Preprint
(01.08.2003)
Date: Fri,01 Aug 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: special relativity theory - relativity - Lorentz transformation laws.
Speed of light in vacuum isn't obliged to be a constant
Alexander M. Chepick
Nizhni Novgorod, Russia
e-mail: redshift0@narod.ru
Absrtact
In this article a part of pros and cons of the light's speed constancy in vacuum are examined, the opportunity of other explanation of these reasons is shown with the help of the new particular (special) relativity theory (NePaRT).
1. Introduction
We have got used to consider speed of light in vacuum as a constant. There are many reasons to this, some of which are undermentioned:
1. Measurement of the lightТs speed
from a source, motionless relatively of the receiver. Speed of light is
determined nowadays as a constant c=299792458,0 (+-1,2) [m/s].
2. Measurement of the lightТs speed
from a moving source or by the moving receiver. Measurements give the same
speed of light in limits of error not a smaller than previous.
3. Measurement of seen movement of
stars in double systems. Measurements show validity of the NewtonТs gravitation
law.
4. Principle of independence of the
lightТs speed: л Speed of light in vacuum is identical in all inertial frame
(IF) ╗, is being a basis of the special (particular) relativity theory (SRT
or PRT) which, in turn, is proved by next experiments:
5. Comparison of speeds of a body
in different IF corresponds to the formula of the relativistic sum of speeds.
6. Measurements of change of
lightТs frequency from a moving source correspond to relativistic formula of
Doppler effect.
7. Existence of cross-section Doppler effect.
8. Measurements of increase in
energy of a moving particle correspond to the formula of full energy (by
Einstein).
9. Existence of proofs of the
General relativity theory (GRT) is the proof of PRT correctness, as its
particular case.
Let's consider each of these reasons. We shall show,
that there is their other interpretation.
Firstly, it will be from the point of view of
measurements. For example, if the error of measurement of an atmosphere
pressure made up 10 % we would have an opportunity to assert, that pressure of
an atmosphere at the surface of the Earth is constant, and to build the theory
of a wind as consequences of strokes of birdТs wings.
Secondly, it will be with use of the new particular relativity theory.
Thirdly, it will be with using of a
rule of the alternative hypotheses proof, which says that there is no other way
of the proof of a hypothesis except of the rejection all of its alternative
hypotheses.
Let's also consider some reasons against a constancy of the lightТs speed.
2.
Supremum of interaction
speed of substance.
The new particular relativity theory.
Basis of the EinsteinТs particular (special) relativity theory (PRT) are two postulants, namely: the Principle of independence of lightТs speed : " Speed of light in vacuum in all inertial frames is constant and does not depend on speeds of a source and a receiver of light "; and the Principle of a relativity: " All physical phenomena at identical entry conditionsа are equally proceeded in all IF ". (in Einstein's formulation [5, p.147]). With their help it is possible to deduce Lorentz's transformations - the ratios that linked all coordinates in various inertial frames.
But Logunov [2] has shown, that for an inference of LorentzТs transformations in the flat Euclidian static Universe the Principle of an independence of lightТs speed is not required, enough one Principle of relativity. Moreover, from the Principle of relativity an existence of a constant (we shall designate it cL Ц a LogunovТs-Lorentz's constant) follows in all IF. It has dimension of a speed, and according to sense of these transformations it is the maximal allowable speed. (In УThe Field TheoryФа Landau and Lifshitz [1] the term the maximal speed of interaction of substance is used. As a matter of fact it is Supremum (the top side) а of interaction speed of substance as the approachability of this maximum is not proved strictly. The independence of this maximum from IF, whichаshown there, gives equivalence of this value and Logunov - Lorentz's constant as in one space two different constants of identical dimension cannot simultaneously be maximal.) аBut as this value at measurements appeared with the big accuracy is equal to speed of light Einstein has made the decision to postulate the Principle of an independence of lightТs speed. As to the theoretical proof of that the constant "ё" in the equations of transformation of time and metric coordinates from one frame into another also is speed of light, so without the Principle of a constancy of lightТs speed such proof simply is not exist!
Therefore in [4] the hypothesis has been offered:
Logunov - Lorentz's constant cL differs from speed of light.
It is natural that this difference if it exists should be less than a modern accuracy of measurement of lightТs speed.
In connection with possible inconstancy of speed of photons it is necessary to make distinction in terminology: "speed of photons" is a speed of light's particles in any given frame; and "speed of light" we shall mean speed of photons of the given frequency in the source's own frame. In this IF photons of an identical frequency radiated by a source, have some speed c, identical in all directions, by virtue of an isotropy of conditions of their spreading.
The theory, that grown out of this hypothesis, and named as the New Particular Relativity Theory, or NePaRT (NeoPRT) , was constructed only on one principle - the Relativity Principle.
As consequence it turns out, that many conclusions PRT are carried out for NePaRT with small difference, namely:
- The size of relative speed of one body in frame of the second body is equal to size of relative speed of the second body in frame of the first body;
- There is a factor of delay of rate of time γL which looks like:
γL=[1-(V/cL)2]-1/2;
- Lorentz's transformations are carried out, they connect values of coordinates in two IF;
- There are formulas of the relativistic sum of speeds and formulas of the sum of their projections; in particular, for the motionless receiver the speed of a photon from a source which is strictly keeping away from the receiver with speed V, it looks like:
c2 = (c-V) / (1 - c V / cL2) аааааа (1)
- It is possible to think about photon as an usual particle, as in NePaRT there is no interdiction to nonzero mass of a photon;
- Formula of Doppler effect in NePaRT is similar to formula of Doppler effect for phaseТs speed VP in the environment in PRT [3,v.1, p.323] or for de Broil waves, in particular, in the receiverТs frame the frequency of a photon f2 depends on frequency of a photon f from a source moving with velocity V that makes a corner a with a direction of the photon velocity vector cа ( take into account: V P =cL2 /V):
f2= f [1- (V/cL)2 ]1/2 / (1 Ц c V cos a/ cL2) ааааааа (2)
3. The analysis of reasons of a constancy of the lightТs speed
1. A constancy of photons speed.
In "The Physical
Encyclopedia" [3, v.4, p.549] speed of light is determined for the present
moment, as c=299792458,0 (+-1,2) [m/s]. Though accuracy here makes
4╖10-9
, at the present stage accuracy of measurement of the lightТs speed
5╖10-11
is achievable. How photons behave within the limits of this error, we do
not know while.
2. Measurements of the lightТs
speed from a moving source or by the moving receiver.
Analysis of the formula of the sum of speeds in NePaRT shows, that the
greatest difference of speed of a body in different IF is reached at opposite
directions of a body velocity and velocity of moving IF, that is in the formula (1).
Let's designate
k= 1Ц c/cLа
is a factor of difference between speed
of a photon and supremum of interaction speed of substance
а in a source's IF, and
k2= 1Ц c2/ cL
- is the factor in the receiver's IF. Then
k<5╖10-11
and k2= k(1+V / cL)/(1
Ц(1Цk)V / cL ) . Today we don't know a real size of k-factor,
but any k>0 gives NePaRT to us, not SRT.
For example, if k<10-32, then k2
will be less than 5╖10-11
for all speeds V, smaller than
cL(1-4╖10-20),
а
that is for all
γL : γL<3╖109
. Even for such big speeds of a source the speed of a
photon will seem to a constant. The same calculations show presence of
"constant", within the limits of an error of measurements, speed of a
photon and for the moving receiver. Thus, seeming independence of the lightТs
speed from speed of a source and speed of the receiver can have other
explanation.
3. Measurement of seen movement of stars in double systems.
Einstein spoke about movement of stars in double systems [5, p.140]: "Measurements show validity of the NewtonТs gravitation law... Lets assume, that speed of light depends on speed of a source... In this case all movement would seem to us extremely confusing and would be impossible to confirm validity of the same law of gravitation that operates movement of our planetary system, t aking into account remoteness of double stars."
а Certainly, first of all under the dependence of the lightТs speed he meant classical GalileeТs "ballistic hypothesis" that says: c ' = c+V, where c ' - speed of light in the second frame moving with speed V relatively to the first frame in which speed of photons is "c". At such dependence non-uniformity of speed of starТs movement on an orbit should be visible, that is the NewtonТs gravitation law should not be carried out. Absence of such observations and practically exact performance of the KeplerТs second law allowed to reject "ballistic hypothesis". Thus the hypothesis of a constancy of the lightТs speed had proved to be true.
But as alternativeness of these hypotheses has not been proved, such conclusion is not right. Really, in NePaRT for speed of a star up to 100 km/sа change of speed of photons appears much less than error of measurement. That is both theories PRT and NePaRT within the limits of an error of measurement give identical result for speed of photons. In this case we also shall not see (within the limits of an error) non-uniformity of movement of double stars and default of Newton laws. Hence, rejection of GalileeТs "ballistic hypothesis" cannot prove theories PRT and NePaRT.
4. Principle of independence of the lightТs speed .
It is the unique argument that directly has been not connected to measurement of physical values. And consequently it is least approvable and most vulnerable - as appeared, the relativity theory can be constructed without it
5. Comparison of speeds of a body in different IF corresponds to the formula of the relativistic sum of speeds.
As the formula of the sum of speeds (1) shows a measurement of speed of a body in different IF in NePaRT gives results, which difference from results of the similar formula in PRT does not fall outside the limits an error of measurement for anyone achievable speed of a body in our days.
6. Measurements of change of lightТs frequency from a moving source correspond to relativistic formula of Doppler effect.
Measurement of frequency of a photon in different IF in NePaRT under the formula (2) gives results which difference from results of formula of Doppler effect in PRT does not fall outside the limits an error of measurement for anyone achievable speed of a source in our days. Besides that a small accuracy of check of the Doppler effect formula surprises - it is told in "The Physical Encyclopedia " [3, v.3, p.501], that in 1986 formula of Doppler effect is checked up with accuracy 3╖10-4.
7. Existence of cross-section Doppler effect.
The formula (2) also shows existence of cross-section Doppler effect in NePaRT which size within an error of measurement is equal to size of similar effect in PRT.
8. Measurements of increase in energy of a moving particle correspond to the EinsteinТs formula of full energy.
The size of full energy in NePaRT E= m cL2 γL also differs from similar size in PRT a little.
Thus, any of the set forth above reasons does not evident for the benefit of PRT as in the same degree they concern and to NePaRT. This conclusion can be distributed to all effects connected with speed of photons.
9. Existence of proofs of the General relativity theory (GRT) is the proof of correctness PRT, as its particular case.
Proofs GRT are only evidence against the Galilee theory and Newton theory. By the above-mentioned principle of the proof it is necessary to construct, and then to reject all possible theories of gravitation, except for GRT. Only then these evidences can be counted as proofs of GRT. Certainly it is not made. Concurrence to some accuracy of experimental and theoretical results cannot appear the proof for the benefit of GRT as it has turned out for PRT above.
4. Analysis of reasons against a constancy of the lightТs speed
In NePaRT photons have an identical nonzero mass, different speeds and different frequencies. Relative speed of two photons is always determined unequivocally. The photon can have own inertial frame (IF) in which it is motionless. The total (relativistic) impulse and average speed of final set of photons are unequivocally determined for this set in any IF.
(Definition: The average speed of final set refers to as average size of movement vectors of all set points for a time unit, divided by this time unit.)
In the inertial frame IF2 moving with small speed in a direction of a vector of a total impulse of set in some IF1, the total impulse will decrease. The total impulse will change a sign of a direction if IF2 has big enough speed. Hence, there is an IF where the total impulse is equal to zero by virtue of its size limitation and a continuity of change. Similarly, there is an IF where average speed of photons set is equal to zero.
Let's consider similar questions in PRT. Here photons have zero mass, identical speed and different frequencies.
1. To what size is equal relative speed of two photons? It is the question that standard PRT is powerless to answer unequivocally, namely: if photons velocities are not parallel, then its relative velocity is constant ё ; if velocities are directed toward one side - it is not determined. And why it is not determined? Unless two in parallel flying photons should not have zero relative speed? In fact, being simultaneously uttered by a source, they will simultaneously get in the receiver. And released by different sources in one direction, they will be at any moment in the points placed on constant distance. That is, PRT formulas are inexact reflect reality.
2. It is well-known, that the photon in PRT has no own frame in which it is motionless, for in such system all bodies cannot have different speeds. Accordingly, a set of the unidirectional photons (ray of light) cannot have own IF also. So, there is no IF where the total (relativistic) impulse of this set can be equal to zero. Also there is no IF where an average speed of this set can be equal to zero.
3. For a set of manydirectional photons we can find frame where the total (relativistic) impulse of this set can be equal to zero. But appeared, as in this case there are sets of photons for which there is no IF where an average speed of this set can be equal to zero.
Example: There is the set containing 3 photons of identical frequency, where 2 photons move in IF1 in one direction, and the third - in an opposite direction. An average speed of the set of photons is equal c/3. But in any IF2, moving relatively IF1 in parallel to the vector of the found speed, average speed of the same set of photons is equal c/3 again, as speeds of photons in IF2 have remained former. Clearly, that in any IF2 moving not in parallel to a vector of average speed of set in IF1, an average speed of set in IF2 cannot be zero because of presence of a nonzero projection of average speed on perpendicular axes. Hence, for the specified set there is no frame where an average speed of this set can be equal to zero. It is clear also, the average speed of this set is found equivocally (despite of unambiguity of its calculation by definition). As at transformation of average speed of set from any IF2, moving in parallel to this speed, under the formula of the relativistic sum of speeds it is received new average speed of set in IF1, distinguished from c/3. That is, average speed of set containing 3 photons is calculated uncertainly.
Such uncertainty of PRT has huge value for in that case there is a reason against the theory of a relativity as a whole: The size, measured (calculated) in first frame and transformed into second frame under PRT laws, is not equal to the size measured (calculated) directly in second frame. And it means, that transformation laws of are wrong, or are not applicable to such size.
5. Conclusions
1. The analysis of reasons in support of the thesis about a constancy of the lightТs speed has shown, that there are no reasons, which are unequivocal its confirmings.
2. Formulas PRT inexactly reflect reality.
3. In PRT the formula of the sum of speeds not correctly transform an average speed of set of photons from one frame into another.
4. There is the particular relativity theory constructed without a principle of independence of the lightТs speed.
The literature:
[1] L.D.Landau, E.M.Lifshits. The field theory , (╠., Nauka, 1988.)
[2] A.A.Logunov. Bases of the relativity theory, (╠., Nauka,1982.)
[3] The physical encyclopedia, (╠., the Soviet encyclopedia, 1988-1992.)
[4] A.M.Chepick, "Bases of the New Particular Theory of the Relativity
", ("Spacetime & Substance", ╣3(18)-2003))
[5] A.Einstein, L.Infeld. Evolution of physics, (╠., Nauka,
1965.)