Flaws in the logic of Einstein's Special Theory of Relativity.
By Ilya Stavinsky
Published in magazine
PHILOSOPHICAL RESEARCHES, #4, Moscow 12/2000
Special theory according to A. Einstein, came into existence as the result of the fact that the propagation of light, which is independent from the speed of its source, could not be explained from the principle of relativity in classical mechanics. From here follows that if one can logically disprove this fact then special theory of relativity will lose its credibility and scientific meaning. In the following article the reader will find not only such an explanation but specific flaws in Einstein's examples as well.
The essence of this theory lies in the fact that it resolved contradiction in physics between the propagation of light which is independent from the speed of its source, and principle of relativity in classical mechanics. The latter states: if, relative to K, K" is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to K" according to exactly the same general laws as with respect to K.
The above mentioned contradiction Einstein describes in the following way. 'Now let us suppose that our railway carriage is again traveling along the railway lines with the velocity v, and that its direction is the same as that of the ray of light, but its velocity of course much less. Let us inquire about the velocity of propagation of the ray of light relative to the carriage. It is obvious that we can apply here the consideration of the previous section , since the ray of light plays the part of the man walking along relative to the carriage. The velocity W of the man relative to the embankment is replaced here by the velocity of light relative to the embankment; w is the required velocity of light with respect to the carriage, and we have w = c - v
The velocity of propagation of a ray of light relative to the carriage thus comes out smaller than c. But this result comes into conflict with the principle of relativity… For, like every other general law of nature, the law of the transmission of light in vacuo must, according to the principle of relativity, be the same for the railway carriage as reference-body as when the rails are the body of reference. But, from our above consideration, this would appear to be impossible. If every ray of light is propagated relative to the embankment with the velocity c, then for this reason it would appear that another law of propagation of light must necessarily hold with respect to the carriage - a result contradictory to the principle of relativity. In view of this dilemma there appears to be nothing else for it than to abandon either the principle of relativity or the simple law of the propagation of light in vacuo…' . ' (Relativity -the special and general theory - by A. Einstein, p 22-23, Three Rivers Press)
Since both laws are real facts of real life, then the only solution to this dilemma will be the one which, while maintaining the law of propagation of light constant in vacuo, could be embedded it in the frame of theory of relativity.
And such solution he has found. Simple logic told him that if the velocity of light must be constant in relation to any above mentioned body of reference, then in the latter time and distance cannot be absolute. Really, if the distance S covered by light with velocity C during time T in relation to body-reference M, equals S = C T, then in relation to system M' the light with the same velocity will cover the distance S' during the time T'. i.e. S' = C T'. In reality it must mean that the time during which the body moves in the system M must be different from the time during which the body moves in relation to the system M'. The same logic applies to the distance. The distance which moving body covers in relation to the system M, will be different from the distance which moving body covers in relation to the system M'. In both cases we consider the same event ( the movement of body) in relation to a different system of reference. In other words, time and distance are not absolute values for all coordinate of references.
But one thing is to suppose and express this supposition mathematically, completely another thing is to show logically that this supposition is true and reflects reality. Einstein understood this very well and for this reason he gave an example of two lightnings which strike at points A and B, simultaneously with the respect to the embankment along which a train moves. "When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at points A and B, where the lightning occurs, meet each other at the mid-point M of the length A à B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A --> B on the traveling train. Just when the flashes of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train. If an observer placed in the position M' on the train did not move at this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated.
In reality (considered with reference to the railway embankment) he is rushing towards the beam of light coming from B, while he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who took the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at an important result. Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers there is no meaning in a statement of the time of an event. Before the advent of the theory of relativity it had been tacitly assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption then the conflict between the law of the propagation of light in vacuo and the principle of relativity disappears." (page 25)
The logic of the above example using relativity of simultaneity holds only at first glance. The first question to arise, will the relativity of simultaneity exist if instead of flash of light we use sound – thunder - which the lightning generates simultaneously with the flash. In this case the observer standing in the mid-point of the embankment, M, will hear the sounds of thunder from lightning strokes A and B simultaneously, because the distance A à M is equal to the distance Mà B and so the sounds from both lightnings will take equal time to reach the observer in mid-point M. (we assume that air is not in motion at that place and that the velocity of sound is constant).
The experiment stipulates that when the lightnings strike, point M' not only coincides with point M but also moves towards the right with the velocity v of the train. As a result, the train-bound observer placed at M' will hear the thunder from lightning stroke in B earlier than the thunder from lightning stroke in A. Naturally, both observers will see light flashes before they hear the thunders: at 300000km/sec light travels much faster than sound at 330m/sec. Thus the relativity of simultaneity is demonstrated equally successfully both with light and sound from lightnings.
However, when our stationary observer at M, using the lightnings' sound, concluded that the lightning strokes A and B were simultaneous, he understood that the time of simultaneity which his watch showed was different from the time of simultaneity indicated by watches placed directly at A and B, where the lightnings stroke. Say the lightning strokes in A and B took place exactly at 3 pm. If distances AM and MB are 3300 metres, the observer's watch at M will show 10 seconds past 3 pm because at 330 m/sec thunder will take 10 seconds to reach him. In conclusion, the time of simultaneity as indicated on the observer's watch differs from the time of simultaneity measured where the events take place.
This logic holds well when applied to the consequences of an event, like flash of light and thunder, but not when applied to the event itself. From the philosophical point of view, flash and thunder represent forms of existence of lightning which itself can be regarded as their content.
This conclusion becomes more obvious if we consider the simultaneity of lightning strokes in relation to one system of reference, the embankment. In this case the simultaneity of lightning strokes must be observed by any observer no matter where he is standing on the embankment. Suppose that our observers are standing at points M and F, furthermore suppose that we have watches at points A, M, F, and B, which show the same time. Since time in one body-reference is absolute then we can state that if the lightning strokes are simultaneous at points A and B, say at 3 o'clock, then the same time will indicated by watches at points M and F. But if the observers at M and F used flash of lightning or thunder in order to determine the exact time of lightning strokes, they would come to different conclusions. The observer at point M would say that the lightning strokes were simultaneous at A and B, but this event took place not exactly at 3 o'clock but a little later, say at 3 + T'.
This difference in time is due to light's travel along the distance AM and MB in order to reach our observer at point M. The observer at point F would state that lightning stroke at point B took place earlier than the one at point A . This is so because the distance FB which the light and thunder travel from point B in order to reach the observer at point F is shorter than the distance AF which the light and thunder travel from point A in order to reach the observer at point F. For this reason the watches will show that the event took place at point B not at 3 o'clock but at 3 + T, where T < T' and at point A at 3 + T", where T" > T'.
The result of this example show that the time of event itself (lightning strokes) is completely different from the time of form of appearance (flash and thunder) of this event, even though it occurs in one body-reference. By way of his example with a train moving along an embankment, Einstein uses this difference in time as a proof of 'relativity of simultaneity' in different body-references. Indeed, at the very moment the lightning strikes the observer in the moving train is at point M. By the time the light or sound coming from point B reaches him, he is at point F thanks to the velocity 'v' of the train. For this reason he will say that the event at point B took place earlier than the event at point A. In reality both events occur when our train-bound observer is at point M.
Consequently, the above mentioned example does not demonstrate the 'relativity of simultaneity' in different systems of references as Einstein proposed it. The Special Theory of Relativity contains other errors of logic First, it makes the velocity of light absolute and equal to 300000 km/sec regardless of the coordinate system where it is measured. According to Einstein everything in the world is relative except for the velocity of light. Second, Einstein imposed the limits of the velocity of light, which is electromagnetic by nature, on all bodies which have nothing to do with it.
V --> M' Train ________________________________________________________________________ _______________________|___________ _________|________|____________|_______ embankment A M F B
We know that the velocity of sound in air is independent of the source of its origin and is constant at 330m/sec. On the other hand the velocity of sound in relation to the source of its origin when it is moving, will be different. Its speed will be less than 330 m/sec in the direction of motion and it will be more in the opposite direction. Because both sound and light are a wave by nature – mechanical and electromagnetic, respectively - we can assume that the propagation of light takes place not in a vacuum but in a medium (ether), which is the gravitational field of planets, stars, galaxies etc,. This gravitational field represents a single entity, whether in the vicinity of a planet, a star or a galaxy. If we assume that light behaves like sound then it will explain why in the Michelson & Morley's experiment the velocity of light is independent of that of its origin. We assume here that Earth carries along its gravitational field and that in its movement the two constitute a single entity.
From this point of view it is easy to explain the abberation of stars assuming that each star with its gravitational field constitutes a single entity moving in relation to the earth and its gravitational field. Another words if the velocity of light from the star in its gravitational field is equal 300000 km/sec then in relation to the moving earth and its gravitational field the speed of light will be more or less depending on wheather the earth at the given moment moves in the direction of propagation of the light from the star or against.
But this assumption contradicts to the propagation of light in water flowing through a tube. Fizeau's experiment showed that the moving water partially carried away ether and the degree of carried away ether by moving body is defined by the refractive index of the latter. For this reason the substance with refractive index = 1, like air, practically must not to carry away ether, which is in conflict with the above assumption.
So we have a dilemma. If our interpretation of Michelson & Morley's experiment is right than the Fizeau's experiment is wrong. The latter is right but its interpretations are not, because they are based on a wrong assumption, namely that the velocity of light in moving water is the same as in motionless water. The optical density of moving water could be more or less than when it is at rest. For example, in the moving water its optical density in relation to the fixed point of tube will be more than when it is at rest. According to physics, greater optical density reduces the velocity of light, and vise versa. For this reason the velocity of light measured against the current of moving water (optical density is higher in relation to the light) is lower than that in water at rest, and the velocity of light measured in direction of the current of moving water (optical density is lower in relation to the light) is higher than that in water at rest.
So Fizeau in his calculations should change V - au to V' - au and V + au to V" + au, where V - the velocity of light in motionless water, V' - the velocity of light measured against the current of moving water, and V" - the velocity of light measured in direction of the current of moving water, 'u' - the velocity of moving water, 'a' - factor of carried away of ether by moving water. Under such conditions he would get different result that 'a' is equal to 1 which means that moving water do not carry away ether.
2L 2L 4Lau ----------- - --------- = ------------------- = T V - au V + au V * V - au * au
1. Light propagates not in a vacuum but in a gravitational field of a planet, star, galaxy, etc., which in conjunction with the planet, star or galaxy constitutes a single system of reference. These gravitational fields move relatively to each other together with their carrier (planet, star, galaxy).
2. Light propagates in this gravitational field at 300000 km/sec, and is independent from the velocity of its source.
3. But the velocity of light in relation to the source of its origin or any moving system of reference is subject to the rule of adding velocity, as described in classical mechanics.
4. In the above described moving systems time and space are absolute, regardless of the system relative to which they are considered.
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