The gauge foundations of special
relativity*
Ó Danylchenko P.
SPE “GeoSystem”,
Contact with author: pavlo@vingeo.com
It is shown here that Lorentz transformations are caused by gauge effect of
motion on matter (principle nonobservability of effect
of motion on matter). This gauge effect of motion is caused by interdependence
and mutual determination of propagation velocity of interaction between matter
elementary particles and of rate of course of matter
proper (standard) time. The Lorentz transformations
are derived without any linearity assumptions and being based only on the
presence of relativistic shrinkage of the length of moving body and on clock desynchronization at its
slowest transfer along this body.
1. Introduction
A lot
of publications, being prejudiced fundamental postulates of Special Relativity
(SR), have appeared recently. The most important among the brought-up problems
is considering such substance as the physical vacuum (PV) to be a physical
reality. After all, PV substitutes absolute ether of classical physics at rest
in many ways. In addition, the possibility to work out the value of peculiar
velocity of absolute motion of the Solar System by anisotropy of frequency of
cosmic microwave background radiation contradicts with the established in the
scientific literature opinion about the absence of special absolute frame of
references of coordinates and time (FR), motionless relatively to the PV.
The aim of the present work is to show that seeming
mutual incompatibility of the fundamental SR postulates with the presence of
the undraggable by a moving body PV and corresponding
to it the unique PVFR is caused only by imperfect understanding of physical
essence of Lorentz transformations. The essence of
these transformations (as it will be shown below) is in the precise
mathematical mapping of gauge effect on matter and its space-time continuum
(STC) [1, 2]. This gauge effect is the cause of principal nonobservability
of any changes, which have realized in the objects and physical processes.
(As we know, influence of electric field on matter is
realized only by spatial increments of electric potentials, not by the values of
potentials. So we can gauge-transform these values. In analogy to this influence, influence of motion on matter, which we can observe in matter intrinsic FR as strengths of graviinertial (removable gravitational) field [3], is
realized only by space-time increments of linear
momentum, not by the values of linear momentum. Therefore, linear momentums
of matter objects and, consequently, velocities (linear momentums are the functions of velocities) also can be gauge transformed by
proceeding from observation of motion of this matter from one FR to the observation of it from another
FR, as well as directly in the same FR - by their change in time, for example,
for accelerating matter, which has rigid intrinsic FR (Möller
FR) [3, 4].)
2. Derivation of the Lorentz transformations
As it was first shown by Fitzgerald and Lorentz [5], at the transformation of a state of body absolute
rest into the state of steady inertial body motion relatively to the PV,
uniquely definable shrinkage of the body size in the direction of its motion
realizes itself in the absolute space. This shrinkage is connected with
isobaric self-contraction of body matter [3]. The self-contraction of
matter is the result of adaptation of its molecules, atoms and elementary
particles to changed conditions of their interactions.
Let the body moves at the absolute velocity 
relatively to the PV. Then
longitudinal size Xij
of the body, and consequently, the corresponding to it size
of length standard, located on the body, shrink along the direction of
motion in the same quantity of times:
.
Where: 
considering the measuring of linear dimensions
in light units of length. As a result of identical
size shrinkage of measured objects, as well as of measurement instrumentation,
motionless relatively to the moving body, no
changes in geometry of its objects in body FR will be found out. And,
consequently, transformations of linear and angular dimensions of the objects
in the absolute space for the moving body and for the inertial FR (IFR),
rigidly bound up with it, will be purely gauge. And the body will be
gauge-self-deformed in this space. Due to such relativistic shrinkage of
longitudinal sizes of the body the duration of absolute time of interaction
between any two body points (or rather located there elementary particles):
, (1)
will increase in G times, where:
, (2)
and:
, (3)
- durations
of time intervals of propagation of interaction waves accordingly in forward
and reverse direction, and: Xij, Yij=Yij 0, Zij=Zij
0 - orthogonal projections of the segment between the
interacting in the process of motion body points. As we see, the increase of
duration of interaction time does not depend on the values of angles between
the direction of body motion and directions of propagation of electromagnetic
wave (virtual photon) in the forward and reverse move. And consequently, the
repetition frequency of all the periodic physical processes, realizing in the
moving body, including processes that used for chronometry, will decrease in G times. And this means, that as the result of
gauge effect of motion on matter, the time on the moving body (in the IFR,
corresponding to it) will course 
times slower than on a body,
motionless relatively to the PV. However, observers and instruments, motionless
relatively to the body, will find no changes in realization of physical
processes, which take place directly on the moving body.
Relativistic time dilation in IFR can’t be observed in
principle by the intrinsic clock of IFR. Therefore, according to (2) and (3),
time intervals 
and 
must have the following durations
by the clock of IFR:
, (4)
, (5)
where: xij≡Xij0,
yij≡Yij0,
zij≡Zij0
- projections dimensions of the moving body segments, observed in its IFR (in compliance
with gauge transformations) with the same value as in case of their observation
in state of body rest relatively to the PV. According to this, the value of the
average velocity of propagation of interaction wave in the forward and reverse
move will be observed in IFR the same as at its observation in the PVFR:
,
This doesn’t allow us to find
out mutual inequality of observed in the IFR and PVFR velocities of propagation
of interaction wave or light, using location or interferometer.
Inequality
of time intervals of the propagation of interaction wave in forward 
and reverse 
move to its average value:
,
is also impossible to
be found out by IFR clock. After all, even in the case of slowest transfer of
the clock along the shortest path from one point of the IFR to another, a
mutual desynchronization of transferred and
motionless in the IFR clocks realizes:
, (6)
where:
,
and: 
is Galilei
difference of vectors of absolute velocities of slowly transferred (V′) and motionless 
in IFR clocks. This desynchronization
is observed only in PVFR. And it compensates in the IFR the difference of the
intrinsic time intervals Δt̃1 and Δt̃2,
which proportionally synchronized with ΔT1 and ΔT2
correspondingly:
,
.
As a result of this, a question appears, if equality
in all the IFR points of proper quantum time (which determines their “age”)
really does exist according to the observations from the PVFR. After all, in
the process of increase of the value of velocity (till the value of uniform
velocity) the motion of different points of the body realizes at unequal
velocities [3]. And this leads to the fact that “age” of different points of the body
(measured by their quantum proper clock) will be unequal, according to (1). And
consequently, the difference of points “age” will essentially depend on the law
of motion of the body points during the process of reaching by them the equal
values of absolute velocity. And as a result, standard time, determining the
body points “age”, should be considered as their path-like proper (standard)
time. To realize the possibility of analysis of dynamics of objects, which move
in the IFR, coordinate-like intrinsic time (unified in all the points) [2, 4] must be
introduced into it.
All of this is a sufficient reason for adoption of the
conception of non-simultaneity of observation in the IFR of events, which
realize simultaneously in the PVFR. The impossibility to observe in the IFR the
desynchronization of the clock at its slowest transfer
from one point of IFR to another:
shows up non-triviality
of gauge transformation of time intervals. Time interval between the events,
fixed in different points of the IFR by its intrinsic clock (which counts IFR coordinate
time), is determined in PVFR, according to (6), by the following
transformation:
, (7)
where: δTij=Γ·V·xij
- observed in the PVFR mutual desynchronization of
events, which have simultaneously happened in the 
and 
points of the moving body IFR.
Considering gauge transformation of size of the parallel to the direction of
motion projection of segment xij, transformations of distance projections
between these points at noncoinciding time moments 
, will be the following:
, 
, (8)
According to (7) and (8) projections
of velocity of the moving object at the transition from the IFR into PVFR and
inversely will be transformed according to Lorentz
rules [4]. In that way,
the velocity of light in free space will not depend in the IFR on absolute
velocity of body, possessing this IFR. This, of cause, is connected with the
equality of the velocity of light in free space to the velocity of propagation
of the wave of electromagnetic interaction, which determines the frequency of
this interaction between elementary particles of matter, and thus, the course rate of the IFR intrinsic
time.
Consequently,
Lorentz transformations are based on real shrinkage
in absolute space of dimensions of objects along the direction of their motion,
as well as on IFR intrinsic time dilation and desynchronization
of slow-transferred clock, which are observed in the PVFR. Due to this, Lorentz transformations guarantee the impossibility to find
out in the IFR any changes, which have happened to objects and physical
processes, realizing in IFR, after the body has changed its state from absolute
rest to its uniform motion relatively to the PV. In that way, the correctness
of the first Einstein postulate about the sameness of realizing of all the
physical phenomena in all the inertial systems is confirmed.
3. Effects, caused by Lorentz
transformations
As the result of time dilation in the IFR the increase
of the value of its effective velocity relatively to the PV (which is
determined, according to (8), by a moving clock when 
) takes place:
. (9)
Therefore, because of bigger in times dash repetition frequency
of motionless relatively to the PV linear scale, the value of its division will
seem to be times smaller in the IFR. And
consequently, according to (7), the path 
, covered by the IFR in absolute space, which is observed in it as
“contracted”, will be perceived in the IFR as times smaller:
. (10)
On the other hand, according to (7) and (8), at the
same IFR intrinsic time 
its different points will be
opposed to the PV points at the moments of absolute time, mutually detached by the interval:
(11)
These moments correspond (as
it is shown in the figure, when 
) to different positions of the IFR relatively to the PV
(events, simultaneous in the IFR, marked in the figure by the symbol “*”).
This will lead to observation in the IFR of
“imaginary” shrinkage in 
times of dimensions of objects,
motionless relatively to the PV. However, considering real shrinkage in
absolute space of the dimensions of IFR objects in times, the resulting shrinkage,
observed in the IFR, of dimensions of objects, motionless relatively to the PV,
will be only in times:
. (12)
That is why, the presence of real shrinkage in
absolute space of dimensions of the IFR objects and the presence of “imaginary”
shrinkage in the IFR space-time continuum of dimensions of objects, motionless
relatively to the PV, leads to observation of dimensions of objects, motionless
relatively to the IFR, in the PVFR and dimensions of objects, motionless
relatively to the PV, in the IFR, as reduced in the same number of times. As
the result of clock desynhronization 
at its slowest
transfer into the IFR, “imaginary” absolute time dilation in Γ2 times in the IFR STC
will also take place. However, because of the presence of real IFR intrinsic
time dilation in times in comparison with
absolute time, the resulting absolute time dilation, observed in the IFR, will
be only in times:
, (13)
where at 
: xij= – VΔt.
Consequently, the presence of real time dilation in the IFR and “imaginary” dilation
of absolute time leads to mutually observed time dilation on objects, moving in
any of the FR. So, mutually observed identical shrinkages of objects and time
dilations in mutually opposed FR are caused only by principle lack of mutually
coincidence of time moments of reading in them of one of the two counts of
space coordinates and principle lack of superposition of points of reading in
them of one of the two counts of coordinate-like time accordingly.
Incomprehension and neglect of this (together with indiscrimination of FR
coordinate-like intrinsic time and path-like proper time of objects [6]) is the
cause of origination in the SR of various imaginary paradoxes. And moreover, it
causes false treatment of SR by some physicists as purely mathematic theory,
which allows explaining observed physical phenomena only with some degree of
conventionality.
4. Conclusions
In that
way, Lorentz transformations correspond to gauge self
-deformation in the absolute space of STC of uniformly moving body. And at this
they image the impossibility of detection of any changes, which have realized
in the objects and physical processes after replacement of state of absolute
rest of the body to the state of its uniform motion relatively to the PV. And
consequently, they image the principle impossibility of detection, in which of
the two states the body is, using direct methods. However, the equality of any
IFR with the PVFR, caused by this, by no means does not deny the natural
occurrence of the unique PVFR, as well as of substance, motionless in it, - the
PV (the absolute ether of classical physics), in which motion of objects,
possessing mass, and propagation of electromagnetic waves take place. The PVFR
in the Lorentz and Poincare
groups of transformations is the element of not only set of the IFR, but also
of sets of any other FR types of gauge-deformed and gauge-self-deformated bodies [2]. Moreover PVFR is the unique common
element of all the possible FR sets.
Gauge invariance of eigenvalue
of the velocity of light (uniquely determined by matter proper quantum clock)
in any of the groups of transformation is caused by interdependence and mutual
determination of time course rate and of the velocity of propagation of
interaction (equal to the velocity of light). In this way the interaction
propagation velocity in space is set in the time. And the course rate of matter
proper time, in its turn, depends on the velocity of propagation of
interaction. After all, the rates of realization of any physical processes,
used for chronometry, are proportional to velocity of propagation of
interaction. That’s why it is impossible here to detect, which of the two
physical parameters (time or the velocity of propagation of interaction) is
initial (first-born). In that way, the impossibility of observing by the proper
clock not only the change of course rate of time, measured by them, but also
the change of velocity of propagation of interaction in the point of localization
of the clock, is a property (postulated by Einstein only for IFR) of any other
possible FR. And the relativity principle of SR is only the consequence of more
fundamental principle – principle of gauge deformation of matter and its STC under the effect of motion and gravity [2].
Reference list
[1]. Danylchenko P., Gauge Justification of Special Relativity,
in: The Gauge-evolutional theory of the Creation,
[2]. Danylchenko P, Foundations of the Gauge-evolutional theory of
the Creation (space,time,
gravitation and the Universe expansion),
[3]. Danylchenko P., Nature of relativistic length shrinkage,
in: Gauge-Evolutional Interpretation of Special and General Relativities,
[4]. Möller C., The Theory of
Relativity,
[5]. Lorentz H., The theory of electrons,
[6]. Danylchenko P., Physical essence of twins
paradox, in: Gauge-Evolutional Interpretation of Special and
General Relativities, Vinnitsa, O. Vlasuk, 2004, p.25
(read
http://pavlo-danylchenko.narod.ru/docs/Twins_Eng.html,
download
http://pavlo-danylchenko.narod.ru/docs/Twins_Eng.rar)
* Supplemented and completed version of the article from the
collection of articles “Gauge-Evolutional Interpretation of Special and General
Relativities”,