
matyVV
2
1
2
2
1242
32tan 2
sp
p
d
y
u
u
x
y
Exiting E2: Post acceleration
c
sc
i
esw
d
dl
V
V
m
myV
1
22
20
Vertical Deflection on screen
21 yyy
The product psw∙c of (23) is equivalent to:
332
2
22 c
u
cm
Vq
cm
cp sw
e
swe
e
sw
Then (25) becomes:
3411
2/1
2
2
2
c
u
cm
Vqmm
yp
e
swe
ei
and
2
2/1
2
2
2
2 1 cmc
ucmVq e
p
ee
y
35112
2
2/1
2
2
cm
Vq
c
u
e
epy
Placing (35) onto (34) results:
36112
2
2
cm
Vq
cm
Vqmm
e
e
e
swe
ei
Finally:
2
2
2
2
1
212
14
cm
Vqd
l
V
VyVV
e
ec
c
sw
2
21
22
12
0
cm
Vqd
dl
V
VyV
e
e
c
scsw
KVVandVV 352000 21
mlandmd cc 1.03.0
mds 01.0 Extended Relativity
cmmy 4.17174.0
Einstein’s Relativity cmmy 4.16164.0
Fig.2 – Deviation from the expected Relativistic deflection.
7
4. Variable Speed of Light
The general relativistic Energy of an
arbitrary charged particle is given by the
product of (25) or (36) with the speed of
light squared:
General Relativistic Energy
3711
2/1
2
2
2
22
c
u
c
umcU
psw
i
or
381122
2
mc
qV
mc
qVmcU
sw
i
A closer look to both expressions reveals a
new factor that might be an alternative to
the variable inertia mechanism:
2/1
2
2
2
22 11
c
u
c
umc
psw
2/1
2
2
1
c
umcu
p
and
22
2 11mc
qV
mc
qVmc
sw
21
mc
qVmcu
Variable speed of light
391122
2
mc
qVc
c
ucu
swsw
0swqV (Always)
usw: speed during acceleration Vsw: local electrostatic potential (during acceleration)
Postulate (5): The speed of light varies
proportional to the magnitude of the local
electrostatic potential.
Based on (38) and (39), the electrostatic
potential Energy becomes:
2
2121 14 cm
Vqcuand
c
u
r
qqU
toto
E
but
r
qqVq
o4
2121
21 qqtot mmm
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Electrostatic potential Energy (q1 in the presence of q2)
1.394
21
c
u
r
qqU
o
E
40)(4
12
21
21
cmmr
qqcu
qqo
or
41)(4
14 2
2121
21
cmmr
r
qqU
qqoo
E
Setting (40) equals to zero:
0)(4
102
21
21cmmr
qqu
qqo
42)(4 2
21
21cmm
qqr
qqo
hcmmbut qq )(
21
Then (42) becomes:
hc
qqr
o
4
21
Fine structure constant (General form)
432
2 21
hc
qqr
o
or
4422
21
cmm
h
rrqq
Postulate (6): The speed of light varies
inverse proportional to the separation
distance between two arbitrary charged
particles or from the surface of each one
separately.
The electromagnetic equivalent of a pair of
forces that might additionally play the role
of a translation screw (see Fig. 1) is two
EM waves having opposite momenta,
forming an EM standing wave. The thrust
mechanism is completed by coupling the
mass (M) within the standing wave.
8
MuR
Thrust
Fext1 Fext2
MuR
Thrust
Tint
Fext1
Fext2
Δp
Δp
Δp
Fint1 Fint2
AC
A frequency or phase shift on standing
wave results to anti-nodes shift that carries
the coupled (trapped) mass (M) away. It is
worth noticing the translation screw
mechanism (see Fig. 3) is within the mass
(M) and can be set in motion either by
external or internal forces (internal torque
Tint).
On the other hand, the standing wave
(electromagnetic translation screw) of a
real EM Inertial Drive is actually created
and set in motion from within the mass
(M), which means the generator is located
and coupled to mass (M) from inside (or
outside for small prototypes and just for
demonstration purposes).
The concept of the moving standing wave
was discovered first by Yuri N. Ivanov in
his work called Rhythmodynamics, which
addresses the nature of motion of an object
in a non-relativistic manner giving results
that are very different from this work.
A standing wave is consisted of two
identical waves and a frequency equals to
2f that corresponds to a π phase. Thus:
shiftsss
ffbutf
f
f
f2
22
c
f
fc
f
f ss
22
Standing wave speed
Based on the standing wave frequency or phase shift
452
c
f
fcu s
sw
EM Inertial Drive Based on the variable speed of light on quantum level
4611
2/1
2
2
2
2
c
u
c
uMM Msw
i
or
471
2/1
2
2
c
uMcuU M
i
482
12
2
c
f
fcuand
c
ucu s
sw
sw
During the standing wave frequency or phase shift
c
f
fcuu s
swM 2
swM uu0
4912
2/1
2
2
2
Mc
c
uMcU M
i
Reaching the speed of light
0 iswM Ucuuif
0u
Faster than Light (FTL)
imaginaryUcuuif iswM
0u usw: standing wave speed
u: propagation speed (velocity) of the electromagnetic waves
Wave-Particle Relativistic Energy
5011
2/1
2
2
2
22
c
u
c
umcU
psw
i
swp uu0
m
qVc
f
fcuu
swsswp
2
Fig.3 – Right: Inertial Drive (Electromagnetic equivalent): Mass (M) coupled within an EM standing wave (EM translation screw).
9
During solar storms, relativistic electrons
have been known suddenly to vanish from
the radiation belt. The strange phenomenon
was discovered back in 1960s and it has
puzzled scientists ever since. Some latest
reports appear to have indications through
satellite probes that the effect appears to be
associated with a ULF or VLF wave-
particle interaction.
Relativistic electrons suddenly vanish (Quantum tunneling through the vacuum)
Wave-Particle Relativistic Kinetic Energy
2/1
2
2
12
c
uand
f
fctau
pssw
51112
22
c
ucmU
sw
ek
or
5211
2
2
2
c
tacmU sw
ek
During the standing wave frequency or phase shift
c
f
fctauu s
swswp 2
2
2
1c
ucu
sw
53112
22/1
2
2
2
c
u
c
ucmU
swswek
Reaching the speed of light
0 kswp Ucuuif
0u usw: standing wave speed
u: propagation speed (velocity) of the electromagnetic waves
Fig.4 – Electrons Relativistic kinetic Energy drops proportional to standing wave (wave-particle) speed squared.
10
5. EM Inertial Drive
The simplest version of an EM Inertial
Drive that may demonstrate its basic
working principle (acceleration over the
redeployment of its center of mass using
internal forces) is consisted of a coil with a
ferrite ring core, a signal generator and a
power amplifier.
L1
Signal Generator
R1
PowerAmplifier
GND GND
A ferrite core is a composite material
(Mn/Zn) having a density of 4900 Kgr/m3
that is close to the monatomic Selenium
element (4819 Kgr/m3). Applying (25) and
(33) for the non-relativistic case, results:
22
2
mc
qV
c
uandcu
swsw
p
1.531122
2
mc
qVm
c
umm
swsw
i
Replacing the electrostatic potential with
an EM wave Energy, (53.1) becomes:
2.5312
mc
UmmUqV EM
iEMsw
The rest Energy of an atom in vacuum is
given by the known mc2. In a different
medium, the atom appears a rest Energy
equals:
r
Mn
mcmcumc
22
3.5312
r
EMi n
mc
Umm
or
4.531
M
EMi
mcu
Umm
The ring coil in Fig. 5 is actually a closed
loop Antenna having a radiation resistance:
5.533
82
2
3
M
Mr
ANRR
RM: radiation resistance of medium
λM: wavelength in medium
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In an arbitrary medium, the propagation
speed of the EM waves is given by the
following general expression: 2/1
2
00 112
rrMu
Metals and ferromagnetic materials for f<200 KHz
6.534
0
r
M
fufor
7.530f
uanduR M
MMrM
The applied power density for a single
particle equals to the applied power density
for the bulk material:
A
RIaDaP
a
PD
A
PD r
ppp
p
p
p
2
8.532
f
RI
A
a
f
PUU rpp
EMEM p
EM Inertial Drive Non-Relativistic basic equation (ferromagnetic material)
9.531
M
EMi
mcu
Umm
fmcu
RI
A
amm
M
rp
i
2
1
Technical data from Author’s conducted experiment 61094.110294.1 24
.)(
219 NmAAandma effRp
181 sec103108500 mcandmSandr OhmRmuHzf rM 29.2sec8185694 1
resistance radiation ring the through currentAI 24.0
Kgrm 251031.1 speedconstant for force (measured) requiredNFF 4.0
massringerritefKgrmF 2.0 force friction staticmeasuredNFSF 6.0 force friction kinetic measuredNFKF 4.0
speedring measured musw sec/01.0
261035.81 Immi
Nfumut
mF MFM
FF 47.0
or mHzfNfumF ssMFF 2847.0
Force to Power Input
KWNWNPF inF /3.212247.0
Fig.5 – EM Inertial Drive prototype.
11
6. Electric Force
The electric force between two arbitrary
charged particles is the derivative of the
electrostatic potential Energy (see (41)):
2
2121
)(41
421
cmmr
r
qqU
qqoo
E
dr
dUF E
E
Electric Force
Between two arbitrary stationary charges Magnitude and Vector form
021qq
54
21
4 2
21
2
21
21
rcmm
r
qqF
qqoo
E
55
844222
22
12
3
21
21r
r
cmm
r
rqqF
qqoo
E
and
021qq
56
21
4 2
21
2
21
21
rcmm
r
qqF
qqoo
E
57
844222
22
12
3
21
21r
r
cmm
r
rqqF
qqoo
E
The expression (55) is consisted of two
parts, an attractive and a repulsive one, e.g.
(Fig. 6) electric force and electrostatic
potential Energy between two electrons.
Then from (56):
eqqe mmmandqqq 2121
584
14 2
2
2
2
rcm
q
r
qF
eo
e
o
e
E
Hence (58), becomes practically the known
Coulomb force when:
04 2
2
rcm
q
eo
e
mr ce 111092.14
100
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Then:
99985.0
1001
4100
2
2
ceeo
ece
cm
qr
2
2
2
2
2
2
441
4 r
q
rcm
q
r
qF
o
e
eo
e
o
e
E
The local maximum of the electric force
occurs when:
0
41
4 2
2
2
2
rcm
q
r
q
dr
d
dr
dF
eo
e
o
eE
mrcm
qr e
eo
e 15
2
2
1022.42
3
42
3
NFE 32.4
NFandNF AttractiveCoulomb 63.895.12
The electric force becomes zero when:
0
41
4 2
2
2
2
rcm
q
r
qF
eo
e
o
e
E
mcm
qrorr
eo
e 15
2
2
10817.24
NFE 00.0
NFandNF AttractiveCoulomb 10.2910.29
The electric force appears a maximum
when the electrostatic potential Energy
goes to zero:
mr
cm
qr e
eo
e 15
2
2
1040855.128
NFE 118
Now the derivation of the electric field of a
single charge requires knowing the
expression of the electrostatic potential:
qqq mmmandqqq2121
q
UV E
E
Electrostatic Potential
At a distance from an arbitrary charge
598
14 2
2
rcm
q
r
qV
qoo
E
12
Electric Field Magnitude and Vector form
EVE
604
14 2
2
2
rcm
q
r
qE
qoo
61164
4222
3
3r
r
cm
q
r
rqE
qoo
The second term of the electric force
appears to have a link to the Casimir force.
Starting from (58):
rcm
q
r
qF
eo
e
o
e
E 2
2
2
2
41
4
ACbE FFF
6216 3222
4
rcm
qF
eo
e
A
Then, from the fine structure constant:
ce
e
o
e
o
e
ce
e rc
q
c
qr
2
44
2 22
32
22 1
4 rcm
qF
eo
e
A
32
2
12
rcm
rcF
ece
eA
ece
e
ce
Amr
rF
3
22 4
c
c
mrrF
ecece
eA
3
24
Thus:
63422
e
e
ce rAandcm
h
644 3r
cAFA
AArAr
e
24
2
Second term of the Electric Force Second term turns to Casimir force at critical distance
6505.2488 4
2
43
2
r
cA
r
cAFA
2ec rrr
3222
4
4
2
1605.248 ceo
e
c
Arcm
q
r
cAF
ecee
c rAr
rr 2422
General form of the attractive Casimir Force
66
05.2484 4
2
3 r
cA
r
cAFA
Deviation from the original Casimir Force
%24.31 Casimir
A
F
F
General form of the repulsive Casimir Force
67
05.2484 4
2
3 r
cA
r
cAFA
Fig.6 – Left: Electric force (two electrons) and electrostatic potential Energy diagrams. Right: Electron’s electric field.
13
7. Universe Properties
The (62) and (64) are based on electron-
electron interaction and can be written as
follow:
242 e
e
ce rAandcm
h
68416 33222
4
r
cA
rcm
qF
eo
e
A
The above might be equivalent to a
gravitational force between two electrons
using a variable gravitational constant:
6916 3222
4
2
2
rcm
q
r
mGF
eo
eerA
and
702
43
2
2
2
r
cr
r
mGF
ce
eer
A
Variable Gravitational constant
7116 2322
4
rcm
qG
eo
e
r
or
72
23
r
r
h
cG ece
r
Setting (71) or (72) equals to Newtonian
Gravitational constant results a number in
the scale of the Universe radius (see Lars
Waehlin, “The Deadbeat Universe”):
Universe Properties
GGr
2
2111067384.6
Kgr
mNG
Universe Radius
7316
23
2322
4
G
r
h
c
Gcm
qrr ece
eo
e
u
mru
28101763.1
Universe Age
sec109211.3 19c
rt uu
or
yrc
rt uu
9103.1243
Back to Contents
Universe Properties
Universe minimum frequency
Hz
tf
u
21
min 100589.42
1
Universe deceleration
212
2
2
sec106509.7 mcr
hG
r
ca
ceeu
u
Universe Mass
KgrG
raM uu
u
55
2
105863.1
Universe Energy
JouleсME uu
722 104277.1
Universe thermodynamic Temperature
KelvinS
fET
u
u 768.24min
422
8
sec106704.5
Km
Joule
uu
u
uu rSandT
S
fED 24min 4
A dimensional analysis of (72) or by
setting:
GGr
euq rrr Minimum possible distance
Quantum Length
mc
hGr
ce
q
58
3107502.6
Quantum Graininess (Science Daily Link)
Quantum Time
sec102501.2 66
4
c
hG
c
rt
ce
q
q
Fine structure constant Linked to the dimensions of the Universe
742
equ rrr
752
4
2 2
ce
qu
o
e
ce
err
c
qr
14
8. Relativistic Hamiltonian
The relativistic Hamiltonian of a charged
particle as influenced by an electrostatic
potential (constant potential) is given by:
76222
VqmcpcH p
p: charged particle’s momentum V: electrostatic potential
The (76) under a non-constant speed of
light turns into:
General Relativistic Hamiltonian Based on the variable speed of light on quantum level
Hc
uH i
2
2
211
c
uc
mc
Vqcu
swswp
77222
qVmcpc
c
uHi
HHcumcqV i 2
Electric Force upon a single charge Partial Hamiltonian Derivative
Ei F
r
H
dt
dp
r
qVV
o
sw4
782
14 22
rmc
r
qqF
o
p
o
p
E
2
2
4 r
qqFcumcqV
o
p
E
or
22 42 r
qqFcu
mc
qqr
o
EPE
o
p
Since the ratio of velocities in (23) equals
to the ratio of momentums, then:
2
2
2
mc
p
c
u swsw
Variable speed of light
7911
2
2
2
mc
pc
c
ucu swsw
Back to Contents
General Relativistic Energy
222
2/1
2
2
1 mcpcc
u
c
umcu
p
LHS RHS
2
2
2
11mc
pc
c
ucu swsw
Velocity (speed) of a single charge Partial Hamiltonian Derivative
pi u
p
H
dt
dr
During acceleration
ppuuVV swpswsw
2
2
2
11mc
pc
c
ucu swsw
80
2/12
22
111
mc
p
mc
pcu p
usw: changing speed (during acceleration) psw: changing momentum (during acceleration)
Post interaction
ppuuVV swpswEPsw 000
cu
81
21 mcp
mpup
up: charged particle’s final speed p: charged particle’s final momentum
15
Conclusion
The discovery of a variable speed of light proposes a new but falsifiable mechanism as the
main cause behind the quantum phenomena, through a single and consisted theoretical
framework.
References
[1] Richard P. Feynman, “Feynman Lectures on Physics” 1963 USA
[2] Ricardo L. Carezani, “Autodynamics” 1999 USA
[3] Ivanov Y. Nikolayevich, “Rhythmodynamics” 2007 Moscow
[4] Lars Waehlin, “The Deadbeat Universe” 1997 Colorado
[5] Nature Communications, “Ultra-low-frequency wave-driven diffusion of radiation belt relativistic electrons”
DOI: 10.1038/ncomms10096
I would like to thank my wife Svitlana Ksidu from my heart for her great understanding, encouragement, patience and support.
Otherwise, it would be impossible the initiation and writing of the work “Towards a New Physics”.
