Preprint (07.03.2003)
Date: Fri, 07 Mar 2003 05:08:18 GMT
From:redshift0@narod.ru (Alexander Chepick)
Organization:
Newsgroups: sci.physics, sci.astro, alt.sci.physics.new-theories
Subject: the new particular relativity theory (NepaRT)
Key words: the particular relativity theory - the relativity principle - Lorentz's transformations - Galilee's transformations

THE PARTICULAR RELATIVITY THEORIES

A.M. Chepick, Nizhni Novgorod

e-mail: redshift0@narod.ru

Contrary to general opinion, the Galilee's classical transformations are not a limiting case of the Lorentz's transformations at infinite speed of light as thus the ballistic hypothesis is not meaningful. In this article the following fact have been proved : in isotropic static Euclidian space exist exactly four variants of the particular relativity theory under condition of performance of the relativity Principle.

1. Introduction

In physics the concept of inertial reference frame (IRF) is widely applied. It is defined as "systems of reference in which the law of inertia is carried out: a material point is in a condition of rest or uniform rectilinear movement, when any forces do not act on it (or act the forces mutually counterbalanced )". [3, v.2, p.145] Implicitly it is meant, that the space to which IRF is applied, is isotropic static three-dimensional Euclidian space. The infinity and a planeness of this space follow from its Euclidianness. In connection with what in this space the forces of gravitation will not be considered, then we shall name any relativity theory in this space the "particular" relativity theory according to the standard value of this term . The German translation of value of this term - "speziell".

For inertial systems of reference two principles of a relativity are known : Galilee [5, p.130] - "If laws of mechanics are fair in one system of coordinates they are fair and in any other system moving rectilinearly and uniformly concerning first system "; Einstein [5, p.147] - "All physical phenomena at identical entry conditions proceed equally in all IRF". 

The Galilee's relativity principle is understanding as "invariance of the equations of mechanics concerning Galilee's transformations: t'=t; r'=r+Vt; (here V - relative speed of two IRFs) ... the classical law of addition of speeds ( as vectors in three-dimensional Euclidian space) follows from the Galilee's transformations". [3, v.1, p.392] In particular, for speed of light this law is called "a ballistic hypothesis " and looks like: c' =c+V, where c' - speed of photons in the second system of reference moving with speed V concerning the first system of reference in which speed of photons is equal "". We shall notice, what actually ballistic hypothesis (BH) has meaning only for finite speed of light. And really, until appearance of the Einstein's particular relativity theory nobody officially did consider Galilee's classical transformations with taking into account of possible infinite speed of light (neither up to, nor after experimental determining of its finite value). Newton in his corpuscular theory did not do it even. The Galilee's relativity principle of a (PRG) together with Galilee's transformations make up the Galilee's relativity theory (TRG).

The Einstein's relativity Principle (PRE) together with a light's speed independence principle (PISL): "Speed of light in vacuum is identical in all IRF" (in Einstein's formulation [5, p.147]), form basis of the Einstein's particular relativity theory (PRT or SR) in which invariance of the equations describing any physical laws is carried out, concerning the Lorentz's transformations, linking values of spatial coordinates and time coordinate for two IRF. The multiplier γ  in these transformations depends on relative speed V of two IRF and value of a constant "", considered as equal to speed of light.

The Galilee's transformations are the Lorentz's transformations at infinite value "" as accounted. [1, p.22]. Value "" can determine the transformations and the formulation of the relativity theory, don't it?

Thus, there are at least two relativity theories in the specified space. Their correctness is determined by the real structure of the universe. The choice has been made for the benefit of PRT. But why? Really it had been proved that in considered space there can not be other relativity theories? Don't these theories are alternative in it?

In offered article an attempt to understand these questions is made.

2. A constant in Lorentz's transformations 

Logunov [2] has shown, that for a inference of Lorentz's transformations in isotropic static Euclidian space the a light's speed independence principle is not required, enough one relativity principle. Moreover, the existence of some constant in all IRFs follows from the relativity principle ( we shall defined it as cL- Logunov-Lorentz's constant). The constant has dimension of speed, and in sense of these transformations it is the maximal allowable speed. At measurements it turn out this value is equal to speed of light with the high accuracy. Einstein's genius was showing in that what he had managed to formulate the light's speed independence principle that got a such value of a constant cL. As to the theoretical proof of what the constant cL in the equations of transformation of time and metric coordinates from one system of reference in another also is the speed of light, so without PISL such proof simply does not exist!

Landau and Lifshitz have shown independence from IRF of the maximal speed of an extending of interaction of a matter. [1] (I think for this conception the term "supremum of speed of a matter interaction extending" is more correct because it itself unites the conceptions of an achievable and unattainable limit.) It gives equivalence of this value and Logunov - Lorentz's constant as in one space two different constants of identical dimension cannot simultaneously be maxima). Precisely the same proof of the equality of cL and speed of light is in case of performance of the Einstein's independence principle. They (as well as others of physics) examined only two hypotheses linked with speed of light: the Einstein's independence principle and the "ballistic hypothesis". After considering of arguments against the second hypothesis (arguments into the first hypothesis's favor actually also are necessary for considering as reasons against the second hypothesis, according to a rule of the proof of alternative hypotheses), they had accounted what they had proved the first one though alternativeness of these hypotheses had not been proved.

Apparently from the previous reasonings, the Logunov-Lorentz's constant is supremum of speed of a matter interaction extending.

Let's consider the existing relativity theories a from the point of view of a ratio of values supremum of speed of a matter interaction extending (cL) and speed of light (c).

We receive, that PRT is carried out at joint performance of conditions: cL=c and cL < ∞. (Hereinafter expression "cL < ∞ means " cL is finite", and expression "cL= ∞" means "cL is infinite", exactly: " For any high value D exists IRF and the objects in it such that speed of interaction between them is greater than D ".)

Accordingly, theory TRG+BH is carried out at joint performance of conditions: cL ≠ c, because in this theory the speed of light cannot be a constant; and cL = ∞, because the limit of speed of objects does not exist, hence, there is not a maximal of speed of a matter interaction extending.

3. Other relativity theories

Natural alternative to the light's speed independence principle is non-execution of this principle. If in such a case ( and in the specified space and a relativity principle working in it) speed of light remains equal cL then (as proved above) the speed of light will be equal to supremum of speed of a matter interaction extending, that is, it will be a constant and independent from IRF, and thus it is performance PISL. Thus, the received contradiction, and also that in the above-stated conditions equality cL =c is consequence from PISL, showed, that performance PISL is equivalent to equality cL =c, and non-execution PISL is equivalent to an inequality cL ≠ c. 

A hypothesis (theory) of a relativity corresponding to this inequality we shall name NePaRT. Its many properties were considered in article "The Basis of the New Particular Relativity Theory" [4]. The inequality cL ≠ c corresponds to the formulation of "antiprinciple" to PISL: "IRF exist in which speed of photons is not identical". The photons, radiated by a source, have in its system of reference some speed c, identical in all directions, because of isotropic conditions of its distribution. In this hypothesis the photons are not allocated in a separate class of the elementary particles having zero mass of rest and infinite time of a life. Therefore this hypothesis is simpler, more natural and beautiful, hence, it has more rights to be true (by Einstein's criteria). 

Thus, NePaRT is carried out at joint performance of conditions: cL≠c and cL< ∞. 

The stayed variant of joint conditions: cL =c and cL= ∞, characterizes some theory of a relativity in which Galilee's transformations operate, but light is spreading momentaryly.

We shall name this theory TRG∞. Neither the reality of this theory, nor its the other properties, that are following from made assumptions, do not interest for us. Existence of the formulation of the theory (hypothesis) suffices for our purposes.

4. Alternativeness of the relativity theories

Let's analyze the Table 1 in which links between 4 considered theories and ratios specifying them are reflected.

Tab. 1

cL = c cL ≠ c
cL= ∞ TRG∞ TRG+BH
cL< ∞ PRT NePaRT

Relativity theories and the ratios specifying them

From Table 1 it's clearly, that in TRG∞ and TRG+BH as well as in PRT, it is necessary to consider separately a relativity principle and a hypothesis about speed of light (a ballistic hypothesis). It leads to that on all above mentioned table one relativity principle operates, because PRE is generalization of PRG, and between them there are no contradictions. 

Also from the table clearly, that PRT  and TRG+BH are not alternative hypotheses under any conditions, hence, they cannot be connected, and cannot follow one from another when one of conditions changes. 

Alternative hypotheses are:
- at cL = ∞: TRG∞     and TRG+BH;
- at cL < ∞: PRT        and NePaRT;
- at cL =  c: TRG∞     and PRT;
- at cL ≠  c: TRG+BH and NePaRT. 

5. Consequences

Contrary to general opinion, the Galilee's classical transformations are not a limit case of the Lorentz's transformations at infinite speed of light because the ballistic hypothesis has not any sense at such a case.

Actually, in conditions of performance of Einstein's relativity principle the light's speed independence principle is not alternative to the ballistic hypothesis , but to an "antiprinciple" of light's speed independence. That is, TRG+BH is a limit case of NePaRT, instead of PRT. 

Though the measuring directly of supremum of speed of a matter interaction extending is impossible, because there are no carriers of such speed, nevertheless, it is possible to calculate it, as its value is equal to cL,that participates in definition of γL: γL = [1-(V/cL)2]-1/2.

How it has been determined earlier in experiments, that cL) was approximately equal to speed of light, and distinction between these values was zero or very small and lay outside of accessible accuracy of measurements. Therefore in our universe the theories TRG∞ and TRG+BH don't work. And for the same reason PRT and NePaRT till now are not distinguished in all an accessible range of speeds. Hence, in conditions of a presence in isotropic static three-dimensional Euclidian space and performance of the Einstein's relativity principle , true particular relativity theory is among two variants: PRT and NePaRT.

Let's sum up:
- All experiments denying TRG+BH, it is necessary to treat for the benefit of and PRT, and NePaRT;
- All experiments denying TRG+BH, it is necessary to interpret for the benefit of and PRT, and NePaRT;
- All experiments which have confirmed PRT, confirm also NePaRT, because of small distinction of their results for all range of speeds accessible till now. So NePaRT and PRT have equal rights for the name "the theory" ;
- NePaRT is more simple, than PRT;
- "Heiress" of Galilee's classical transformations is not PRT, but NePaRT.

Thus:
the choice of the theory that is more corresponding to actuality is Yours!

P.S. PRT is particular case of RT.

6. Conclusions


1. In isotropic static three-dimensional Euclidian space and in conditions of performance of the Einstein's relativity principle, a construction of 4 particular relativity theories is possible in all, and in two of them Galilee's transformations are carried out.
2. The others two relativity theories (PRT and NePaRT) have equal rights as the theories, because of small distinction of their results for all range of speeds accessible till now. because all experiments denying TRG+BH, necessarily to consider for the benefit of both PRT and NePaRT; all experiments that confirmed PRT, have confirmed also NePaRT, because of small distinction of results of these theories in all a range of speeds accessible till now.
3. NePaRT is more simple than PRT.
4. The Galilee's classical relativity theory is not a limit case of PRT at infinite speed of light because the ballistic hypothesis has not any sense at such a case.
5. TRG+BH is a limit case of NePaRT.

The literature:
[1] L.D.Landau, E.M.Lifshits. The field theory , (., the Science, 1988.)
[2] A.A.Logunov. Bases of the relativity theory, (., 1982.)
[3] The physical encycLopedia, (., the Soviet encycLopedia, 1988-1992.)
[4] A.M.Chepick, "Bases of the New Particular Theory of the Relativity ", (Internet - magazine on physics, , 2003)
[5] A.Einstein, L.Infeld. Evolution of physics, (., the Science, 1965.)

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