The nature of relativistic length
shrinkage*
Danylchenko P.
SPE "GeoSystem", Vinnitsa, Ukraine
Contact with author: pavlodanylchenko@gmail.com
It is shown here, that
relativistic shrinkage of the length of moving body appears itself (without the
influence of external forces). This shrinkage is caused by isobaric
self-contraction of body matter and by propagation of the strength of inertia
forces field together with the front of body intrinsic time. A mechanism of
kinetic energy filling (accumulation) of a body is considered and propagation
of the phase waves of perturbation of gravitational field at supraluminal
velocity is substantiated here.
1.Introduction
Physical processes during their separate stages can be accompanied and can be not
accompanied by transfer of matter or its excited state in space. In the first
case, they are characterized by group velocity V of transfer of particles and quasi-particles (photons, phonons, excitons
etc.). This velocity cannot exceed the velocity of light in free space (equal
to one if distances are measured in light units of length). In the second case,
they are characterized by phase velocity U of propagation of change of collective
space-time state of matter. The change of this state of matter realizes, as
suggested here, together with the change of
graviinertial stressed state in a space, filled with matter. Therefore, not
only propagation of change of collective space-time state of matter but also
propagation of induction of strength of inertia forces field in intrinsic frame
of reference of space coordinates and time (FR) of hypothetical incompressible
(perfectly rigid) body will happen momentarily (u ≡ ∞). Phase velocity of propagation of induction of
spatial distribution of the strength of inertia forces field in an
incompressible body, which moves relatively to the hypothetically physically
homogeneous physical vacuum (PV) at a constant velocity V, in the PVFR will not be infinitely high, but equal to: U = c 2/V = V -1 (c = 1). This fact
is connected with translational motion of body, in which a wave front of
induction of graviinertial stressed state propagates.
2.Derivation
of relativistic length shrinkage
Let the incompressible body moves uniformly in
pseudo-Euclidean Minkowski space-time of the PVFR at absolute velocity V0 (before the induction of the strength of
inertia forces field in it). Also let the initial
distance along the movement route between two arbitrary points (i and j) of the body in the PVFR absolute space (in which frequency of
universal background is isotropic) is equal to Xij0. Then after body transition into new steady state of
its uniform motion at absolute velocity Vj = Vi = V, the distance between these two points will be equal
to:
, (1)
where:
(2)
and:
(3)
- the durations of time delay of accordingly
induction and removal of the strength of inertial forces field in point j, regarding point i (equal to desynchronizations, observed in the PVFR, of
all the other events, which are synchronous in these points in the inertial FR
(IFR) of moving body);
δXi and δXj are the traversed paths in absolute space
of accordingly points i and j from the moments of induction Ti0 and Tj0 till the moments of removal Ti = Ti0 + δTi and Tj = Tj0 + δTj of strengths of inertia forces field in
these points; Γ0 = (1 Ц V02)-1/2
and Γ = (1 Ц V 2)-1/2 are characteristics of the accordingly
initial and newly-formed IFR;
U0 ≡ V0-1 and U ≡ V -1 - velocities of propagation of fronts of
processes of induction and removal of strengths of inertia forces field in the
PVFR accordingly.
LetТs assume that Xij is a function just of V and depends neither on the value of V0 nor on the law of body motion before it takes
on the value of inertia motion velocity V. Then, according to (3), δTij does not depend on V0 and on this law of body motion either. Basing on this
fact and on the condition V0 = 0, let's choose a uniformly accelerated motion (as the
simplest law of irregular motion) of the point i of the body before it takes the value of velocity V:
, (4)
where ai = dVi /dT is the acceleration of the motion of point
i. Then multiplying the left and the right parts
of the equation (4) by dT and
considering the immobility of the point j
during the time δTijа (dXj = 0), we will
obtain the following differential equation:
, (5)
solving which we will find : 
,
. (6)
When V0 = 0:а Xij = xij / Γ, and δTij = ΓVxij,, where:а
xij = Xij (0) is the distance between the points j and i, measured in the IFR of moving body and equal to the distance
between them in absolute space in hypothetical state of body absolute rest
relatively to the PV.
So, if an incompressible body proceeds
from the state of rest relatively to the PV into a new-steady state of inertial
motion, then relativistic shrinkage of body length along the direction of
motion takes place. The value of this shrinkage is determined by the analytical
dependence, discovered by Fitzgerald and Lorentz independently from each other,
and does not depend on the law of change of strengths:
of removable gravitational
(graviinertial) field, which originates in the intrinsic FR of the body. And
consequently, the value of this shrinkage does not depend on the law of motion
of body points during the proceeding of body from the state of rest or inertial
motion into the state of inertial motion at another velocity. Here: PA and HA - accordingly linear
momentum and invariable energy (conservative Hamiltonian) of free-falling (motionless in the PVFR) particle A,
which are definite in intrinsic FR of
the accelerating body; 
а- improper values of
the velocity of light in free space in body intrinsic FR (unequal in different
points of physically inhomogeneous intrinsic space of body in proper quantum
time t of point i);аа Pj and mj
- accordingly linear momentum in the PVFR and eigenvalue of mass of the point
object (particle) j of the body. At
this, conditions:
,
, (7)
which follow from (1-3), always guarantee simultaneity
of removal of strengths of inertial forces field in body intrinsic FR in all
body points. And consequently, they also guarantee a momentary transition in
this FR (without any transient process) of an incompressible body into
equilibrium state of inertial motion. And the fulfillment of these conditions
is possible only at the following distribution of strength of inertia forces
field along the moving body:
. (8)
Where, as we supposed, Gi(V) can vary with time
according to the arbitrary law. And it specifies at that any law of body
motion. At that spatial distribution of strength of graviinertial field
(inertia forces field) unconditional realization of the identity will take place:
.
3. Equations
of irregular motion of body points
According to (8), the motion of any point of the body
in the process of its transition from inertial motion at absolute velocity V0 to inertial motion at
absolute velocity V can be described
by the same parametric equations as motion of the point i:
, (9)
, (10)
or in another form by the equation:
(11)
Where:
, (12)
, (13)
and:
(14)
is a coordinate of an asymptotic limit (singular
plane) of intrinsic space of moving body, which can be considered as an
observer horizon of the body FR (Gc = ∞);
, (15)
is a coordinate in absolute space of hypothetically
initial position of the observer horizon of body at the beginning of its motion
(V = 0) on condition that distribution of strengths of inertia
forces field along the body from the beginning of its motion is the same as at
the given identical velocity of all its points Gi(0) = Gi(V) = const(V);
, (16)
is a hypothetical moment of absolute time, when the body
motion in the absolute PV space would begin, if distribution of strengths of
inertia forces field along the body were stationary. At that, Tc(0) = Ti(0). And at coincidence of the points of origin in
absolute space and in intrinsic space of the body in its hypothetic state of
rest relatively to the PV (Xi(0) = xi(0)) and also Xc(0) = xc(0). When dependence of strengths of inertia forces
field on absolute velocities V of
body points is weak, equation (11) corresponds to quasi-hyperbolic motion of these
points. If the distribution of strengths of inertia forces field along the
moving body is stationary (Gi ≡ const (V)), then all the body points
perform in the PVFR not quasi-hyperbolic but definitely a hyperbolic motion. And the moving body (even if it is
compressible) will be resting in an appropriate to it Möller rigid
accelerating FR [1,2]. A proportional mutual synchronization of quantum clock,
located in different points of physically inhomogeneous intrinsic space of this
FR, is possible only in this FR. But in general case, events in different
points are considered just to coincide with each other, if they happen at the
same instantaneous values of absolute velocities V of these points. Events, not having direct cause-and-effect
relations with each other, are
meant here under coincident events. But in the presence of common cause, mutual
correlation of coincident events can take place. These events correspond to
definite collective space-time state (microphase state) of particles of body
matter. And they are simultaneous according to quantum clock, only in the case
of homogeneity of intrinsic time t,
which is possible only in the case of stationarity of spatial distribution of
the velocity of light in free space in co-moving FR:
.
And it is possible only in Möller FR [1, 2].
From the condition of the absence of increment of
action S: 
, corresponding to invariance of collective space-time state
of matter, we will have:
where L
- Lagrangian of body matter. In view of
this, the front of induction of strength of inertia forces field in
incompressible body (the same as the front of propagation of change of
collective space-time state of matter) is identical to the front of coincident
events.
According to Lorentz transformations, the front of
coincident events of any body, which moves relatively to an observer at
velocity
, will be moving in observer FR, as well as in the PVFR, not
at infinitely high, but at finite phase velocity u = vc2/v.
4. Propagation
of the changes of graviinertial stressed state and elastic deformation in
compressible bodyа
For an elastically compressible (deformable) body,
the distance 
аbetween the points i and j in its uniform and stable metrical intrinsic space (where the
motion of its points in the process of elastic deformation of the body matter
is observable) can be connected with the distance between them xij in inseparable from the
body its nonuniform and metrically instable physical intrinsic space by the
following dependence: 
= α(V)xij.
Where: α(V) is a
coefficient of the elastic shrinkage of body size along the direction of its
motion, that depends on the velocity of the body when the strength of inertia
forces field is instable (G ≠ const(V)).
аIn contrast
to a hypothetical incompressible body, in metrical intrinsic space of a
compressible body, only microobjects (elementary particles) have purely
relativistic size shrinkage along the direction of motion. It is connected with
the elastic deformation of matter macroobjects that also can be observed in the
body intrinsic FR. As well as in incompressible body, this shrinkage is caused
by elementary particles adaptation (and by adaptation of the matter as the
whole, owing to Van der Waals forces, which have electromagnetic nature) to
changed conditions of elementary particles interaction. This adaptation
guarantees in the first place the isotropy of interaction frequency and becomes
apparent in co-moving FR at the absence of anisotropy of the radiation spectrum
of radiation sources, motionless relatively to the body. Lorentz considered
processes, which are connected with this adaptation, first in detail [3] on the
example of electrical and electromagnetic phenomena. The possibility of such
adaptation follows from the wave nature of elementary particles and of matter
as the whole. ThatТs why relativistic size shrinkage realizes at elementary
particles level and is connected with longitudinal self-contraction (which is
initiated by motion) of wave-like formations, which correspond to elementary
particles [4].
Relativistic size shrinkage along the direction of
the body motion will guarantee isotropy of the velocity of light in free space
only in physical intrinsic space of the compressible body. In metrical
intrinsic space (considering the observability of body deformation in it) the
velocity of light in free space will be anisotropic. Moreover, in contrast to
physical intrinsic space, in metrical intrinsic space definition of an interval
between two world points (which is invariant to transformations of coordinates
only in physical spaces), as well as the definition of energy and momentum of
any objects has no physical sense. That is why the analysis of dynamics of body
compression and of the motion of objects is impossible in principle in this
space [5]. Dynamics of the objects can be analyzed only in physical intrinsic
space of a compressed body using continuous renormalization of all the
measurements and spatial characteristics, determined in it, considering their
change in metrical intrinsic space of the body.
In elastic compressible body, as well as in
hypothetical incompressible body, the front of induction of strengths of
graviinertial field in it can be identified with a wave front of change of
collective space-time state of body matter. That is why, also in an intrinsic
FR of elastically compressible body the
propagation not only of quantum of action, but
also of change of space-time distribution of the strength of graviinertial
field (the main characteristic of collective space-time state of matter), takes
place momentarily in principle. This is caused by the wave nature of elementary
particles of matter, which becomes apparent also in collective space-time state
of matter.
Let the linear momentum and therefore velocity of an
elastic compressible body increase in a result of a shock action (impact). Then
in the PVFR (as well as in FR of any body that moves at another velocity) a
phase soliton (phase packet) of modulation of strength of graviinertial field
will run along the moving body at supraluminal phase velocity. This soliton
changes the value of relativistic shrinkage of molecules of body matter and does
not cause their elastic deformation. After that, a soliton (wave packet) of
elastic deformation and excitation of matter molecules will run along the body
at a velocity of sound. Body filling with additional kinetic energy, as it were
transferred by graviinertial phase soliton at supraluminal velocity, as a
matter of fact is not connected with ripple-through energy transfer in it. This
filling is an inert process and realizes only due to accumulation of difference
of Doppler energies of exchange virtual elementary particles and
quasi-particles, which propagate in the process of interaction of elementary
particles, atoms and molecules in and against the direction of soliton
propagation. These are virtual pi-mesons that during the process of strong
interaction maintain collective dynamic equilibrium between protons and
neutrons in an atom. And these also are virtual photons that during the process
of electromagnetic interaction maintain collective dynamic equilibrium between
protons and electrons in an atom, as well as between electrically and
magnetically polarized atoms and molecules. At this, the work is executed by
the forces, which disturb the mechanical equilibrium of the matter. These
forces are equal to inertia forces (they are, like gravitational forces,
actually only pseudoforces [4]), but they are directed oppositely. Neither
entropy nor enthalpy of the matter in the body intrinsic FR vary during the
process of the body filling with kinetic energy. That is why neither free
photons nor phonons or any other quasi-particles are generated and transferred
in the body. And therefore, ripple-through energy transfer and energy
dissipation are absent. In the contrast to total energy, Helmholtz energy of
body matter increases in the PVFR not only due to increase of linear momentum
and of relativistic shrinkage of molecular volume, but also due to decrease of
Planck relativistic temperature. The energy of soliton of elastic deformation
(which runs after the phase soliton) will be dissipated and transformed into heat
after multiple reflections from the body boundaries.
In this case, before coming of a soliton of elastic
deformation of matter, motion of points of compressible body can be described
by the same equations (8-16) as motion of points of incompressible body. Now
let the body linear momentum increase due to a long-lived force. And thatТs why
the front of removal of the graviinertial stressed state runs along the body
after the induction of a definite elastic deformation of its matter. Then
motion of the body points before the front running can be described by
equations, different from the ones (8-16). The distance between the points j and i 
аin elastically
deformated state of the body matter will be used in these equations instead of
the distance xij. In this
case, removal of graviinertial stressed state will realize the same way as in
an incompressible body, but considering the change of the distances xij to distances 
аthat take place at a
point in time when the front of removal of the stressed state is passing
through the point j.
Relativistic shrinkage of the length of moving body
realizes itself (without influence of any external forces) and its matter does
not exhibit resistance to contraction. Therefore work on relativistic
contraction of matter:
,
executes by
internal forces due to decrease of heat content (enthalpy) of moving body
matter:
,
where: 
and 
- accordingly relativistic value and eigenvalue of matter
molar volume; 
- Lagrangian of enthalpy 
, and 
а- internal energy of
the one mole of matter. At that the energy of thermal oscillatory motion of
matter molecules partially transforms into kinetic energy of their ordered
motion.
5. Effects
caused by equivalence of removable (graviinertial)
and irremovable gravitational fields
Momentary propagation of induction of graviinertial
stressed state (physical inhomogeneity of the body intrinsic space, that can be
identified to a gravitational field) in the body is well matched in
Einstein-Podolski-Rosen paradox [6,7] with a momentary intercoordination of
changes in the quantum-mechanical characteristics of previously correlated
photons or elementary particles after mutual self-distancing of the ones at
arbitrary long spacing. This points at the possibility of momentary propagation
of disturbance of proper gravitational field (in intrinsic FR) also in free
space. Also this points at rigid connection in space of gravitational field to
macro- or microobject, which creates it, (at the impossibility of time delay of
displacement of spatial distribution of gravitational field strength relatively
to displacement of this object). That is why the carriers of gravitational
field in free space are photons, elementary particles and any moving
macroobjects, consisting of them, but not hypothetical gravitons (their
existence is impossible in principle as it was shown in [4]). Any moving
macroobject (body) can be characterized by de Broglie frequency. And it lets us
consider moving body also as a Уgraviton
waveФ, which transfers energy.а
During the rotation of a negatively charged body around
a positively charged body, electromagnetic radiation is generated. But similar
specific radiation is not generated during the rotation of planets around the
Sun. Otherwise the planets finally would fall on the Sun due to continuous
energy losses. That is why only the matter, the accretion of which happens from
one star to another in a compact system of double star, can be considered as
Уgraviton radiationФ.
Phase gravitational waves (caused, for example, by
the rotation of astronomical body around the point, which is not coincide with
its centre of mass) that propagate in free space at supraluminal velocity give
rise to disturbance in the motion of another astronomical bodies, not executing
any work. At this, only transition of internal energy of the matter of
astronomical bodies into kinetic energy realizes, as it does during a free fall
of macroobjects in terrestrial gravitational field. These phase waves are progressive waves of metrical and physical microinhomogeneities of space in the form of space-time
modulations of permittivity and permeability of PV, which uniquely determine
metrical and physical properties of the space, filled with PV. Space-time
modulations of permittivity and permeability of PV also appear in the process
of propagation of radiation because of the presence of negative feedbacks,
which guarantee self-restriction of improper values of electric and magnetic
strengths of electromagnetic wave. And these negative feedbacks also cause the
formation of wave packets of quanta of electromagnetic energy (soliton-like
photons) nearby elementary particles because of the presence of very
significant metrical and physical microinhomogeneities of space in their
neighbourhood.
6. Conclusions
The relativistic shrinkage of the length of moving body
is purely kinematics effect. This effect is connected with the change of
relativistic values of matter thermodynamic parameters and not connected with
matter elastic properties. At any law of body motion this shrinkage appears and
varies during the process of isobaric self-contraction of matter. This process
always passes ahead of the process of change of matter elastic compression. And
this is caused by propagation of changes of the strength of inertia forces
field together with propagation of changes of collective space-time state of
matter (propagation of front of body intrinsic time).
Phase waves of perturbation of removable
(graviinertial) and irremovable gravitational fields donТt transfer energy
themselves. They only create necessary conditions for energy transfer in the
process of the interaction of matter elementary particles. This energy transfer
realizes due to accumulation of difference of Doppler values of energies of
exchange virtual elementary particles and quasi-particles, which propagate in
and against the direction of the body motion. ThatТs why these waves can
propagate at supraluminal velocity.
Reference list
[1]. а Möller C., The Theory of Relativity, Clarendon Press Oxford, 1972
[2]. а Danylchenko P.,а Phenomenological justification of relativistic shrinkage of the
length of moving body, in: The Gauge-evolutional theory of the Creation,
Ukraine, Vinnytsia, 1994, 1, 5
[3]. а Lorentz
H., The theory of electrons, Leipzig: Teubner, 1916
[4]. а Danylchenko P., Foundations of the
Gauge-evolutional theory of the Creation (space, time, gravitation and the
Universe expansion),
Ukraine,Vinnytsia,1994
[5]. а Danylchenko P., Nonrigid frames of reference
contracting in Minkowski space-time, in: The Gauge-evolutional theory of the
Creation, Ukraine, Vinnytsia, 1994, 1,
52
[6]. а Einstein A., Podolski B.,а Rosen N.,
Philos. Rev., 1935, 47, 7
[7].аа Vigier
J.-P., paper on Einstein-Podolski-Rosen paradox, in Einstein Centenarium, ed.
H.-J. Treder Berlin: Akademie Verlag, 1982
*а Supplemented and completed version of the
article from the collection of articles УGauge-Evolutional Interpretation of
Special and General RelativitiesФ, Vinnitsa, O. Vlasuk, 2004