By B.E. Rowe, L.E.M. Tarantoga
While explaining the optical phenomena like stellar light aberration and Michelson – Morley experiment by Special Theory of Relativity (STO) there appear certain difficulties (in our opinion). Here we show, that those difficulties, however, are only apparent and could be eliminated by two additions to STO proposed by authors:
- Mobility hypothesis, which claims, that there exists an absolute, privileged frame (system) of reference bound directly to the electromagnetic wave itself (light wave). Let’s call this system as “Light – system” or “C-system”. Movements and velocities of any body or reference system, additional to ever existing speed of light of “C-system”, we will call as “additional movement” and “additional velocity”. This system is not inertial system of reference.
B) Autocorrection hypothesis, which claims, that there ever will be a turn of front of electromagnetic wave (light wave) when a source of light and a receiver (observer) are in mutual movement relatively to each other and their relative velocity is perpendicular (or at any angle >0) to the direction of the light wave propagation. This turn of light wave front exists even when a source and an observer are in rest relatively to each other, but both have an “additional velocity” with respect to the “C-system”.
Introduction. Description of the problem.
I) Stellar light aberration was first discovered and explained by J. Bradley between 1725-1727. The term “aberration” refers to the various displacements of the apparent direction of a star consequent on the finite velocity of light, combined with transverse motions of the star and observer (on the Earth). The annual aberration is about 20”. 5 (seconds of arc). 1,2,3
As it is well known aberration of stellar light is due to the orbital motion of the Earth around the Sun with the speed of 30 km/sec. Speaking more correctly,
J. Bradley did not discover aberration, but rather the annual changes of it. For instance, the displacement due steady movement of Solar system relatively to stars in its neighborhood and rotational movement of our spiral arm of Galaxy around its core with the speed of ~220 km/sec are unobservable due its constancy for a long period of time.
Later G. Airy performed in 1871 his famous experiment using telescope filled with water and surprisingly received the same value of aberration*. Both, of J. Bradley and G. Airy experiments were successfully explained by classical theory of light using Fresnel formula for partial entrainment of the light wave by moving media, and by STO1, 2
The difficulties in explaining aberration from STO positions lay, in our opinion, in contradiction it causes between principle of relativity (1st postulate of STO) and principle of light speed constancy (2nd postulate of STO). Indeed, aberration can occur only if there is a mutual relative movement of light source and observer, when their velocity and light wave propagation direction are perpendicular to each other.
Let’s assume for a moment, that the Earth rests with regard to the Sun and the star is moving with the same speed of 30 km/sec in the opposite (to orbital movement) direction. The question is: whether will we observe aberration on the “motionless” Earth? According to 2nd postulate of STO, the speed of light wave emitted by a moving light source is not affected by this movement and remains the same constant “C”. Thus, this light wave does not posses any “transversal” to sight line velocity and aberration on the motionless Earth will not be observed. But this claim contradicts to the 1st postulate of STO, principle of relativity, which states, that aberration in this case should be observed, since both, the star and the Earth are equal inertial frames of reference (within certain assumptions).
[It is interesting to mention that, according to “emission” or “ballistic” principle of Ritz (c’ = c +_ v), the light wave, emitted by moving source, will receive an additional transversal speed and thus aberration will be observed. But the Ritz principle contradicts to general wave theory and is not supported by experimental findings] 1,2,4,5,6,8
As we can see the attempt to explain stellar light aberration produces the contradiction between two basic principles of STO: if both systems (star and Earth) are inertial systems of reference, they are equal and aberration should be observed in both cases. But that means, that the light wave should posses an additional transverse velocity, which opposes to the light speed constancy principle.
B) Michelson – Morley (M-M) experiment 1,2,7. Here two effects predicted by STO explain its negative results: length contraction and time dilation at moving reference frame. However, there are no explanations of “strange” behavior of transversal to vector of Earth orbital velocity beam.1, 2,4,5,6,7 Again, if principle of light speed constancy is correct, this transversal beam must be not affected by Earth orbital movement and must experience a “backwards” deflection. This “backwards” deflection of ~2.2 mm surely could be detected even by unaided eye, not to mention excellent sensitivity of M-M apparatus of 0.01λ. But in all descriptions of M-M. experiment we see this transversal beam being deflected “forwards” as if it is entrained by Earth movement. No deflection backwards of transversal path was observed in the experiment too. Thus producing the same contradiction between two principles: if the light speed constancy principle is correct, this transversal beam should not be affected by Earth movement and hence to be deflected backwards. But this contradicts to the relativity principle – by this deflection backwards we can observe “from inside” of inertial system the absolute motion of the Earth.
We reject, a priori, a possibility of “fully entrained ether” as well as any deliberate technical arrangements of M-M experiment by sending this transversal beam “a little forwards” 7. The same regarding the Ritz principle.
We will try to show below, that in both cases those contradictions are only apparent and can be eliminated by two proposed assumptions: mobility and autocorrection hypotheses.
- Mobility hypothesis (MH) claims:
- There exists the absolute and privileged system (frame) of reference bound to electromagnetic wave itself. Let’s call this system as “Light-system” or “C-system”.
- This “C-system” is not inertial system and thus all physical laws are not invariant relatively to this system. It’s uniqueness consists, that there is no inertial reference system which can move with the same speed (speed of light) and this “C-system” cannot be stopped relatively to any inertial system. Photon, as it is well known, takes unique position in the table of elementary particles.
- Movements and velocities of any bodies and systems relatively to the “C-system” we will call as “additional movements” and “additional velocities”. (Additional to ever existing speed of light of this “C-system”) Any calculations of those additional velocities are in accordance with STO formula.
- Introduction of the absolute system of reference automatically generates the notion of absolute movement relative to this absolute “C-system”. This notion is in straight contradiction with relativity principle, which denies any kind of absolute movement. But by assuming that this “absolute” movement cannot be observed principally by observer inside the inertial frame of reference using any possible physical phenomena, including optical, we eliminate the abovementioned contradiction.
- There can be two situations in the system: Light source – Light wave – Observer.
e-1) If light source and observer are in rest relatively to each other and both are inside inertial system of reference. Here is no principal possibility by any physical means to detect an “additional movement” of the system relatively to “C-system”. (Principle of relativity)
e-2) If light source and observer have a mutual relative velocity regarding to each other. Then this movement can be observed either, by aberration and/or by longitudinal and transversal Doppler effects.
- Here can be asked question: what for is needed to introduce such an absolute “C-system,” if absolute movement is principally undetectable?
A. Einstein called not to introduce notions, which cannot be observed principally. The answer is, that no Doppler effect, nor aberration, length contraction and time dilation can be observed inside the moving inertial system, but it does not eliminate an existence of such effects. And second, there are situations, physical circumstances, which we will show later, where we do need such an absolute system.
- Autocorrection hypothesis (AH) claims: **
- When a light wave is reflected from “additionally moving” mirror, the front of reflected wave experiences certain turn, an additional to “usual” predicted by law of geometric optics. The angle of this turn can be calculated from the formula tan = v/c, where v — is an additional velocity of the mirror, and c – the speed of light, or more precisely,
tan φ = β/(1—β2)1/2, where β = v/c. This is the same formula as for calculation of aberration angle
- If the light source is moving relatively to observer and is emitting a light wave perpendicularly to its velocity, the front of this emitted light wave will experience the turn forwards. The angle of the turn will be the same as in previous case.
- The observer on moving flat surface which velocity lies at the same flat plane, is detecting a perpendicularly falling light wave front from external light source as not perpendicular, but as turned by angle φ. where tan φ = β/(1 – β2)1/2. There are no physical means for this observer to differ this perpendicularly falling light wave from the inclined one. (By “observer” we mean any possible physical devices, serving as sensors of parameters of light wave as phase, amplitude, frequency etc. We don’t mean here any optical system, which can change a direction of falling light wave, like mirrors, lenses, prisms, diffraction grids etc) 1,9
Both hypotheses are bound to each other and cannot be used undependably.
- Application of these two hypotheses regarding to the abovementioned phenomena.
Earth is moving and star is in rest relatively to, say, the Sun. Observer on the Earth finds that the light wave from the star does not come perpendicularly to his movement’s direction, but slightly inclined from the front. This is in accordance to autocorrection hypothesis, thesis AH — “c”.
Earth is “motionless” relatively to the Sun, star is moving in the opposite to Earth orbital velocity direction. Here too, observer sees aberration of the stellar light, according to autocorrection hypothesis, thesis AH — ‘”b”, slightly inclined in the same direction as it was in previous case.
Since in both cases we observe the same effects and the speed of light remains constant –“C”, there are no contradictions between two basic STO principles.
It seems interesting to mention the difference in effects predicted by Ritz principle and autocorrection hypothesis. If the moving flat plane in the case AH – “c” will be exchanged by a mirror, then perpendicularly falling light wave will be reflected “forwards” in the movement direction according to the emission principle of Ritz, and it will be reflected “backwards”, according to thesis “c” of AH. This claim, of course, needs to be verified experimentally.
- Michelson – Morley (M-M) experiment. The behavior of transversal beam in this experiment can be explained by AH, using all tree theses (AH – a, b, c) mentioned. By the use of theses AH –a and AH –b we can explain the deflection of transversal beam “forwards” as it appears in all descriptions of M-M experiment. We would like to describe in more details this experiment from the point of view of autocorrection hypothesis; but we are unable to do so because of lack of place. Generally speaking, the M-M experiment’s explanation is more complicated, than it appears in the literature.
We must stress, that there can be certain difference between two light paths: longitudinal and transversal, even, if they are equal into motionless system. But this difference remains constant at any possible orientation of M-M apparatus relatively to Earth velocity direction. The very process of preliminary tuning of apparatus, “annulling” it from the beginning, could eliminate this difference, which will be no longer observed.
As we can see, both postulates of STO remain untouched thanks to use of proposed MH and AH.
[Here the same question rises again: why do we need this mobility hypothesis at all? One reason is — the explanation of M-M. experiment. As we have mentioned, the turn of light wave front occurs only when there is some movement. Relatively to what? Light source’s movement relatively to observer? But here they both are in rest to each other. (Experiments of
D. Miller and R.Tomashek using the Sun and stellar light don’t change here anything, since there has to be certain Earth bound optical system which directs this light on the beam splitter of M-M device 5,6.) For internal, bound to the Earth observer, there is no possibility to use even Fitzgerald – Lorentz transformations, since there is no relative movement of observer and light source, there are not two moving inertial systems, only one – Earth with M-M apparatus. So, we need certain reference system, relatively to which M-M apparatus is moving. The Sun? The sphere “motionless” stars, galaxies or any other reference frame? But if we have not at our disposal all above reference systems, the only applicable system of reference for “internal” observer remains “C – system”.]
- Effects bound to autocorrection hypothesis.
Autocorrection hypothesis predicts some additional effects in the cases of observation of emission or reflection of electromagnetic radiation by very fast moving sources or reflectors: e.g.:
Prominences on the Sun (here, according to AH – b, an aberration has to be observed, changing the apparent position of the prominence from its real position);
Fast moving binary stars (here, according to AH – b, an aberration will change the “real” position of the stars and cause apparent positive and negative accelerations of moving stars non consistent with spectral Doppler shifts and change proportion between a longitudinal and a transversal Doppler effects 10);
Fast moving clusters of plasma and fast moving mirrors (in latter case, according to AH – a and c, an additional turn of reflected beam has to be observed). Generally, in all above cases there will be certain additional deflection of coming or returning light wave besides the “usually” expected. Of course, experimental proof or disproof could confirm whether AH is right or wrong.
- Final discussion. Proposed mobility hypothesis is not so strange or unusual as it seems at first sight. In many articles on the problems of optics of moving media one can find phrases like “media is moving relatively to electromagnetic wave” etc. In the field of Relict Radiation or Cosmic Microwave Background (CMB) are too remarks like: “real motion of the Galaxy relative to the fixed background” (about dipole anisotropy of CMB). Here, as far as we can understand, “fixed background” means CMB. “If the light wave and the observer have no motion relative to each other” – citation from M. Born book.2 Furthermore, by introducing the “C – system” we eliminate the need of inadvertent use of absolute time and space, which exists in physics until now. As an example of such a use we can take a definition of velocity. The velocity of a point is the time rate of the distance “S”, as the derivate of “S” with respect to the time V = dS/dt. Here velocity “V” is the function of two independent variables “S” (space) and “t” (time). But, according to STO both “S” and “t” are functions of “V” at any speed. Thus we encircle ourselves into vicious logic circle: function is defined by “independent” variables, which are, in turn, dependent on the function. Much better may be to take velocity as primer notion and space — time as secondary and to define the velocity as a part of velocity of light, “V” = kc, where k<1.
Summarizing, we would like to say, that the abovementioned proposals consist one principle, i.e. mobility hypothesis, and one possible physical mechanism (AH –a –almost apparent, AH – b – discussible and AH – c – most questionable), additional to STO effects, which together with the latter explains and supports two basic principles of STO.
- Einstein, A., Lorentz, H.A., Minkovski, H., Weyl, H., The Principle of Relativity, 1952, Dover, Toronto
- Born, M. Einstein’s Theory of Relativity, 1962, Dover, New York
- Kulikov, V., Fundamental Constants of Astronomy, 1964
- Feynman, R., Leighton, R, Sands, M., The Feynman Lectures on Physics, 1963, Addison – Wesley, Reading
- Tonnelat, M–A., Les Principles de la Theorie Electromagnetique et de la Relativite, 1959, Masson, Paris
- Panofski, W., Phillips, M., Classical Electricity and Magnetism, 1962, Addison – Wesley, Cambridge
- Michelson, A. A., Studies in Optics, 1995, Dover, New York
- Michelson, A. A., Effect of reflection from a moving mirror on the velocity of light, 1913, J. Optical Society of America
- Landau, L., Lifshitz, E., Electrodynamics of continuous media, 1964
- Ives, H., Stilwell, G., An experimental study of the rate of a moving atomic clock, J. Optic Society of America, 1938, v. 28, #7
Foot — notes
* Result of Airy experiment could be explained also by assuming, that refraction index of the medium remains constant irrespectively of mutual relative movement. Then, light wave propagates through the water, an optically isotropic medium, transversally due to the Earth movement, with velocity v’= v/n (where v – Earth orbital velocity, and n – refraction index). Since a light speed c is affected by medium (water) by the same factor n, i.e. c’= c/n, thus tan remains = v/c.
** The theses, described below, appear partially in Fresnel wave theory and STO,
however, they are not being notable enough. Besides a turn of light wave front there will be also changes of frequency, but that is not, what we are trying to stress.
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