Preprint (07.10.2004)
Date: Thu,07 Oct 2004 21:51:18 GMT
From:redshift0@narod.ru (Alexander Chepick)
Organization:
Newsgroups: sci.physics, alt.sci.physics.new-theories
Subject: the special relativity theory
Key words: the special relativity theory - inertial frame - transformations of coordinates - Lorentz transformations
PACS: 03.30.+p

The analysis of the book of A. Einstein, L. Infeld
" EVOLUTION OF PHYSICS "

A.M. Chepick, Nizhni Novgorod,
 e-mail: redshift0@narod.ru

By a century of the relativity theory

Abstract
Reasons and the statements of SR stated in the book A. Einstein, L. Infeld "EVOLUTION of PHYSICS" ("Nauka", 1954) are analyzed ,

1. Introduction

In the beginning of XX century in mechanics a performance of a relativity principle of Galilee and transformations Galilee for inertial systems of reference (IFR) was considered established. But the law of transformation of coordinates between two concrete IFRs cannot depend on what type of interaction we consider, electromagnetic or mechanical; it describes the unequivocal dependence in these systems of reference between change of position of objects in time without dependence from these objects are actuated by what type of interaction. Thus, for definition of communication between IFRs it is necessary to consider in common any interactions, in particular mechanics and electrodynamics.

But it turn out that such union has led to to the contradiction. The way to the solvability of crisis in physics has been found in new theory.

In the chapter "FIELD and the RELATIVITY" authors of the book consider and analyze problems of the description of the physical effects connected to an electromagnetic field. A motivated refusal of representation about absolute character of time and the space, used in classical mechanics, became a result of this analysis. They offered and argued the principles on the basis of which new representation (named "Relativity") about space and time have been constructed. 

With the great respect to authors of the book I ask to read unbiassedly offered in this article the analysis of their arguments concerning special theory of a relativity (SRT).

2. Logic of SR proof

Authors of the book defined inertial system of coordinates and have chosen as the basic three positions of electrodynamics and mechanics: experimental data about speed of propagation of electromagnetic waves, experimental data about possible invariancy in IFR of laws of mechanics and electrodynamics (on their basis the principle of independence of speed of light and a principle of a relativity of Einstein have been formulated accordingly), and classical transformations of coordinates (the theoretical assumption). Then they have considered such bound with light a real and imaginary experiments, explanations of which, in their opinion, demanded execution or showed nonexecution of those or other basic statements. As representation about movement of light's waves has been closely connected to theories of movement of an ether these theories have been involved in the analysis also.

In spite of the fact that the proof of any postulates is considered impossible without the reference to other postulates, authors so have constructed the analysis of the available facts and imaginary experiments and so have made an argumentation that they came to a conclusion - the principles of the theory of a relativity offered by them cannot be nonfulfilled:

"We already tried to change the first two  principles and came to disagreement with experiment. All theories of ether's movement have demanded a changing of first two principles. But it did not bring any advantage. Once again we convince ourselves in severity of our difficulties. The new way is necessary. It is a way of a recognition of the first and second statement as base, and though it and seems strange, of refusal from the third statement." [p.145]

In other words, authors of the book have considered that by them it has been proved that nonexecution of the postulates in the specified formulation has been " in disagreement with experiment ". Thus, the specified postulates should be carried out, that is, their fulfilment is obligatory one, hence - they are proved.

Further in article the analysis of their argumentation is given.

Let's replace the name "system of coordinates" with more modern "frame of reference", implying, generally speaking, that in each system a clock and a ruler can be distinct from another system. Authors prove it on pages 150-153, and make conclusion about change of a moving  segment's length, and about change of a moving clock's rate of time :

"Our reason can be formulated differently: if speed of light is the same in all systems, then moving  segments should change their length, moving clocks should change the rhythm, and the laws managing these changes, are strictly determined. [p.154]

3. Einstein's postulate of a relativity

In the book the Galilean relativity principle is considered, and definition of inertial system of coordinates is given in the following formulations:

"   "If laws of mechanics are fair in one system of coordinates they are fair and in any other system moving rectilinearly and evenly concerning first system."

If a coordinates system is moving non-evenly relatively another one then laws of mechanics cannot be fair in both systems simultaneously. "Good" systems of coordinates, in other words in which laws of mechanics are fair, we name it inertial systems."[p.130]

The Galilean relativity principle in mechanics follows from this, that the time, the distance, force and acceleration do not varying at Galilean transformation. But its fulfilment cannot be checked up with sufficient accuracy in experiments:

"If experiment is executed carefully, it finds out discrepancy with the theory, obliged to rotation of the Earth or, otherwise, to that fact, that laws of mechanics how it here are formulated, are not strictly fair in the system of coordinates rigidly connected to the Earth." [p.128]

By virtue of that, that Lorentz has found out a nonclassical kind of transformations of coordinates between IFR, which the Maxwell equations are invariant for, Einstein has expanded applicability of a principle of a relativity, having added in him firstly laws of electrodynamics, and then and all laws of physics. But the terrestrial system of reference is not inertial. Therefore accuracy of a checking of the Einstein's relativity Postulate is limited and cannot be increased. Hence, this Postulate cannot be considered, as the general experimental fact.

4. A postulate of independence of light's speed

Authors of the book recognize " independence of light's speed" in IFR as a initial position of the theory that is generalizing the experimental facts by definition of speed of light, supervision of double stars and a rotating wheel, and also the Michelson-Morly experiment.

As far as in classical mechanics the speed of light cannot be limited for all inertial frames, and classical transformations do not allow to laws of an electromagnetic field (Maxwell equations) to be invariant relatively IFR, the contradiction between classical mechanics and laws of an electromagnetic field turns out.

"...we shall assume both the ether is entrapped by movement of a room and a light's source; and classical transformation.

If I switch on light which source is rigidly tied to my room then speed of a light's signal is equal 300000 kilometers a second as it is experimentally proved. But the external observer will notice movement of a room and consequently, and movement of a light's source, and as the ether is entrapped by movement, he should draw a conclusion: speed of light in external system of coordinates is various in various directions. It is more, than the established speed of light, in a direction of movement of a room and is less in an opposite direction. Our conclusion is those: if the ether is entrapped by movement of a room and a light's source and if mechanical laws are fair then speed of light should depend on speed of a light's source. Light, getting in our eyes from a moving source, would have the greater speed if the source was coming toward us, and smaller if it moved away from us." [p.139-140]

 As results of supervision do not confirm these reasonings it is obvious that some of the made assumptions and conclusions are not carried out may be in part:
- Speed of a light's signal from a source, motionless concerning the receiver in anyone IFR, is a constant;
- The the ether is entrapped by a moving room;
- The classical law of the sum of speeds is carried out;
- Speed of light depends on speed of a source.

Authors of the book analyze last three statements, and an opportunity of nonfulfilment of the first statement at all do not consider, supposing its as precisely established experimental fact. Actually with enough big accuracy it is established not this fact, but at least others two:

A. Interval of time been measured in anyone IFR (at passage, along a segment of a direct line, of a light's impulse from a source, motionless concerning the receiver) by two clocks (located at the ends of the segment and synchronized with the help of a light's signal or slowly moving clock), corresponds to time spent by a light's impulse for passage along this segment with speed, conterminous with a constant value, approximately was equal 300000 km/s;

B. Interval of time been measured on one clock in anyone IFR, at round-trip (along a segment of a direct line in a direction there and back) of a light's impulse from a source, motionless concerning the receiver, corresponds to time spent by a light's impulse for passage along this segment with speed, conterminous with a constant value, approximately was equal 300000 km/s.

Alas, these both facts do not contradict anisotropic speed of light in given IFR.

Besides that, even on assuming identical speed of identical photons in identical conditions of homogeneous and isotropic spaces in some IFR, we cannot tell, that photons with other characteristics (frequency, polarization) should move with the same speed.

"Speed of light is always identical in all systems of coordinates irrespective of, whether the light's source moves or not and irrespective of the fact how it moves.

We shall not discuss in detail many experiments, of which this important conclusion can be made. However we can show a very simple argument which if does not prove, that speed of light is independent of movement of a source nevertheless does this fact very convincing and clear.

In our planetary system the Earth and other planets move around of the Sun. We do not know about existence of other planetary systems similar to ours. However there are many systems - so-called double stars, - consisting of two stars moving around of a point, named their center of gravity. Supervision of movement of these double stars detects that for them the law of gravitation of Newton is fair. Now we shall assume that speed of light depends on speed of a radiating body.

Then the ray of light which has  emitted from a star, will be spreading faster or more slowly, according to  speed of a star at a moment of light's emanation. In this case all movement would seem to us extremely confused, and because of remoteness of double stars it would be impossible to confirm validity of the same gravitation law that operates on movements of our planetary system. "[p.140]

Really, the movement of double stars would seem to us extremely confused if to assume that speeds are summed under the classical law. The considered example shows that so to consider it is impossible, hence, Galilean transformations are not fair. In authors's opinion this contradiction testifies about "independence of light's speed from speed of a source". At a deducing of this statement Einstein instead of a phrase: "classical dependence of light's speed from speed of a source" (actually to which he had to construct the contradiction) has left simply "dependence of light's speed from speed of a source", may be because then there were not other known formulas of speed's transformations; and then he has constructed the alternative statement to the second phrase, instead of to the first one.

But this contradiction at all does not speak about independence of light's speed from speed of a source because there can be many formulas of transformations of coordinates which will provide such "addition" of a source's speed and speed of photons, that the result of transformation will be very close to light's speed "before addition". And the change of light's speed received on these formulas will be within the limits of accuracy of its measurement for enough large range of a source's speed. It is impossible to prove experimentally absence of different "unilateral" speed of photons in our system of coordinates, if change of this speed less of accessible accuracy of measurement.

Thus, full logic alternative to the statement "classical dependence of light's speed from speed of a source" is the statement "non-classical dependence of light's speed from speed of a source", but not an Einstein's conclusion: "independence of light's speed from speed of a source" which only is one of possible alternatives.

Here it is impossible to tell anything about isotropy of light's speed, for in the considered experiment a light from two sources comes to the observer in one direction.

The similar mistake has been made by authors of the book and in deductions from the third experiment with a rotating wheel:

"Let's consider an other experiment, based on very simple idea. We shall imagine a wheel that is rotating very quickly. Under our assumption, the ether is entrapped by movement and accepts participation in it. The light's wave, passing near to a wheel, would have various speeds, in dependence by, whether there is a wheel in a rest or in movement. Speed of light in a unmoving ether would differ from speed of light on ether, entrapped by movement of a wheel just as speed of a sound wave changes in quiet and windy days. But such distinction is not observed! Irrespective of the decisive experiment which we think out, the conclusion always contradicts the assumption, that the ether is entrapped by movement.

Thus, the result of our researches maintained by more detailed technical arguments, is those: Speed of light does not depend from movement of a emitting source. It is impossible to assume that the moving body entraps a ether surrounding this body." [p.141]

In such categorical formulation the statement about an ether can be non-executed. By virtue of the limited accuracy of measurement it is impossible to speak about full absence of the entrapping. But if the entrapping of ether is present, then it is in extremely small degree. Therefore this experiment shows with some accuracy an absence of the entrapping of an ether, but does not prove its absolute absence.

Further the authors have analysed possible inconstancy of speed of light in IFR of the receiver and came to a conclusion:

"If our assumption is correct, speed of light in a direction of movement of the Earth would differ from speed of light in an opposite direction. It is possible to count up turning out differences of speeds and to invent corresponding experimental check. For from the theory follows, that here take place only small differences of times it is necessary to think up very witty installation. It has been made in well-known Michelson-Morly experiment. Result of it was the death sentence for the theory of the immobile ether sea through which all matter moves. Any dependence of light's speed on a direction was not detected." [p.144]

Drawing thus a conclusion that speed of light from speed of the receiver does not depend, authors are based again on the only theory - classical transformations Galilee. But also in this case the alternative is constructed by them incorrectly. Full logic alternative to the statement "classical dependence of light's speed from speed of the receiver" is the statement "non-classical dependence of light's speed from speed of the receiver", but not an Einstein's conclusion: "independence of light's speed from speed of the receiver" which only is one of possible alternatives.

In well-known Michelson-Morly experiment (MMX) both in direct, and in a perpendicular direction there is a movement of light "there and back" where (by already mentioned item �.) a possible different speed of light is compensated. Therefore this experiment and to speed of light in one direction, and to a constancy of speed of light has no of the relation. Thus possible dependence of light's speed from speed of the receiver is not rejected.

If to attempt to take into account that performance of principles can be checked up only with the limited accuracy, then not the single Lorentz transformations  follow from inexact "principles" but there are other theories with other transformations of coordinates which within the limits of errors of experiment describe the same phenomena, as SR.

"The relativity theory necessary arises from serious and deep contradictions in the old theory from which, seemed, there was no exit. Force of the new theory consists in a coordination and simplicity with which it solves all these difficulties, using only few very convincing assumptions.

Though the theory has arisen from a problem of a field, it should sweep all physical laws. Difficulty, apparently, appears here. Field laws on the one hand and laws of mechanics on the other hand, have completely various character. The equations of an electromagnetic field are invariant in relation to Lorentz transformations, and the equations of mechanics are invariant in relation to classical transformations." [p.160]

Authors mean the equations of an electromagnetic field as Maxwell equations. But Maxwell itself counted his four equations true in IFR concerning which "ether" is motionless. Maxwell equations have been received for homogeneous space of which physical properties do not vary with time, and do not show ferromagnetic properties. That is why in vacuum according to these equations the light's spreading speed is isotropic. But it is impossible to apply Maxwell equations in a few IFR that are moving relatively each other, for, at least one of IFR will move in the ether. For this case there are Dalamber equations and the speed of light is not obliged to be isotropic.

5. Properties of relativistic laws of mechanics and definition of IFR

We return to consideration of the most important concept (though the most imperceptible one) in SRT - to definition of inertial system of reference:

" "Good" systems of coordinates, in other words in which laws of mechanics are fair, we name it inertial systems."[�.130]

If in this definition were implied relativistic laws of mechanics then it would be senseless to search for the contradiction to classical transformation of coordinates as in relativistic laws such is not present. Hence, authors of the book started with classical laws at definition of IFR.

In SRT the relativistic laws of mechanics (properties of which essentially differ from classical) should be carried out. For example, in SRT a longitudinal length of a body should depend on speed of his movement, therefore the basic classical property of a solid body - preservation of the form - is not carried out. The moving sphere should have the form of ovoid (or "pancakoid") compressed along a direction of his speed of movement. And turns of this sphere already cannot be presented by the rotation of a solid body - the ovoid will not rotate similarly of a coin fallen on floor. Hence, in SRT a classical definition of a solid body does not work and classical law of Hooke is not carried out.

"But the relativity theory demands that all laws of the nature were invariant in relation to Lorentz, instead of to classical transformations. The last are only limit, special case of Lorentz transformations when relative speeds of both systems of coordinates are very small. If it so then the classical mechanics had to be changed to coordinate it to the requirement of been invariant in relation to Lorentz transformations. Or in other words the classical mechanics cannot be fair if speeds aspire to speed of light. Transition from one system of coordinates to another can be carried out only by one way - through Lorentz transformations." [p.160]

So, authors on the basis of the analysis of experiments in inertial systems of reference, made a conclusion that "the classical mechanics should be changed". The sense of definition (given by authors) of the IFR thus will change. But in the book there is no proof, that the system, inertial in old sense, will be inertial and in new sense.

Presently other definitions of the law of inertia and inertial system of reference are used.

"The law of Inertia - the law of mechanics according to which the body at a mutual balancing of all forces working on him maintains a condition of rest or uniform rectilinear movement, until the enclosed forces do not force its to change this condition." ["Phis. Enc.", v.3, p.146]

"Inertial system of reference - system of reference in which the law of inertia is fair: the material point when there are no forces working on it (or there are forces mutually counterbalanced), is in a condition of rest or uniform rectilinear movement." ["Phis. Enc.", v.3, p.145]

These definitions allow to avoid the discrepancy marked above between classical and relativistic kinds of laws of mechanics. But it turns out that modern SRT and SRT of Einstein are based on the definitions formulated differently. Therefore there is a question: whether are Identical the Einstein's SRT and the modern SRT?

And three more remarks to the previous citation from p.160 of the book:

1. Classical transformations are not "limit, special case of Lorentz transformations when relative speeds of both systems of coordinates are very small". Aspiration to zero of relative speed give a limit kind of transformations: t ' =t; x ' =x, but not classical. If we want to remain the members containing only V in the first degree we shall obtain: t'=t-Vx/c²; x'=x-Vt in which time depends on distance; and at x> c²/V we shall obtain a time's formula not classical in the areas remote from a zero point of IFR.

2. Two IFR equal if and only if any event has equal coordinates in them. So, among IFRs of Galeean theory couldn't be more than one IFR equal to someone IFR of SRT. Thus, almost all IFRs of SRT aren't IFR of  Galeean theory, and nobody has rights to build the relativity theory on the base of  IFR of  Galeean theory.    

3. The relativity theory demanded an invariancy of laws of the nature, but whether the Nature demands it, we do not know.

5. Conclusions

1. Classical transformations of coordinates cannot be carried out, and it was shown correctly in the book.

2. Performance of a relativity principle Galilee and the law of inertia could not be checked up with sufficient accuracy. It have been checked up only for small speeds and with small accuracy. Therefore it cannot be considered as the experimental facts how it was made by Einstein. The relativity principle  of Einstein also is not the experimental fact. As well as the Galilean relativity principle it can be only interpretation of experimental results which are obtaining owing to some other laws. Invariancy of physical laws is only our desire, for the Nature it is not obligatory.

3. Full logic alternative to the statement "classical dependence of light's speed from speed of the source or the receiver" is the statement "non-classical dependence of light's speed from speed of the source or the receiver", but not an Einstein's conclusion: "independence of light's speed from speed of the source or the receiver" which only is one of possible alternatives.

4. Speed of light could be not independent of speeds of a source and the receiver.

5. "Unilateral" speed of photons in IFR can be miscellaneous.

6. In Michelson-Morly experiment both in direct and in a perpendicular direction there are a round-trip movement of light, therefore results of experiments do not contradict possible different speed of light.

7. The equations of an electromagnetic field are not only Maxwell equations, but also Dalamber equations. In them speed of light is not obliged to be isotropic.

8. Classical transformations are not a limiting case of transformations of Lorentz when relative speeds of both systems of coordinates are very small.

9. The SR, whose transformations of coordinates that are deduced for inertial frames, where by definition classical laws of mechanics are carried out, demands, that laws of mechanics had a relativistic kind. Hence, SR demands change of this definition of inertial frame. �obody has rights to build the relativity theory on the base of  IFR of  Galeean theory

10. Thus, choice of SR principles logically is not justified. Reasoning and arguments of authors of the book do not allow to define transformation of coordinates unequivocally. Here is example of the transformations which are not contradicting to the discussed facts:

  t'=t(1-V²/c ²)^1/2; x'=(x-Vt)/(1-V²/c²) ^1/2; y'=y; z'=z

Let's name this transformation as Kuprjaev-Obukhov-Zakharchenko Transformation (KOZT), considered by them at the end of 20 century. The theory bound to these transformations, is named the Theory of the Stationary Luminiferous Aether (LAST). By this theory an increasing of a lifetime of fast muons, both Doppler effects, and other effects have been explained.

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Last correction 21.02.2008 23:23:18