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Replacement of Einstein’s Relativity Theory with a New One: Why the Second Postulate is Superfluous?

Mamaev А. V.

Candidate of engineering sciences, Bureau Chief, JSC “Lianozovo Electromechanical Plant Research and Production Corporation”, Russia

Abstract: My purpose consisted in creation of a new relativistic space-time theory instead of Einstein’s Relativity Theory, but basing upon only one postulate. This could become feasible only if a law of light propagation in a moving inertial reference frame could be made a consequence of the relativity postulate. It was made a reality by P.M. Rapier’s discovery of a quadratic dependence of the light speed upon the light source speed. Considering various ways of making the second postulate superfluous the most short of them was through introducing into the theory of a new concept “light speed in a moving inertial reference frame” by means of usage of the known four-dimensional Minkovski’s formalism. This new light speed was defined as equal to a fourth component of a four-dimensional speed of any moving particle. Then using this newly introduced concept the time-measurement unit was calculated for a moving light clock that occurred to be equal to the time measurement unit of a stationary light clock. And as a very happy event the time dilation effect was deleted from the theory.

Keywords: special relativity theory, light speed in a moving inertial reference frame, Galilean speed or velocity, Lorentz speed or velocity, proper time, light clock, time measurement unit

Citation: Mamaev А. V., Replacement of Einstein’s Relativity Theory with a New One: Why the Second Postulate is Superfluous?. International Journal of Physics, 4 (5). 140-145. January 2016. doi:10.12691/ijp-4-5-5

1. Foreword

The history shows that all theories and sciences evolve in such a way, that realness of phenomena visible by eyes are gradually changed by realness of phenomena perceived mentally. For example, movement of the Sun and far stars and immovability of the Earth visible to Ptolemy’s eyes after some time were replaced by movement of the Earth around the Sun and with respect to far stars perceptible by Copernicus’s brain.

The first stage of any theory or any science therefore is based upon seeing any phenomenon by means of eyes. And the eye sees only the light – electromagnetic radiation with wavelengths between 380 nm (violet color) and 780 nm (red color). What else do we know about the light? We know that the light propagates in vacuum having the velocity equal to 299 792 458 m/s. At that this value is measured in the stationary inertial reference frame (IRF). At what speed the light propagates in any moving IRF we can only guess. In order to answer this question we, first of all, should form a concept “light speed (or velocity) in vacuum of a moving IRF”. Why we must perform this task?

We must perform this task due to todays situation when we know only speed of light in a stationary IRF. Because it has happened in such a way, that in 1905 Albert Einstein [1] defined only speed of light in a stationary IRF and introduced two postulates:

1. A relativity postulate: “The laws, by which the states of physical systems undergo change, are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion”.

2. A postulate of light speed independence on the speed of a light source: “Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity , whether the ray be emitted by a stationary or by a moving body”.

Keeping in mind that any of two IRF, moving each with respect the other at some specific speed , may be called as a stationary one (at that the other one should be considered as a moving one), from these two Einstein’s postulates it was concluded, that the speed of light in vacuum of all IRF (irrespective of whether each of these IRF is considered to be a stationary one or a moving one) is equal to the same value = 299 792 458 m/s.

Such erroneous conclusion was used by Einstein himself when he derived Lorentz’s transformation of coordinates from one IRF to another IRF, namely he wrote: “…Light (as required by the principle of the constancy of the velocity of light, in combination with the principle of relativity) is also propagated with velocity when measured in the moving system”.

But neither Einstein in 1905, nor his numerous admirers in the past did not take into their minds, that an assumption about equality of light speed in a moving IRF to the light speed in a stationary IRF results in contradiction between the effect of time dilation in Einstein’s special relativity theory (SRT) and the relativity principle.

Indeed, it is well known that a light clock (consisting of two parallel mirrors, a photoelectric sensor on one of mirrors, a pulse counter connected to the output of the photoelectric sensor and a light pulse circulating between mirrors) is a physical system, which must comply with the relativity principle.

Because the relativity principle with respect to such physical system as the light clock must read:

The laws, by which the indications of light clock undergo change, are not affected, whether these changes of indications be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.

That means that time dilation effect existing in the SRT according to the relativity principle should be absent. Indeed, if we consider that distance between mirrors of a stationary light clock is equal to , then the time measurement unit for a stationary light clock is equal to the value

[picture] | (1)

And the time measurement unit for the same light clock, moving at the speed in a direction perpendicular to planes of light clock mirrors, in case of an assumption that light speed in a moving light clock also is equal to will be equal to the value

[picture] | (2)

where is the distance (according to the SRT) between light clock mirrors, moving at the speed .

Thus, the assumption that the light speed in a moving IRF is also equal to the same value , leading to the existence of time dilation effect in the SRT, leads to a contradiction with the relativity principle (indications of a light clock depend on what IRF these indications are referred to). Therefore it is expedient to consider what value of the light speed in a moving IRF will not lead to a contradiction with the relativity principle that is to consider what value of light speed in a moving IRF will result in equality of time measurement units for stationary and moving light clocks of the precisely similar design.

2. Introduction of a New Physical Concept

First of all let us form a new concept “light speed in vacuum of a moving IRF”. It is unlikely that this concept has been considered as having some positive sense up until todays time. As opposed to this concept the concept “light speed in vacuum of a stationary IRF” was widely known because it was included into the Einstein’s second postulate (see above) [1].

How can we practically perform measurement of the “light speed in vacuum of a moving IRF”? We can perform such measuring in accordance with Figure 1.

Figure 1. Propagation of light in a light clock in two IRF moving each with respect the other

Let us consider two IRF and K (x, y) moving each with respect to another one at the velocity (see Figure 1). In all points of the unprimed IRF K named with letters (points A₀, N, M) there are clocks that are synchronized (show the same time at any time moment of the IRF K). The primed IRF in Figure 1 is a stationary IRF. That means that an arbitrary light clock with stationary mirrors in points and of the primed IRF is at rest in this primed IRF and the moving unprimed IRF K is moving in a direction, that is parallel to planes of mirrors and .

At the zero time moment of the both systems, when a point B₀ of the IRF coincides with the point A₀ of the IRF K, two light sources in the point B0 radiate simultaneously two light pulses, one of which propagates from the point B₀ to a point B₁ of the IRF and the second pulse propagates from the point B₀ to the point A₀, where a spot on the X axis of the unprimed coordinate system K is marked. When the light pulse radiated in the point B0 arrives to the point B₁, a light source in the point B₁ radiates a light pulse that puts a spot mark in a point N of the IRF K. Simultaneously a pulse arrived from the point B₀ is reflected by the mirror in the point B₁ and moves back to the point B₀. When the pulse reflected from the point B1 arrives back to the point B0 a light source in the point B₀ puts a spot mark in the point M of the IRF K and stops a clock situated in the point M (at a time moment tM).

Then an observer being at rest in the “moving” IRF K measures the optical length of light ray path S = A₀N + NM in the moving IRF K and makes read out of the indication tM of the clock being at rest in the point M of the IRF K and being stopped at a moment, when the light pulse in the IRF returns back to the point B₀ after reflection from the mirror in the point B1. Then the “light speed in vacuum of the moving IRF” may be calculated using the formula

[picture] | (3)

So the value “light speed in vacuum of the moving IRF” can be rather simply measured and calculated in the experiment, if the light in Figure 1 propagates in vacuum.

By the way, as the time moment tM of the light pulse arriving to the point M of the IRF K coincides with a time moment of the light pulse returning back to the point B₀ in the IRF , and the optical length of light pulse path S = A₀N + NM in the IRF K is greater than optical length of the light pulse path in the stationary IRF , the value of “light speed in a moving IRF” exceeds the value of “light speed in the stationary IRF” , that means that > c₀. Thus, during the time travel of the light pulse from the point B0 to the point B1 and back from the point B1 to the point B0 at the speed in the stationary IRF the same light pulse performs in the moving IRF K a travel from the point A₀ through the point N to the point M at the greater speed . So, considering a rectangular triangle A₀NP in the Figure 1, we have

[picture] | (4)

or

[picture] | (5)

Now let us consider the same situation from the point of view of the SRT in Minkovski’s four-dimensional world [[2], p. 12].

3. Real Physical Sense of the New Concept

Terletskiy [[3], p. 53] said “From a point of view of the four-dimensional geometry of space-time the real physical sense can be ascribed only to four-dimensionally covariant values. In mechanics of a particle such values are a four-dimensional scalar known as a proper mass m, as well as four-dimensional vectors of the velocity , the acceleration and the momentum ”.

First of all we shall consider now a four-dimensional vector of the velocity .

Formation of a four-dimensional vector (4-vector) of the velocity is introduced in the SRT similarly to a three-dimensional vector in the three-dimensional space, where position of a particle is specified by a three-dimensional radius-vector and a three-dimensional vector of the velocity is defined as a derivative from the three-dimensional radius-vector .

To define a 4-vector of the velocity as a time derivative (’s fluxion) of the 4-vector is prohibited in the SRT. We require a 4-vector of velocity therefore we may divide the increment of a four-dimensional radius only by a scalar. In the SRT neither the time, nor its differential are invariants of the Lorentz’s transformation. Therefore in the SRT we can take as an invariant value depending upon time either the four-dimensional interval

[picture] | (6)

or the proper time

[picture] | (7)

where is the relativistic factor and V is the velocity of a particle.

So, let us introduce a 4-vector of a particle velocity

[picture] | (8)

In the coordinate representation this 4-vector of the velocity can be written in the following way

[picture] | (9)

where i = 1, 2, 3, 4.

It is well known that three first derivatives in the formula (9) can be written as

[picture] | (10)

where α = 1, 2, 3; are projections of the 3-vector onto the respective coordinate axes (x, y, z).

The values, defined by equalities (10), are the first three components of 4-dimensional Galilean vector changing from zero to infinity (hereinafter the velocity, changing from zero to infinity we can name as Galilean velocity and designate it with a letter u, in order to distinguish it from the Lorentz’s velocity, changing from zero to the velocity of light in vacuum of the stationary IRF , that we hereinafter will designate using a latter V. At that relation between Lorentz’s and Galilean velocities are defined by means of equalities [4]

[picture] | (11)

Taking into account that in the SRT , as well as the equation (7), let us find the fourth component of the 4-velocity. We obtain

[picture] | (12)

As from equalities (7), (11) and (12) it follows that

[picture] | (13)

then in the moving IRF (if V ≠ 0, γ ≠ 1) we obtain .

Consequently, the value

[picture] | (14)

which is the fourth component of the 4-velocity of a particle in vacuum of a moving IRF, we define as the light speed in vacuum of a moving IRF.

Physically the light speed in vacuum of a moving IRF can be in the SRT not equal to the value because of change of the longitudinal (along direction of movement) size of moving vacuum volumes in the result of which the values of the dielectric permittivity and magnetic permittivity of vacuum volumes can also be changed.

4. New Calculation of a Time Measurement Unit of a Moving Light Clock

Now (after introduction of the definition for the 4-velocity of light in vacuum of a moving IRF) let us take a light clock (two parallel mirrors at a distance each from another equal to L₀, in the very IRF, where this light clock is at rest, between which, alternatively reflecting, a light pulse is circulating, on one of mirrors a source of light pulse, photo diode and pulse counter are situated).

The unit of time measurement of this light clock, stationary in an immovable IRF, is determined by equality (1).

Now let this light clock move so that planes of the both mirrors of this light clock are perpendicular to the light clock direction of movement.

As we have determined earlier, see equality (14), the light in vacuum of a moving IRF propagates at the speed

[picture] | (15)

where is the speed of light in vacuum of a stationary IRF; is the relativistic factor determined by expressions (13).

Then after radiation of the light by a source, situated on the backward mirror of the light clock, the velocity of light closing with the foremost mirror of the light clock will be equal to , and the velocity of light closing with the backward mirror after light reflection from the foremost mirror will be equal to , where is the velocity of light in vacuum of a moving IRF, u is the Galilean velocity of light clock. Therefore the unit of time measurement by the moving light clock will be determined by the formula:

[picture] | (16)

where is the distance between mirrors of the moving light clock, measured in the IRF, with respect to which this light clock moves at the speed u.

Having substituted into the formula (16) the values , and , we shall obtain that

[picture] | (17)

Thus, using the above stated new physical concept the time measurement unit of the moving light clock becomes equal to time measurement unit of the stationary clock (the right part of the formula (17) coincides with the right part of the formula (1)).

Now let us return to a case, shown in Figure 1, when the light clock is situated so that planes of its parallel mirrors are parallel to the direction of light clock movement.

A time interval between radiation of a light pulse from the point B₀ and its return to the same point B₀ in the stationary IRF after reflection from the mirror in the point B₁ is equal to

[picture] | (18)

If we designate with symbols Δt a time interval in the moving IRF K between radiation of the same light pulse from the point A0 and a moment of its arrival to the point M, then the path passed by this light pulse in the moving IRF K can be determined using the Pythagorean theorem

[picture] | (19)

But the IRF K moves with respect the stationary IRF at the speed u (Galilean speed). Therefore we must consider, that speed of propagation of this light signal in the moving IRF K along straight lines A₀N and NM is determined according to the expression (15) (this means that it is equal to the speed of light in vacuum of the moving IRF). As a consequence the time interval Δt = tM – t₀ (where t₀ is a time moment of light pulse emission in point A₀) can be determined by dividing the light path S, determined by the equation (19), by the speed of light in the moving IRF K, determined by the expression (15). We shall obtain

[picture] | (20)

Solving the equation (20) with respect to the value , we have

[picture] | (21)

Taking into account the equality (13), the expression (21) takes the form

[picture] | (22)

The formulas (18) and (22) mean that the time interval between some two events in the moving IRF K connected with propagation of light is equal to the time interval between the same events in the stationary IRF .

Consequently, introduction of the concept "the speed of light in vacuum of a moving IRF" excludes from the space-time theory such an effect as time dilation in the moving IRF and converts into the unscientific space opera the statement about possibility of journey in the future of the Earth by means of long traveling in space at large speeds (close to the speed of light).

5. New Space-time Theory and the Velocity Addition Laws

Introduction of the concept "the speed of light in vacuum of a moving IRF" excludes from the space-time theory such an effect as time dilation in the moving IRF and the so called Einstein’s SRT needs to be replaced by a new space-time theory, based upon only one relativity postulate. Such a theory was developed and published in [5]. Main content of the paper [5] is as follows: A new relativistic space-time theory (NRSTT) based upon a single principle of relativity is considered. A new concept of “speed of light in vacuum of a moving inertial reference frame” (IRF) is introduced, depending upon speed of the IRF motion according to a quadratic formula. This dependence provides introduction of a new and uniform understanding of such astronomical phenomena as microwave background radiation, red shift of far star spectrums becoming more shifted as the distance to a star increases, novae and supernovae, pulsars, object SS-433 etc. These astronomical phenomena are considered from a point of view of NRSTT with more details in [6].

Coordinates and time transformations of the NRSTT have the form

[picture] | (23)

[picture] | (24)

where , , , and are coordinates and time of any event in the unprimed and primed IRF, respectively, is the speed of one IRF with respect to another one.

These transformations provide invariance of the four-dimensional interval and give a possibility to detect real properties of moving bodies: contraction of their longitudinal sizes without time dilation, without prohibition of superlight speeds, without dependence of mass upon the speed, but with dependence of particles electrical charge values upon their speeds. A solution of the muon-electron universality problem is given and an approach to the merchantable method of cold nuclear fusion is discussed.

In the NRSTT there is its own law of speeds addition. It can be written in two forms: 1) the first one is

[picture] | (25)

where ; ; v, s are the summands; w is a sum of two summands, w is a sum of two speeds (v, s, w are Galilean speeds) and the second form is

[picture] | (26)

where ; ; ; u, s, w are Galilean speeds (they can vary from zero to infinity).

6. Conclusion

The latest and most advanced (simplest) considerations of the NRSTT issues are made in a report for the Congress-2016 “Fundamental problems of natural sciences and engineering” in Saint-Petersburg [7].

The report [7] considers self-contradictoriness of Einstein’s SRT and a new relativistic space-time theory based upon the only relativity principle, without ban of superlight speed, without lag of a moving light clock with respect to a stationary light clock (without time dilation) and with dependence of a particle electrical charge upon its speed of motion. A new concept “light speed in a moving inertial frame of reference” is considered, which provides equality of time measurement units in a moving light clock and in a stationary light clock. It is shown in the report that experiments on particle accelerators do not contradict the new theory, if the known experiment by Neddermeyer S.H. and Anderson C.D., earlier considered to be experimental confirmation of existence in nature of particles with a mass intermediate between the mass of a proton and the mass of an electron, is interpreted in favor of experimental detection of charge dependence upon speed and superlight speeds.

The content of the report [7] is given below (numbers of pages are given in accordance with [7]):

- Introduction (p. 91),

1. Self-contradictoriness of Einstein’s SRT (p. 92),

2. Derivation of coordinates and time transformations of the NRSTT (p. 95),

3. Absence of prohibition for superlight speeds of motion (p. 99),

4. Transformation of electromagnetic field parameters in the NRSTT (p. 100),

5. New relativistic particle dynamics (p. 103-116),

6. Alternative interpretation of the experiment by Anderson and Neddermeyer in 1938 (p. 117),

- References (17 items) (p.p. 119-120),

- Translation into Russian of the paper by Neddermeyer S.H., Anderson C.D. “Cosmic-ray particles of intermediate mass” (p.p. 120-122).

So, the answer to a question put in the title of this article (why the second postulate is superfluous) is the following: Einstein’s second postulate is superfluous because it is wrong, the law of light propagation in a moving inertial reference frame is a consequence of the relativity postulate and the space-time theory can be constructed basing upon not two, but only one postulate – principle of relativity (according to Occam’s razor principle). It is important to underline that the constancy of light speed is not necessary now because it is wrong, and prohibition of superlight speeds is also wrong. Both light and particles are allowed to move at any speed whatever great it could be. And Einstein’s second postulate is wrong for the reason that the time measurement unit for a moving light clock is not equal to the time measurement unit of a stationary light clock if the second postulate is true. But they should be equal in order to prevent determination which of two IRF moving each with respect the other uniformly and rectilinearly is at rest by measuring a value of the time measurement unit.

Acknowledgments

I am grateful to reviewers for their contributions to improve the paper.

References

[1]   | Einstein А. On Electrodynamics of moving bodies, June 30, 1905, [url]http://www.fourmilab.ch/etexts/einstein/specrel/www/[/url].
[2]   | Minkovski G. Space and time. In book. “Principle of Relativity”, М., Atomizdat, 1973, p.167 (in Russian).
[3]   | Terletsky Y.P. Paradoxes of Special Relativity, М. Nauka, 1966, p. 53 (in Russian).
[4]   | Rapier P.M. A recent application of detection and estimation practices in radio and radar astronomy. Spectroscopy Letters, 4 (9), 303-311 (1971).
[5]   | Mamaev A.V. New Relativistic Space-Time Theory. “The Way of Science”/ 2014. No.1 (1), p.p. 10-84. (In Russian). [url]http://scienceway.ru/d/706321/d/the-way-of-science--1-%281%29-march.pdf[/url]
[6]   | Mamaev A.V. “Astronomical phenomena disprove Einstein’s Special Relativity Theory, “The Way of Science”/ 2014. No.5 (5). p.p. (10-19).

[7]  
Mamaev A.V. New Relativistic Space-Time Theory. International Congress-2016 “Fundamental Problems of Natural Sciences and Engineering”, Saint Petersburg. July 25-30 2016. In a book Congress-2016 Proceedings “Fundamental problems of natural sciences and engineering”. Issue 37-2, p.p. 91-122 (In Russian).