Journal of Modern Physics, 2011, 2, 431-446
doi:10.4236/jmp.2011.26053 Published Online June 2011 (http://www.SciRP.org/journal/jmp)
431
Lorentz’s Transformations and Gravitation in the
Granular Space Theory
Vladimir Konushko
Protvino, Moscow, Russia
Received October 19, 2010; revised March 10, 2011; accepted April 12, 2011
Abstract
Research into the read structure of space at ways leads to the conclusion on the existence of a privileged
(absolute) system of reference, with all the equations remaining invariant about Lorentz’s transformations.
The expansion of these transformations makes it possible to obtain easily the Schwarzshild matrix and, also,
all the results of Einstein’s theory of gravity. The untangling of the physical meaning of velocity as a meas-
ure of relative deformation of elementary space cells eliminates, at last, all the paradoxes of Lorentz’s trans-
formations and allows visual observation of the mechanism of gravity and Coulomb interaction in imaginary
experiments.
Keywords: Lorentz’s Transformations
1. Absolute Space Reality
The radical change in our ideas of space and time ex-
pressed in Lorentz’s transformations has a deep effect on
the whole physics. This fact makes every subsequent
generation of researchers reanalyze the unusual ratios
following from these transformations since there are a lot
of paradoxes here. The results of modern physics force
us again to discuss such basic concepts as reality, space
and time.
Here we want to understand something real and the
meaning of this reality rather than just to manipulate
formulas and predict correctly the results of experiment.
When formulating his laws of mechanics Newton in-
troduced the concept of absolute space that always re-
mains the same and static. It was relative to this space
that he determined acceleration of bodies. This accelera-
tion was absolute by nature and inertia is considered with
reference to this absolute space.
If a gyroscope is placed on the Earth so that it can
freely rotate around three mutually perpendicular axes, it
retains the directions of the rotating axis with respect to
the inertial coordinate system. Therefore, the gyroscope
seems to be moving relative to the rotating Earth. Thus,
the rotating axis of a free gyroscope is always directed to
one and the same star (the proper motion of the star can
be neglected due to its huge remoteness).
This example makes us consider again the nature of
inertia effects. If the Earth were covered with clouds all
the time, we would certainly try to explain the “strange”
motion of the gyroscope about the Earth involving New-
ton’s idea about the existence of absolute space to the
reference of which the Earth rotates. Indeed, any attempt
to find a visible cause of gyroscope axis motion would
be vain.
According to Newton, space exists even when it is free
of all physical bodies; the effect of inertia will exist in
this case as well. It is Newton’s opinion that absolute
space is only able to act on bodies (to resist to their ac-
celeration) but matter cannot act on this space. Later,
criticizing this Newton’s theory Einstein said that this
declaration contradicts our scientific understanding of
effects: how can we visualize something that can exhibit
an effect but cannot be acted on?
In 1902 Puancaret in his book “Science and Hypothe-
sis” wrote that “… there is no absolute space and we
only get to know relative motions.” When studying this
book Einstein said in his first description of the Universe
model in 1917 that “… in the successive relativity theory
there cannot be any inertia about “space” but just mass
inertia about each other.”
Even materialist-philosophers, however, interpreted
the concept of matter as an indestructible and unreadable
basis of the entire existing matter.
Later Einstein studied this problem again and consid-
ered the case of two bodies infinitely removed and so not

432

V. KONUSHKO
exhibiting a gravitational effect of ball-shaped bodies
which rotate relative to the axis passing through the cen-
tre of one of them.
Actually and in Einstein’s theory of gravity the rota-
tion of a body is absolute motion which was first noted
by Weyl.
The introduction of this hypothesis (abstraction) as
absolute space turned out to be very fruitful, and only
350 year later we can reanimate this assumption by stat-
ing that it is not only space but also all the bodies in the
Universe are made up of only one element of a tree-di-
mensional elementary cell the size of which was deter-
mined by Planck in 1900 [1].
If we accept this assumption, we get a privileged sys-
tem of reference—absolute. In practice its role is played
well enough by system of reference related to far-re-
moved star called the system of “state” stars whose pro-
per motion can be neglected because of their huge re-
moteness.
2. Equality of Rights of Inertial Systems
At present all the inertial systems of reference are con-
sidered to be physically equivalent and none of them can
be preferred to the others. So, inertial systems are equiv-
alent in two respects:
1) Equivalent about the form-invariance of natural
laws.
2) Equivalent about the course of physical processes.
From the second statement it follows that any of two
inertial systems can be considered static. If the stationary
observer wished he would say to the moving one, “Your
watch is slow.” But the moving observer could say
equally well, “My watch is right but yours is slow” be-
cause, from his point of view, he is motionless and the
so-called stationary observer is moving with the same
velocity in the opposite direction.
There is no question that the physical equations in
each individual system of reference are equal but the
second statement that any inertial system can be referred
to as stationary is doubtful.
Let us consider a specific case when two trains, A and
B, move to meat each other with the same velocity to-
wards the station where the observer C is standing. The
observers A and B begin moving from the same distance
to the station C, all of them having high—precision
(atomic) watches previously synchronized.
The observer A can consider himself at rest, then it
will seem to him that the observer B is moving to meet
him with the velocity and all the physical
processes for the observer B must slow down with the
factor

2vv c

:
2
2
4
1v
c
  .
The observer B, in his turn, can consider himself mo-
tionless, and all the processes will slow down in the train
A with the same factor γ. When the trains meet, all the
three observers register the time by their watches and
then compare the results. To their surprise A and B will
find that they are absolutely wrong because they have
made two mistakes.
1) Their watches will show the same time.
2) The readings of their watches are slower than that
of C not by the factor γ but by

:
2
2
1v
c

.
Right was the observer C who moved slower about the
absolute reference system (fixed stars). To escape errors
all the three observers were to take only the reference
system C, connected with the platform, as a static one.
This imaginary experiment can be easily made real but
the result of this experiment is quite clear, we have just
set it forth.
For over half a century physicists have been observing
the deceleration of a physical process in a fast flying
elementary particle, a muon, - an increase in lifetime.
The observer in the reference system of the flying muon
will think that he and the muon are at rest whereas the
Earth flies at a huge rate to the opposite direction. Hence,
from their standpoint, the rest muons on the Earth move
very fast with the Earth, and their lifetime increases as
compared to the muons in their system. This conclusion
is invalidated completely by the semi-centennial obser-
vations. No matter how we manipulate reference systems,
a fast-moving muon will always live longer than a static
one. So, a real situation cannot be equalized with an
imaginary one. Space itself “knows” which muon flies
faster about fixed stars.
Finally, let us analyze the clock or twin paradox that
has been written about a lot but everybody avoided find-
ing the right solution of this paradox. There was a wish
to retain the reciprocity: an inertial system where the
twin-astronaut is at rest and the Earth flies away to the
opposite direction at the same velocity with the astronaut
is believed no worse than a system where the Earth is at
rest and the astronaut is moving. As this takes place, the
imaginary reference system has equal rights with the real
one.
Reciprocity is needed for Lorentz’s transformations to
form a group. Once Einstein said that «mathematics is
the most perfect way of pulling your own nose». It can
be just a maidservant of physics but never the queen.
It is stated that a twin-astronaut undergoes acceleration

V. KONUSHKO
433
and deceleration several times, that is why his physical
processes are slowed down to a greater extent. The fact
that a twin-traveler may fly away from the Earth, with
the same velocity, over a distance of one thousand or one
million kilometers is ignored is this case. In the second
case the deceleration will be one thousand tines larger
than in the first case even though the time of acceleration
and deceleration is the same. As a result, the solution of
this paradox sounds like a spell: the role of the accelera-
tion undergone by a twin-astronaut is that at the turning
point be passes into another noninertial reference system
and from this point a different time reading begins.
It is well known that, as physics was developed, all the
great achievements brought prejudices and myths which
were sometimes helpful and sometimes very harmful for
further progress of science. History of science knows a
lot of really wonderful ideas which have stood mankind
and science in good stead but, nevertheless, have left the
stage of science since have not turned out to be real ob-
jectively. For example, using the representation of
“heatgen” scientists have deduced formulas for thermo-
dynamics not rejected even today.
Absolute space ascertains, finally, a hierarchy of iner-
tial reference systems—another natural law which is not
worse at all than the law of conservation of energy or
momentum: all physical processes are decelerated to a
greater extent in the inertial system moving at a higher
velocity about the absolute system of reference.
Only one hundred years after the birth of the specific
theory of relativity the granular space theory solves the
twin paradox in the most natural way, without stretches
and speculations. The reference system in which the twin
0’ flies into space and the twin 0 stays on the Earth is
real. The Earth moves with a lower velocity about sta-
tionary stars, and so we consider it static; and since the
twin 0’ flies in his rocket with a high velocity about sta-
tionary stars, all his physical processes, including bio-
logical ones, are decelerated.
When the twin 0’ in the rocket thinks that he is at vest
about the stars and the Earth flies away in the opposite
direction from him, this system is not real but imaginary
and unrelated to the existing situation: no matter what he
thinks, his rocket flies faster than the Earth and the proc-
esses are slowed down or him as before. Thus, neither
acceleration nor the inclusion of gravitational affects
(Einstein’s equivalence principle) are related to this pa-
radox. To solve this paradox we have to go beyond the
existing paradigm and to accept absolute material space
de facto.
It should be said that Einstein did not like rather a poor
word “relativity” introduced in physics by Planck and
continued to refer to specific theory of relativity as the-
ory of invariants. Of interest is the following phenome-
non: such things can be observed by as for a hundred
years but, nevertheless, ignored due to prejudices about
what is essential and what is not. The mathematic re-
quirement of reciprocity and, hence, the existence of the
elegant Lorentz’s group has exceeded the physical part
of natural phenomena.
The direct Lorentz’s transformation can be expressed
as:

2
x
vt
x
lvc




,



2
2
tvcx
t
lvc

 


,
where the primed quantities belong to the moving refer-
ence system. It is easy to get the inverse Lorentz’s trans-
formation:

2
x
vt
x
lvc



,



2
2
tvcx
t
lvc



.
And this fact was a source of a mistake. Indeed, the
physical situation has not change at all: the primed ref-
erence system K’ moves, as before, faster than the sys-
tem K about fixed stars and the physical processes are
slowed down to a greater extent in this system. Starting
from 1905, however, it has been stated that the K’ system
can be considered at rest and the K system in this case
will move with the velocity ν in the opposite direction.
This free handling with mathematic symbols has given
birth to many paradoxes in Lorentz’s transformations and
distorted their physical meaning.
It is often written that a moving clock is decelerated
but this is in conflict with the principle of relativity. The
clock speed in all the inertial reference systems remains
constant. They register the physical time similarly in
their inertial reference systems. It is not the clock speed
that changes but the time of the physical process. The
durations of local physical processes measured by a
clock in a certain inertial reference system and in any
other system are different which again proves the ab-
sence of process-invariance.
At present there is even not a hint at why all physical
processes are retarded in fast reference systems as well
as in gravitational fields. Nobody has ever observed ac-
celeration of processes. It is very surprising to see that
the formula incorporating the deceleration of physical
processes is the same for fast reference systems and for
gravitational fields.

434 V. KONUSHKO
In case of a gravitational field formed by the mass M
the relation between the invariant intrinsic time τ and the
coordinate time t can be expressed thus
  
2
2
2
d1d 1d
g
rGM
t
rcr

 
 
 


2
t
and near the surface of M
 
2
22
2
2
d1 d
vt
c


 

 ,
where rg is the mass gravitational radius, v2 is the escape
velocity.
In a similar manner, if particle flies with the velocity v
about a motionless reference system, its life time t in-
creases according to the formula
2
22
2
2
1vt
c


 


,
where τ is the life time of a particle in the intrinsic refer-
ence system. The fact that these two formulas are abso-
lutely similar shows again that velocity describes both
dynamics and statics. In other words, v2/c2 is the relative
deformation of space cells.
The kinetic energy of a moving particle carries a mass:
E = mc2. This mass deforms the cells near the particle
thus hampering its decay.
The gravitational field in the granular space theory
constitutes deformed space cells acting on the particle in
quite a similar manner, that is, they hinder its decay thus
increasing its life time. That is why we have never ob-
served acceleration of particle decay but only decelera-
tion. And again we can draw the conclusion that all
physical and biological processes can be reduced to one:
and that is deformation of elementary space cells.
We can say that an essential element of progress in
science is the evidence of invalidity of either a theory, on
the whole, or some its theses. Despite the fact that all the
physical laws in inertial systems have one and the same
form, their behavior in most cases is different. The irony
is that in 1905 Einstein in his article “Electrodynamics of
moving media” studied, maybe, the only case when both
the situations conform to reciprocity—the Faraday ex-
periment on initiation of electromagnetic induction.
Let as have a coil with conducting wire around it and
connected with a galvanometer and a magnet.
The first situation: the coil is at rest, the magnet is
moving—a current is induced in the coil.
The second situation: the magnet is at rest, the coil is
moving with the same velocity—the same current is in-
duced in the coil; the coil is moving in the opposite di-
rection.
As applied to the twin paradox, the second situation
could mean that we slowed down “by hand” the rocket to
the speed of the Earth and imparted the speed of the
rocket to the Earth, but in the apposite direction.
Thus, after considering a real experiment complying
with reciprocity Einstein drew a wrong conclusion (a
typical example of a logical error) regarding the com-
plete equality of inertial systems which caused the abso-
lute reference system and absolute space to be negated
and delayed the study into the real material structure of
space for a hundred years.
There is another apparent paradox. Let a body fly with
the velocity u = – 3/4c about an inertial reference frame,
and another body flies with the same velocity v = 3/4c to
meet it. According to the classical law of composition of
velocities, the bodies can met with 3/2c > c. But Lor-
entz’s transformations give a different law of composi-
tion of velocities

2
24 !
25 1
uv c
uc
uv c



Both imaginary and real experiments show that the
approach velocity of two bodies is 3/2c but this conclu-
sion does not contradict Lorentz’s transformations. In
this case we can observe the underwater part of velocity:
v2/c2 is the relative deformation of space cells. In Lor-
entz’s deformations u and v conceal the degree of defor-
mation of elementary cells which cannot be higher than
the maximum deformation relating to c [2].
One of the most difficult and unusual Einstein’s
statements is that the velocity of light is constant in any
inertial system independent of the method of its meas-
urement. The sequence of this postulate is the contraction
of length of the moving object. Since a body moving in
field-free space is not acted upon by any forces, this con-
traction is called “kinematic”. So, this term conceals our
unability to understand the essence of this contraction.
To reveal this mystery, let’s consider the following
imaginary experiment that can be easily become real.
Let an observer A stand on a platform and B in a fast
moving train. When the back wall of the carriage comes
up with the observer A, the lamp fixed on this wall flares
up and the photons begin to travel towards the front wall.
Both the observers fix the time of the flash and the mo-
ment when the photons reach the front wall. Besides, the
observer A on the platform measures the distance L cov-
ered by a photon in the time ΔT.
The observer B in the carriage measures the photon
path, too, which equals the carriage length l and its travel
time Δt.
Then both the observers calculate the velocity of light
in their inertial systems:
vLTc


and

V. KONUSHKO
435
ultc.
From the standpoint of A the observer B is wrong be-
cause he has measured wrongly the photon travel path
equal to l and, hence, the velocity of light measured by B
must be different. Everything became clear when the
observers compared the readings of their watches:
22
1tT vc,
where v is the carriage speed. But in this case the relation
22
1lL vc
holds true.
Thus, there is neither real nor “kinematic” contraction
in length of objects; this “contraction” means that the
observers in different reference systems measure differ-
ent lengths.
In the second part of this experiment both the observ-
ers measure the velocity of light in the case when the
photons move from the front wall to the rear, i.e. oppo-
site to the train. All the physical processes will be re-
tarded, as before, near the observer B, and the distance
covered by the photons is equal to l. But the time of
movement of the photons from the front wall to the rear
one is shorter than t and, hence, the measured velocity of
light C2 is higher than in the first case: C2 > C1.
The perfect accuracy of atomic clock at present is suf-
ficient to detect the difference in the velocity of light
being measured. The importance of this experiment can-
not be overestimated for the following reason. Starting
from Galileo, for the following reason. Starting from
Galileo, 400 years ago, it has been believed that when
being inside an inertial system and not looking out of it
we cannot determine whether we move or remain sta-
tionary which, in its turn, causes absolute space and ab-
solute reference system to be negated. As it has been
noted, absolute space eliminates equality and sets the
hierarchy of inertial systems.
Both our imaginary experiment and a future real one,
however, fully invalidate this opinion and provide sup-
port for the existence of absolute space.
This conclusion could have drawn before by analyzing
Sagnac experiment. Michelson experiment, however,
averages the velocity of light in different directions and
has nothing to do with our consideration.
It is worth noting that both Poincare and Einstein did
not accept the existence of absolute space.
The Sagnac effect has been used so far to prove that
we can defect the motion of a no inertial frame of refer-
ence without leaving it. The importance of this effect,
however, is much greater. The essence of this experiment
consists in the following. One light beam moves towards
the mirrors in a rotating frame of reference and another
beam moves to catch up with the mirrors. The velocity of
light measured for these beams is different: C1 ≠ C2. This
situation is a replica of the above experiment where the
velocity of light was measured in two directions in iner-
tial systems.
Does all this mean a downfall of Einstein’s hypothesis
for steadiness of the velocity of light in inertial systems?
The granular space theory gives a “negative” answer to
this question since it is the velocity of light that is hides
responsible for the maximum deformation of space cells
in any inertial reference system.
It should be also noted that for the observer B the ob-
jects of the observer A will be elongated (seeming) rather
than contracted. This enables as to understand the physi-
cal meaning of Schwarzschield’s solution.
3. Physical Meaning of Velocity and
Acceleration
Present-day physics does not reveal the real physical
meaning of velocity, so the question arises. If absolute
space exits, how must we explain the fact that uniform
motion in absolute space does not cause any observable
effect while acceleration does?
Our studies just into three physical effects of many
other have enabled us to reveal the following natural law:
absolute space establishes a hierarchy of inertial refer-
ence systems; this law is a manifestation of the velocity
of uniform motion.
There is quite a number of physical situations when
velocity characterizes rest but not motion. Several phe-
nomena of the kind, paradoxical at first sight, are con-
sidered by Feynman in his lectures in Physics [3].
Let us consider the instance when the electric charge
and the magnet are at rest. Let a point charge be at rest
near the center of a magnetic bar (Figure 1).
Everything is at rest, so that energy doesn’t change
with time either and are constant. But Poynting’s vector
show the presence of energy fluxes here because is not
zero. If we observe the energy flux we can be sure that it
circulates around this system.
The energy, however, remains constant: all that enters
Figure 1. The charge and the magnet result is Poynting’s
vector circulating along a closed loop.

436 V. KONUSHKO
this volume flows out of it again. This resembles the cir-
cular flow of incompressible water. So, in this seemingly
static situation we observe an energy flux which looks
rather absurd!
To our regret we can observe that in this case energy
“travels around a circle” but, as we know, the energy and
momentum fluxes are proportional to each other, so here
we have momentum circulation. But momentum circula-
tion means the presence of a momentum. Hence, a sta-
tionary field possesses a momentum. This enigmatic cir-
culating energy flux, which seems at first something in-
comprehensible, is in fact absolutely necessary. But there
is also a real momentum flux.
The following situation is not of less interest. Imagine
two electrons whose velocities are perpendicular so that
their paths intersect but, nevertheless, the electrons do
not collide. At a certain moment their relative position
will be as shown in Figure 2.
The charge q2 is only acted upon by an electric force
since on its way q1 does not set up a magnetic field. But,
besides an electric field, it is also a magnetic field that
acts on q1, so that it moves in the magnetic field set up by
the charge q2.
The forces acting on these particles do not balance
each other, so the action and the counteraction are not
equal and the full momentum of substance must change;
it does not remain constant. But in this situation the field
momentum changes, too. The momentum present by
Poynting’s vector is not constant. But the variation of
particle momentum is exactly compensated for by field
momentum, so the total momentum of the particles and
the field is retained all the same.
And here a stationary field acquires a momentum, the
velocity characterizes rest again.
Spin is a key property of matter, though still imper-
fectly understood. Initially spin appeared in physics as an
intrinsic moment of momentum Me of electron: Me = ħ/2.
Planck’s constant has the following dimension:
mvr.
Since inside an electron there are no clusters (quarks)
consisting of deformed cells, that is, no inner structure it
has been so fare believed to be extremely small:
re < 10–17 cm. But the size of any elementary particle
is its fundamental characteristic and must be determined
only by world constants and rest mass:
rmc 

 .
Assuming that the size of a particle is negligible, as it
has been believed so far, the spinning electron hypothesis
offered by Kronig was rejected by both Pauli and Gei-
senberg with Lorentz as it would have suggested that
matter moves with a velocity much higher than that of
(a)
(b)
Figure 2. The forces between two moving charges are not
always equal and opposite. “Action” is not equal to “coun-
teraction”.
light.
The granular space theory makes us accept that the
size of any elementary particle cannot be less than its
Compton wavelength.
Nevertheless, this discovery cannot solve the spin
problem: with this size an electron must rotate with the
velocity of light c which can be rejected at once. The
velocity of light enters into the well-known mass— en-
ergy ratio E = mc2 which characterizes a body at rest.
We could give more instances of physical effects
where the velocity ν is characteristic of statics rather than
dynamics. This intriguing conclusion changes our con-
cept of the physical meaning of velocity ν: the velocity ν
is on iceberg, its peak being usual travel speed of an
object about the fixed count body. The underwater dee-
per part of the iceberg is related to the deformation of
elementary space cells. More specified is the following
statement: the quantity ε = ν2/c2 denotes the relative de-
formation of space cells.
This statement enables us to observe almost visually
the particle spin: the quantity c in the spin formula (1)
characterizes not the speed of electron rotation but the
relative deformation of the cells making up the “body” of
particle—spiral or torsional deformation—whereas ra-
dial cell deformation denotes gravity and electric
charge.
The following model gives a rough idea of spin struc-
ture. Let us place domino pieces along a circle at inter-
vals equal to the length of one piece and then drop one of
them. The falling pieces form a peculiar alignment sym-
bolizing torsional deformation. Similarly, a moving
charged particle form around itself the same spiral de-
formation of space cells designated by us as the magnetic
field. Only now we can understand from where space
gets spiral properties (Figure 3).

V. KONUSHKO
437
Figure 3. Model of torsional deformation of elementary
space cells.
In another work we shall consider Geisenberg ine-
qualities and stability of hydrogen atom. Bohr’s attempt
to solve this problem involving Geinsenberg inequalities
is rejected by experiment, and only a new concept of
velocity, momentum, kinetic and potential energy can
solve the problem of hydrogen atom stability.
The theory of granule space enables us to observe al-
most visually not only the velocity ν—deformation of
elementary space cells but also the acceleration a—the
gradient of this deformation. In its turn, this statement
allows understanding the principle of equivalency of an
accelerated reference system and a uniform gravity field
for all physical processes which represents the funda-
mental principle of Einstein’s theory of gravity. In more
detail this subject will be discussed in a separate article.
It is well known that a new theory raises more new
questions than it can answer old ones. The key questions
of a new theory are related to radial and axial deforma-
tion of elementary space cells as well as their clusteriza-
tion. And the only way of unraveling these secrets is
guessing. Even new, when we have not got an accelera-
tor with E  1019 GeV, we must mentally increase an
electron to the size of a football and try to guess its sur-
face structure since this simplest elementary particle is
the key to a huge number of mysteries of the Universe.
Without unraveling the electron structure we shall
never be able to solve either the problem of elementary
particle mass spectrum nor the boundary line separating
animated nature from unanimated.
In our previous works we set forth in detail the con-
cept of granular space and here we are going to recall
some foundations of this theory for coherency [4].
The granular structure of space was first mentioned by
ancient philosophers, and then, in 1900, Planck found the
size of this cell:
*3
3
21.6 10сm. G
Lc


3
In 1972 Beckenstein introduced inexplicitly the ele-
mentary cell area (L*)2  10–66 cm2 and in 1975 the au-
thor extended this series by postulating the minimum
volume of elementary cell (L*)3, and the whole Universe
turns out to be composed only of one element—a cell.
According to Wheeller, “space is made up of cells of this
size on its deepest level” [5]. At present more and more
physicists believe that space has a granular structure and
specifies an absolute system of reference [6,7].
In the theory being developed by us a cell is material,
three-dimensional and flexible; excessive specification of
its characteristics at the first stage of development of the
theory may only lead to rough mistakes. All elementary
particles are part of space as Klifford foresaw. The for-
mation of a particle demands an additional amount of
matter called mass; this mass deforms the inner cells of
the particle providing their confinement and, in case of
stable particles, produces their stable surface. The
“body” of the particle is made up of space cells. It is
evident that the rest mass of the particle is invariant be-
cause this invariance does not depend on the reference
system we use to observe it. But how is the additional
matter (mass) arranged in space which is all filled with
cells? The most natural thing that can occur is that part of
the cells will be pushed out into the area of space exter-
nal about the particle surface and the cells inside the par-
ticle will be deformed. It is obvious that the larger is the
mass spent to produce a particle, the stronger is the de-
formation of inner and outer cells which results in a di-
rect mass-size relationship: the larger the mass, the
smaller the size of the particle. Quantitatively this is ex-
pressed by the formula for Compton wave length of the
particle:
.
mc
 
Consequently, contrary to the existing public opinion,
the electron is the largest particle in size—it is the light-
est particle if the neutrino is equal to zero.
4. Has Neutrino Get a Rest Mass?
Present-day experiments aimed at a search for neutrino
oscillations at the same time point out to the existence of
a rest mass in an electron neutrino, mν < 1 eV. In this
case the size of this particle rν = ħ/mνc ~ 10–5 cm which
is a thousand times larger than the atom size. This is ab-
solutely impossible because as such a particle moves in a
medium, the atoms of the medium will pass unimpeded
through the particle without interacting with it and with-
out destructing it.
The second cause of absence of a rest mass in a neu-
trino is the following. As known, neither an electron nor
a muon have neutral partners. Hence, the electric charge

438 V. KONUSHKO
structure (clusters on the particle surface) is a necessary
element for forming a stable surface of these particles.
As the neutrino has no electric charge, space cannot form
its closed shell; the spin alone is unable to do it.
These two causes completely denounce the hypothesis
of massive neutrinos and spare experimentalists farther
searches for a rest mass in a neutrino. But the oscillating
character of motion of both a photon and a mass-free
neutrino cannot prohibit neutrino oscillations. The same
oscillatory motion of all elementary particles discussed
in our article “Weak Interaction and the Nature of Virtual
Particles” supports the existence of Ko- and Bo-meson
oscillations.
In this case it is very important to note that this mutual
transformation of the neutrino K˚- and B˚-meson is
caused by the interaction between the non-stationary
surface of the particles that “breathes” and the pulsating
matter carried by kinetic energy.
The different degree of compression of this matter
serves as “a trigger” that makes, for instance, the K˚-
meson decay into two or three particles; it also transfers
one type of neutrino into another one.
We have every ground to suppose that it is just this
interaction that is responsible for disturbing CP- and
T-symmetry.
As part of the particles are forced out into outer space,
the external layers of cells are overloaded with matter
and their radial and axial (torsion) deformation is taken
by other particles as various types of physical fields and
a particle spin.
It is evident that the excessive matter made by
forced-out cells is equal to the mass of the resultant ele-
mentary particle—this peculiar Archimedes effect in
microphysics does not depend on whether a particle has
either an electric or a strong charge, or a spin. It is just
this excessive matter arising so naturally as a result of
particle birth that is called by us as potential energy. The
intensity of physical interactions depends on which part
of this excessive matter can be transferred by space to
the interacting particles, and real space hasn’t got any
other infinite energy.
The deformation of the cells inside a particle may give
birth to clusters, that is, bunches of deformed cells
known as quarks, and the deformed cells between quarks
cause as to introduce intermediate (exchange) particles
referred to as gluons. Consequently, neither quarks nor
gluons can exist in free state. Outer cells from a layer
structure, the former planes in this case are deformed to
piece-smooth curved surfaces which gives grounds to
introduce an extremely conditional curvature of space.
We cannot have a look at our real three-dimensional
space from “outside” since there is not the fourth spatial
measurement. We can observe the deformation of cell
layers by increasing mentally the cell size.
Now let us consider another type of energy—kinetic.
Kinetic energy means the amount of substance (matter)
transferred by a particle in a given reference system.
This matter is arranged asymmetrically: it is running
ahead of the particle.
The absence of bond energy between space cells
makes it possible to conserve inertia which means that
space has zero viscosity.
In the non relativistic limit the kinetic energy:
22
2 0
02
1
22
mv v
Emc
c

 


.
The coefficient ν2/c2 shows which part of matter (mass)
spent to form the particle itself is constituted by the addi-
tional substance moving ahead of the particle. It is this
substance that form new particles as two corpuscles col-
lide.
The result of annihilation of electron and positron is
that the inner cells making up the bodies of these parti-
cles are left in place, the particles give back the space
what they once borrowed to build their “bodies” and
their mass is spent to form the “bodies” of two photons.
Lomonosov used to say that nature «does not like to
luxuriate excesses of things».
In our article “Weak Interaction and Nature of Virtual
Particles” we show that the motion of a particle is oscil-
lating by nature and the maximum size of propagation of
cell deformation is referred to as the wavelength . The
wavelike motion of the matter running ahead of the par-
ticle was responsible for the formation of a «centaur»,
that is, a particle-wave, in its turn, has culminated in nu-
merous misunderstandings in considering quantum phe-
nomena. An electron, for example, has quite a definite
size and its spread is out of the question.

This new look on the space structure made as forget
about the “centaur” and introduce a new object: “a rider
on a horse”.
“Horse” means the substance (the mass), carried by
kinetic energy moving ahead of the particle, the «rider» -
the particle itself.
A periodic contraction and then a spread of cell de-
formation to the size of wavelength enables considering
the wave phase. The fact that in reality it is difficult to
observe experimentally this complicated motion is one of
the sources of probability in quantum theory.
The principle of calibrated symmetry is the principle
of relativity in charge space. It was first applied by Fock
in 1926 when he could show that the Klein-Fock-Gordon
equation for a particle in an electromagnetic field is in-
variant about the simultaneous phase transformation of
the ψ-function and gradient transformation of electro-
magnetic field potential:

V. KONUSHKO
439


ief x
xe ,
 
A
xAx fx

.
This extremely morbid situation with probability and
indeterminacy will be considered in more detail in the
next article.
The rough model of physical field suggested by Max-
well did not comply with reality, and this fact negatively
affected the studies into the real space structure. There
was a false idea that an electromagnetic wave did not
need a carrier and it could freely propagate in empty
space. But we are astonished by the sagacity of Faraday
and Maxwell who in electric and magnetic lines could
see physical reality. As a result, they concluded that
electric and magnetic energies are embedded not in the
bodies, their source, but in the space around these bodies.
This fact gave birth to the concept of a physical field that
carries an energy propagating from point to point with a
finite velocity. The theory of granular space is a specific
realization and materialization of the ideas of these great
investigators of Nature. The idea that kinetic energy
transfers to mass, and voice verse, mass transforms to
kinetic energy is badly perceived in present-day literature.
In actual fact, both mass and kinetic and potential ener-
gies mean the amount of substance (matter) used to form
elementary cells but this matter is distributed in different
regions of space.
Any inertial system, be it an elementary particle or a
rocket moving about fixed stars has a kinetic energy and,
hence, the space cells around it are overloaded with sub-
stance and lose flexibility which explains the decelera-
tion of the processes in this inertial system; the higher is
the velocity, the stronger is the deceleration.
5. Spatial Structure and Gravity Effects
When developing his gravitation theory Einstein used, on
the one hand, the discovery connected with Galileo
which says that all bodies fall equally fast and, on the
other hand, the equality of heavy and inert masses. It is
evident that there existed a fundamental relation between
the dynamic acceleration of the body dependent on inert
mass and the gravitational acceleration conditioned by a
heavy mass.
On the basis that an accelerated reference system and a
uniform gravitational field are equal for mechanical
processes Einstein wrote that his conclusions will be
fundament only when this equality is valid for all physi-
cal processes or, in other words, if physical laws remain
valid with the accelerated reference system replaced by a
gravitational field. In this case, when we study theoreti-
cally the effects occurring about a uniformly accelerated
coordinate system, we can visualize the course of effect
in a uniform gravitational field.
When formulating this principle being a version of the
principle of equivalence Einstein mode use of the fol-
lowing imaginary experiment.
Imagine an observer A in a light-tight box far removed
from gravitational masses. Now impart uniform accel-
eration along a direct line to the box. The observer in this
case is to perform a number of physical experiments in-
side the box.
The second observer B is in a similar box optically
isolated from outside but placed in a uniform gravita-
tional field, on the surface of the Earth for example. The
observer B performs in his experiments similar to the
ones carried out by A.
The principle of equivalence says that, if the boxes are
not too big and the experiments are made for a short time,
all the physical processes will equally in both the boxes
and the observers optically isolated from outside are un-
able to find out if their boxes are in a gravitational field
or move with equal acceleration.
And now let us try to understand how, knowing Lor-
entz’s transformations and using the principle of equiva-
lence, we can describe the influence of a gravitational
field on physical processes.
Let a non inertial reference system I’ move at the mo-
ment relative t0 an inertial reference system I. Knowing
the acceleration of I’ about I we can at each instant of
time determine the velocity of I’ about I. And knowing
the velocity we can with the help of Lorentz’s transfor-
mations relate the coordinates and the time of any event
in the system I to the coordinates and the time of the
same event in the system I’. It turns out that knowing
Lorentz’s transformations we can establish the relation
between the coordinates and the time in different refer-
ence systems but also between other quantities, forces,
for example. In other words, if we can describe the
physical effects in I, we can describe them in I’ using
Lorentz’s transformations. But the acceleration of I’
about I is equivalent, as we know, to the existence of a
gravitational field in I’. Consequently, it is possible to
calculate the effect of a gravitational field on the course
of the physical processes under consideration and answer,
for instance, the question: how the gravitational field of
the Sun influences the shift of Mercury’s perigelium.
At present more and more physicists understand that
Lorentz’s transformations are applicable not only for
inertial reference systems but also in non inertial (accel-
erated) ones [8,9].
6. Schwarzschield’s Solution
One of the first great discoveries, after Einstein created

440
l

V. KONUSHKO
his theory of gravity, was Schwarzschield’s solution of
space-time geometry around a point mass. Let us assume,
too, that space-time has Minkovsky’s geometry at a very
long distance from a point mass. So, there is such a radial
coordinate r that at a very long distance from the point
mass the distance dl between two close point on the same
radius is equal to the difference dr of their radial coordi-
nates r2 – r1.
Besides, there exists such a time coordinate t that at a
long distance from the point mass the time interval dt is
equal to the difference t2 – t1.
Let a system connected with the Sun be a fixed refer-
ence system and the reference start be placed on the Sun.
Since any planet moves faster than the Sun about “fixed
stars”, two factor should be taken into account in the
presence of the linear element ds: the deceleration of all
the physical processes on the planet and the “kinematic”
increase in length of sections from the viewpoint of the
observer on the planet.
Let us define the way of measuring the rod length
from the viewpoint of two observers. Let l0 denote the
rod length in the fixed reference system connected with
the Sun and l be the length of the same rod measured by
an observer on a planet, the Mercury for example.
Let the ends of this rod X1 and X2 be fixed at the same
time instant by the observer in the fixed reference sys-
tem:
12
TT.
This allows us to reduce the interval in the fixed
system only to the spatial portion:
2
12
S

2
22
122 10
SXX . (1)
The some interval in the moving reference system is:

2
22
122 121
SсTTX X
 

. (2)
But, according to Lorentz’s transformations, we have:

21212 1
2
v
TTTTX X
c


 
 


.
Substitution of this value into (2) gives:
2
12 2
22
1v Slc

 




. (3)
By comparing (1) and (3) we get;
0
2
2
1
l
l
v
c


.
This purely “kinematic” effect is unrelated, of course,
to the real length of the rod; its physical mechanism is
considered above.
All the present-day monographs dealing with Lor-
entz’s transformations give another method for measur-
ing the rod length. And again a rod with its length l0 is at
rest in the Sun’s system. But now the ends of the rod
1
X

and 2
X

are fixed at the some time instant by the
observer in the moving reference system:
12
TT



.
Replication of the above-given calculations gives quite
the opposite result:
2
02
1v
ll c 
.
which means a decrease in rod length.
These results indicate again that there exists an abso-
lute reference system and, in spite of the from-invariance
of physical laws relative to Lorentz’s transformations, all
physical processes, even in inertial systems, come about
in different ways, that is, there is no process of invari-
ance.
Correlation of the principles of classical and relativis-
tic cosmology must contain a structure of absolute space
as a general system of reference for classical and relativ-
istic description of the Universe.
Below, when considering the motion of planets around
the Sun, we can get Schwarzschield’s metric without
using such a cumbersome body of mathematics as tensor
calculus only on condition that the rods fixed in the sys-
tem of the Sun elongate if they are measured by an ob-
server on a planet.
In the reference system the interval has the form:


2222 222
dd sindddSctr r   
2
Taking into account two above-mentioned effects tak-
ing place in a moving reference system (the system of a
planet) we can transform the expression for interval in
spherical coordinates:

2
2
222222
2
2
2
2
2
d1 dsindd
d
1
v
Sctr
c
r
v
c
2





 





 


. (4)
When writing this element we are guided by the fact
that Lorentz’s transformations are applicable not only to
inertial reference systems but also to non inertial (accel-
erated) ones.
In regular Lorentz’s transformations the quantity v
means the velocity of motion of a planet around the Sun.
Using the interval (4) we can calculate four gravitational
effects once studied by Einstein. To our surprise, all the

V. KONUSHKO
441
results turn out to be half as much as the experimental
ones. Here we could stop trying to use Lorentz’s trans-
formations in describing gravitational effects but the ap-
pearance of “two” natural numbers, puts us on our guard.
In one of our articles we cited E.Kronecker’s words that
“natural numbers are created by God and all the rest is
man’s handiwork”.
The doublet structure of hydrogen atom was marked
by the birth of spin, a unique characteristic of elementary
particles. We also know well Tomas’s half and Einstein’s
and de Haas’s experiments where a “two” was present,
too.
The gravitational field near a massive body is charac-
terized by two velocities: orbital – v1 and escape – v2. It
is v2 that is responsible for the real intensity of gravita-
tional field since the object needs this velocity to escape
a massive body. The relation between these velocities is
very important for our considerations:
22
21
2vv.
According to granular space theory, ε = v2/c2 denotes
the relative deformation of elementary space cells and
velocity characterizes not only motion but also rest. This
problem was considered in detail by us in one of our ar-
ticles “Week Interaction and the Nature of Virtual Parti-
cles” [10].
This discovery enables us to introduce generalized
Lorentz’s transformations where the velocity v entering
the well-known root 22 1vc must denote a maxi-
mum value characterizing this physical effect (situation).
The motion speed of a planet as it revolves around the
Sun is an analogue of the orbital velocity, but the gravi-
tational field of the Sun near the planet is characterized
by a velocity the square of which is twice as much—an
analogue of the escape velocity. And then the physical
meaning of the well-known root changes considerably:
22
12
22
2
111
vv
cc

2
1
2
v
c
,
where v1 means the motion speed of a planet along an
orbit.
Furthermore:
2
1
22
2 2
11 1
g
r
GM
v
r
crc

 ,
where rg = 2GM/c2 is the gravitational radius of the Sun
first introduced by Schwarzschield in 1916.
Finally, for outer space the following expression is va-
lid:

2
2222222
d
d1d sindd
1
g
g
rr
sctr r
r
r


 
 
 


.(5)
This expression for interval was first received by
Schwarzschield in 1916.
In reality a theory can be developed both on a simple
and clear basis and (by getting equivalent results) on
qu
e basis of a minimum number
of
be an unstationary object.
d only 90
ye
ca
ysics
ph
nge
sim
ccel-
er
propellant, in the other
ca
ite an opposite one. Experience shows, however, that
elaborating a theory on th
independent axioms is the simplest and the most
truthful way.
The essence of Freedman’s works consists in the idea
that the Universe evolution dynamics results in the ine-
quality H  0 (H is the Hubble constant), that is, the
Universe must
But there is a twist of fate here, too: though the first
model of Universe expansion was built on the basis of
Einstein’s theory of gravity, the basic conclusions can be
drawn within Newton’s theory of gravity.
From the viewpoint of history, this slightly paradoxi-
cal phenomenon was demonstrated by the English astro-
physicists Miln and Maccry in 1934, more than 10 years
after Freedman’s works were published. An
ars after Schwarzschield’s works were published, we
studied a material granular structure obtained the same
results, though much simpler, without using the cumber-
some body of mathematics of Riemannian geometry.
Many fundamental physical relations have an ex-
tremely simple form. One may say that a very important
physical form is certain to have a simple form no matter
how complicated its deduction is (the beauty of a physi-
l formula consists, in essence, in this fact).
Eventually, the simplicity of a formula means a high
degree of understanding any phenomenon, so high that it
allows constructing its very simple physical model.
Bohr told that when you don’t understand a ph
enomenon, you write a lot of formula, and when you
understand at last you have one or two formula left.
Einstein was not the first to be amazed by a stra
ilarity between gravitational and inertial phenomena.
What is this statement based on? Our conclusion is not
less striking than Einstein’s assumption: both the a
ation a and the velocity v are another characteristic of
deformation of elementary space cells. And if the veloc-
ity v characterizes uniform deformation of cells, the ac-
celeration a accounts for the deformation gradient. Con-
sequently, acceleration as well as velocity are character-
istic of not only dynamics—motion, but also statics—an
object at rest or a physical field.
A lift moving with the acceleration g produces a gra-
dient of cell deformation which changes with the lift, the
same gradient g arises near the resting Earth. In one case
the gradient is produced by the
se by the mass “body” of the Earth.
The simplest concept of space structure is given by
honeycomb there one can see direct lines and planes. But,

V. KONUSHKO
442
es which coat the
pa
as a particle is formed, the outer cells are deformed
forming not planes but curved surfac
rticles like onion layers. The whole complex of these
curved surfaces can be referred to as three-dimensional
space curvature, and to see this curvature we needn’t
enter the fourth measurement. Deformed space cells
practically visualize the curvature introduced by Einstein
into the theory of gravity.
The structure of outer layers manifests itself most viv-
idly in case of a heavy particle if it exists—a planceon
with its mass m consisting just of one cell:
5
1, 610
2
c
mG


 gr
The numbe cells in the subsequent layr ofers coating
the particle grows as N ~ r2, so with an increase in the
distance from the particle the deformof space cells
decreases constantly. (This is, however, not just a mo-
no
l level in a hydrogen atom begins with
on
t is an energy level?
r one?
an electron between levels:
sm
is table?
racteristic of a gravitating body is
th
ansfor-
mhysical meaning as an in-
str
ation
tonous decrease but a striking physical effect, that is,
collectivization or clusterization of cells in certain layers).
Every layer is a two-dimensional surface, so the defor-
mation of one cell will change to the deformation of a
cluster containing already four cells. The numbers 2 and
3 of a cell are excluded because granular space is uni-
form and isotropic since it is composed of similar cells.
The minimum distance at which four cells become a
cluster is r1 = 4r0 because this spherical layer can be
coated with clusters consisting of four cells. The next
cluster contains nine cells, and distance to the second
spherical layer increases up to r0 = 9r0, and so on. We
can observe almost visually the formation of gravita-
tional energy levels or, in other words, the quantization
of a gravitational field. The quantization of the Coulom-
bian field in a hydrogen atom was considered by us in
another article.
The same dependence of Coulombian and gravity
forces on distance means that their energy levels are
formed at the same distances from the proton. But if the
first gravitationa
e elementary cell, an electric cluster has 4, 17*1042
cells.
The granular structure of space enables us to answer
numerous questions where Bohr’s model and quantum
mechanics are at a deadlock:
Wha
Why is an electron retarded on a level?
Why is half the energy of an electron released as it
passes from one level to anothe
What is the motion of
ooth or stepwise?
Why doesn’t an electron throw off a photon on the
ground level which means that the atom
What is time asymmetry?
A fundamental cha
e square of escape velocity at the distance r from the
body rather than of circular velocity. Lorentz’s tr
ations acquire their real p
ument of account for the maximum deformation of
cells in a given reference system. These transformations
can be called as generalized Lorentz’s transformations.
To calculate correctly physical processes we should sub-
stitute the maximum value (v2/c2)max into the well-known
root 22 1vc taking into account not only the veloc-
ity of an object in a given reference system but also the
escape velocity of the massive body within the bounda-
ries of which a physical effect is considered. It should be
notedquare of escape velocity is equal to the
twice potential of gravitational field:
that the s
2
2
22 GM
vr

.
Schwarzschield’s solution is only related to a gravita-
tional field whereas the metrics found by us with the use
of generalized Lorentz’s transformtions can be ob-
served in any field of forces if only it had a spherical
sy
aterial
gr
a
mmetry and the basis had only radial velocities.
The first attempts, including those of Einstein, to ap-
ply Lorentz’s transformations to studies of gravitation
failed because the nature of “the two” remained a mys-
tery that could be revealed just by turning to the m
anular structure of space.
Besides, in the granular space theory the expression:
2
2
c
ha
As it has been said above,here is similar to the
escape velocity and characterial deformation of
space cells at the distance r from the massive body M.
g/r has not been
kne
n exist in
Sc
he gravitational field potential at the
bo
22
2
g
v GM
rr rc  ,
s quite a different physical meaning.
2
v
zes the re
The fact that the true meaning of r
own so far enables us to maka surprising conclusion
that in the Schwarzschield’s solution contains a singular
sphere where the meanings of dxo and dr vary.
Physicists have so far been trying to solve the problem
of quantum gravitation development which is needed to
explain physical processes occurying in singularity.
In our case there is no singularity at all. It ca
hwarzschield’s metrics in the limit with r = rg which is
unattainable for a real body since in this case β = v2/c =
1, i.e. 2
v = c!
Even in his own reference system the outer observer
can never get the gravitational radius rg. The statement
that we are living inside a huge black hole is rather in-
triguing since t
undary line of the Universe reaches the squared veloc-
ity of light: φ ≃ c
2 and, hence, all physical processes

V. KONUSHKO
443
some problems dealing with cosmology in a sepa-
ra
ound his famous wave equation. But most of
th
already did it when we found out that the for-
m
ele-
m
ounted
by
slow down to zero. But we don’t feel uncomfortable at
all.
This, at last, enables us to get rid of all the difficulties
relating to singularity both for a massive body and for
the Universe on the whole. In more detail we shall con-
sider
te article.
It is of great interest to look back into history. Gei-
senberg was the first to formulate the foundations of
quantum mechanics—matrix mechanics. Short time later
Shrödinger f
e physicists, including Dirack, preferred working with
matrix quantum mechanics. Shrödinger had nothing to
do but to show that the two formulations of quantum
mechanics were equivalent which he performed with
success.
We have to solve a similar problem: as the results of
Einstein’s theory of gravity and the theory of granular
space coincide, we must find points of their contact. Par-
tially we
ation of any particle is responsible for the fact that the
former spatial planes consisting of cells form, as they
turn to curved surfaces, a laminated structure around the
particle. The curved surfaces of individual layers permit
using curved (spherical) coordinates, the third coordinate
makes it possible to account for the change in cell de-
formation depending on the distance to the particle and,
finally, the fourth coordinate, the time coordinate, ac-
counts for the deceleration of the processes during the
deformation of the cells surrounding the particle. This
deceleration has so far been a striking physical effect,
though quite incomprehensible. And only in studying the
real material structure of space we can get a round grasp
of this phenomenon. It is rather puzzling that nobody has
ever observed the acceleration of physical processes.
This problem can be easily solved by observing a
moving particle in an imaginary experiment. In our arti-
cle “Weak Interaction and the Nature of Virtual Parti-
cles” [10], we determined the wall thickness of an
entary space cell –Δl ≃ 10–100 cm. It is quite probable
that the mass carried by kinetic energy fills the cells sur-
rounding the particle, the walls become thicker.
This excess matter reduces the elasticity of elementary
cells surrounding a massive body which, in its turn,
causes the velocity of light to drop. The radial velocity of
a light signal is equal to r C when the time is c
a far-remote clock:
2
2
2
d11
d
g
r
rv
r
Cc c
tr c
 
  
 
 
hat empty space, only due to its
curvature, cannot help either slowing down the course of
physical process or stopping light. In this case material
space is needed.
The theory of granular space, like Einst’s gravity
theory, predicts that a rotating body sets up around itself
bo
rsion deformation of the space cells
ar
stein’s equation works perfectly in
tre
ormed by massive
bo
ss, energy and momentum. Thus, space
cu
is a
so
a”
m
.
It should be noted t
ein
th a static (potential) field and a stationary rotational
field that looks like the stationary magnetic field of a
rotating charged body due. Its rotational character is
caused by the to
ound the body.
It is evident that in this case the acceleration of physi-
cal processes is completely excluded.
We have just resolved into components such a com-
posite object as the curvature of four-dimensional
space-time used in Einstein’s theory. All this enables us
to state that Ein
e-dimensional material space by describing the de-
formation (curvature) of cell clusters f
dies and thus ruling out the idea of void curvature. In
our further work we shall consider in more detail the
mechanisms of both gravitational and Coulomb interac-
tions. Here we want just to note that the attraction of
bodies occurs when the deformation of cells beyond the
bodies is larger than between them and their repulsion is
characterized by a high deformation of the cells between
the bodies. The difference in cell deformation sets up a
deformation gradient referred to as force. The former
straight lines formed by the cells as a result of their de-
formation become curved and the planes turn to curved
surfaces which form the basis for space curvature men-
tioned by H. Lobachevsky, J. Bolyai, G. Riemann, Gauss
and Einstein.
It is well-known that Einstein’s theory of gravity has not
any gravitational field at all, it only contains space-time
curvature formed by moving masses. The theory of gra-
nular space states that it is only material space that can
be characterized by curvature. An “empty” geometry
lacks both ma
rvature becomes a secondary effect, while the defor-
mation of material space cells acts as “first violin”.
All the attempts to quantize directly Einstein’s theory
have failed because of the presumed tensor nature of the
gravitational field and due to interaction nonlinearity.
The essence of nonlinearity consists in the fact that
gravitational field possesses potential energy and, hence,
mass since E = mc2. The conclusion, that this mass
urce of gravity by itself, is mistaken. This additional
gravity field, in its turn, acts as an additional source of
gravity and so an. As a result, a peculiar “matreshk
ade up of field sources is formed which gives rise to
nonlinearity.
For counterexample it should be noted that a Coulomb
field, too, possesses potential energy and, hence, mass
but it cannot form any additional gravity field and re-
mains linear.

V. KONUSHKO
444
al field is deformed apace cells around a
m
e being is the same distance dependence of
bo
nergy levels that
fo
s of this radiation away from
th
nal and
e bodies initially
inated
. The lay-
ers dies are opposite in
urvature, their actions on each other weaken the total
up
According to the theory of granular space, the essence
of any physic
aterial body (a particle). Being elements of a gravita-
tional field these particles do not set up any additional
field. A prominent example of gravitational field linear-
ity for the tim
th Coulomb and gravitational fields.
Consequently, Schrödinger equation is suitable for
both the fields and predicts the existence of both gravita-
tional and Coulomb levels.
In our work «Gravitational Energy Levels and the
Problem of Microwave Radiation of the Universe» [11]
we could find that it is gravitational e
rm quasi- black-body radiation with T ≃ 2.7 K around
the Earth but neither WMAP nor PLANK have yet
measured the absolute flaxe
e Earth in order to be sure of its terrestrial origin rather
than to remove the term «relict». We need just one figure
—the quantity of absolute intensity of cosmic microwave
background radiation in the millimeter range? Measured
far away from the Earth to study the problem of “relict”
radiation and graviton. This measurement should have
been done even forty years ago.
Gravitational energy levels are of great importance for
cosmology. Only owing to them, particles get together
forming stars and planets just as electrons are arranged
on the energy levels formed by nuclei.
7. Mechanism of Gravitatio
Coulombian Interactions
Not let us unravel the gravity mechanism by studying in
an imaginary experiment two massiv
resting in a system of fixed stars. Each body a lam
structure of deformed space cells around itself
of space cells between the bo
c
curvature, i.e. decrease the deformation of the cells in
inner space. The curvatures of the layers behind the bod-
ies coincide increasing the total deformation. Thus, a
difference in cell deformation in front of and behind the
bodies is set up—the potential gradient φ only remains
for us to state that the bodies begin inevitably to move to
meet each other (Figure 4):
The bodies are not attracted together but it is space
that brings them together due to the cell deformation
gradient. Huygens was wrong when he blamed Newton
for his law of gravitation because the latter had not un-
raveled the mechanism of gravitation. As Newton an-
ticipated, the mechanism of gravitation would be cleared
only 350 years later.
The substance of the destructed cells behind the body,
whose deformation is larger, is forced out into the front
Figure 4. The simplest mechanism of gravity.
semisphere where the deformed cells are subjected to
destructive interference. This process demonstrates real
material transfer of potential energy to kinetic one. The
source of potential energy has already been considered.
Space as a
oney-lender because it does not take any interest from
these forces on the charges
an
people were looking for
th
eates a gravitational force. The exchange mecha-
ni
in this situation acts as a creditor and not
m
the debtor. As these bodies collide, part of the substance
of kinetic energy called the bond energy will be released
and, if we try to pall them apart at the former distance,
we have to return the same amount of substance that was
released, to the space.
If the particles have electric charges, the substance
transferred to the by space is a lot of times larger than the
substance imparted to a neutral particle by gravitation.
The mechanism of Coulombian interaction very much
resembles that of gravitational interaction which results
in the same dependence of
d the distance between them.
The positive and negative curvatures of the clusters on
the surfaces of a position and electron demonstrate a
unique possibility of space either to pull together parti-
cles (attraction) or to repel them from each other (repul-
sion).
Over two thousand years ago
e cause of gravity offering various hypotheses, but only
the research into the real structure of space has shown
how deep the mystery of gravitation was hidden: the dif-
ference in cell deformation in front of and behind the
body cr
sm offered by W.Gilbert, a court physician of Eliza-
beth, queen of England, turns out to be groundless. Only
as two particles collide, energy and momentum can be
transferred from the shell-particle to the target-particle,
and here we can speak of exchange interaction but the
mathematical description of a collisional process, as op-
posed to the static one, becomes so much more difficult
that it is beyond the worst expectations. Indeed, in a col-
lisional process the deformation of a huge number of
cells, ~1060, assumes the most fantastic forms.
The maximum deformation of cells is an objective
property and is independent of the reference system in
use. But it is velocity of light that is hidden behind it.

V. KONUSHKO
445
d the ob-
se
of both gravitational and Coulombian interac-
tio
lo
go
This foot makes the velocity of light constant in any in-
ertial system far away from gravitating bodies as well as
independent of the motion of the source an
rver.
However the velocity of light measured in different
reference system will differ according to the direction
(along and against) of motion as it has been said above.
This also makes it impossible to convey information at
a rate higher than the velocity of light. The gradient me-
chanism
ns removes, as last, the antagonism between short-
range and long-range interactions: the force arising on
the particle surface is transferred from cell to cell at a
ng distance smoothly realizing far-range interaction.
For example, the force acting on a planet is the sum of
forces acting on every elementary particle of this planet.
The local nature of force unravels the enigma of origin
of such forces as centrifugal, Coriolis and the force sus-
pending a gyroscope and preventing it from falling on
the Earth. These forces have so far been considered ficti-
tious since we could not point out to a body which would
act on the object under consideration. Later on we are
ing to consider in detail the action of these forces but
now we want to note that any attempt to understand these
phenomena in purely a geometrical way is ungrounded.
Guided by the idea “everything from geometry” Einstein
interchanged cause and effect: cause—the deformation
of elementary space cells, effect—the change of the ar-
rangement of cells and their physical properties, that is,
what is called now as the curvature of four-dimensional
diversity of space-time.
In Einstein’s theory of gravity the linear element be-
comes a generalized quadratic form:
2
ddd
s
gxx



.
In the description of gravitational field the metric ten-
sor gµv takes the central place. According to Einstein,
th
e general case is 10
because gµv = gvµ. In gravitational fields of individual
heavenly bodies, stars and planets for instance, a refer-
en
ese values act as “gravitational potentials”. The num-
ber of “independent potentials” in th
ce system can be usually chosen so that the quantity
g00, that is, the coefficient before dt2, would be the most
essential. In Schwarzschield’s solution considered above:
2
00 22
22
11
v
gcc



 




appearing in Einstein’s equation of gravity describe
elasticity of space and the component g00 suggests clearly
that the quantity ε = v2/c2 characterizes the relative de-
fo
tion completely
ru
dictated by Fock’s wish to clar-
y of gravity by getting rid of mean-
ivity in it.
Only
m
in
Theory,”
Sputnik, Moscow, 1999.
The Feynman Lectures on Physics,” Addi-
son-Wesley Publishing Company, London, 1963.
al of Modern Physics,
ision,” Springer Verlag, New
Black
Holes,” Scientific American, No. 3, 2006, p. 17.
.
This quantity cannot act as a gravitational potential
since it is dimensionless. As far back as 50 years ago
Zeldovich was right to state that the tensors Rik and R
the
York, 1968.
[6] T. Jacobson and R. Parentani, “The Echo of the
rmation of elementary space cells that plays a domi-
nant role in the theory of granular space.
As Newton thought, free fall occurs due to the gravita-
tional force. Moreover, all the gravitational effects in the
solar system (Mercury’s perihelion displacement, light
deflection by the Sun, radio signal lag, hyroscope pre-
cession) are caused by gravity force. The mechanism of
gravitational interaction under considera
les out a gravitational shadow and, on the contrary, the
Earth’s attraction by the Sun increases when the Moon is
placed between them.
8. Conclusions
Fifty years ago Fock reasoned that “generally speaking,
there is not any relativity in the general relativity theory”
12]. These words were[
ify Einstein’s theor
ingless general relat
The theory of granular space extends farther: untan-
gling the physical meaning of velocity, introducing gen-
eralized Lorentz’s transformations and proving, in the
general case, the absence of process—invariance with
form-invariance of all physical laws—shows that the
Universe does not know the concept of relativity.
ind makes use of different reference system to simplify
the procedure of obtaining quantitative results, but Space
performs all its calculations in one reference system—
absolute.
At present many physicists create an extremely com-
plicated and speculative inflationary hypothesis [13].
A study into the real structure of space is able even
now to give us, at least, a rough idea of the processes of
attraction and repulsion and even to observe the mecha-
nisms of all physical interactions. We shall go on study-
g the real structure of space in our next work.
9. References
[1] M. Planck, “The Unity of the Physical Patter of the
World,” Nauka, Moscow, 1996.
2] V. Konushko, “Concepts of Granular Space [
[3] R. Feynman, “
[4] V. Konushko, “Granular Space and the Problem of Large
Numbers,” International Journ
2011 (In Press).
[5] J. Wheeler, “Einsteins V

V. KONUSHKO
446
mption and Myth in Physical Theory,”
and A. Polnarev, “Surprising Univers
of Vir-
odern Physics, 2011 (In Press).
r
[7] A. Smolin, “Atom’s Space and Time,” Scientific Ameri-
can, No. 4, 2004, p. 20.
[8] H. Bondi, “Assu
Cambridge, 1967.
[9] V. Braginsk e,” [
Nauka, Moscow, 1985.
[10] V. Konushko, “Weak Interaction and the Nature
tual Particles,” International Journal of Modern Physics,
No. 4, 2011, pp. 45-57.
[11] V. Konushko, “Gravitational Enerdy Levels and the
Problem of Microwave Radiational of the Universe,” In-
ternational Journal of M
12] V. Fock, “The Theory of Space Time and Gravitation,”
Pergamon Press, London, 1959.
[13] A. Levin, “Trillion Years before Big Bang,” Popula
Mecanics, No. 6, 2010, pp. 47-50.