Eintein and an urban myth
It is commonly assumed that Special Relativity is that which was written in 1905, or at least most of it. This is not so. In propounding General Relativity, of which 1905 was effectively a 'first draft', Einstein had to resolve the significance of light. There are two key words in 1905. When stating the two postulates, he writes that they are: "only apparently irreconcilable". This is, of itself, a peculiar statement, because he is proposing a new theory which is based only on these ("These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies"). And both are understandable statements in their own right. Yet he is already aware of a potential conflict. That is, all the variables as stated in 1905 cannot co-exist in a cohesive theory.
The first postulate (the principle of relativity) is a logical truism, ie for physical laws to be valid they must hold whatever reference point is used. Another way of putting this is that physical existence is independent. Use of phrases such as 'frame of reference' have nothing to do with observation, per se, they are about referencing. That is, as there is no known absolute, everything has to be deemed in terms of its relativity, ie difference when compared to another. And in order then to ensure comparability, that reference must be used consistently, and logically (as opposed to practically) any potential reference could be chosen. But there must be one, otherwise a judgement cannot be made. Something is only X when compared to something else, and the calibration of X is dependent upon that reference. But the physically existent state which manifests X does not alter.
In respect of the second postulate about light, this is correct physically, as written. Light is created as the result of an atomic interaction (ie not a collision), and therefore always starts with the same physical speed. That is, the speed of that which was involved in the interaction is irrelevant. From the perspective of a sensory system, that resultant physical effect-light-is a representation of what was involved in the interaction, but of itself, it is a physical entity. And as such, it will continue to travel at that speed, just like any other physical entity, unless impeded in some way. Impediment does not occur in vacuo, by definition, a condition invoked in 1905.
It has to be remembered that the start point was concerns about light speed, earth movement and ether. This did not appear to be, or perhaps actually was not, borne out by the Michelson and Morley experiments. But to counterbalance that apparent result, and hence maintain the presumptions about light, the hypothesis was proposed that matter physically alters in dimension in the line of motion. That is, when forces acting thereon become imbalanced, the shape and momentum of the matter changes whilst that circumstance obtains. Equilibrium is subsequently restored, and matter regained its original shape and resumed its travel at a constant momentum. Whether this is physically correct or not is another issue. So, 1905 has a combination of alteration consequent upon alterations in force, with an 'unaffected' light. That is, it is in vacuo, but everything else is not. There must be one common condition.
The resolution of the 'apparent irreconcilability' was pursued by Einstein in section 7 of SR & GR 1916. The example used is incorrect, the ray of light and man walking are not equivalent (to be precise, the man is of the earth system, the ray of light is not). He has not considered light as a physically existent entity, and the application, as opposed to the principle, of relativity is flawed. So this has not proved his point from the previous section, that is, that the Theorem of the Addition of Velocities employed in classical mechanics, was no longer valid. And this cannot be so anyway, because in order to effect any judgement, a reference is necessary, and the calibration of the attribute will be a function of that reference. In simple terms, the variable of dimension alteration became subsumed by the supposed variability of time, but time does not vary and is not physically existent, there is only timing. Therefore, in essence, the problem was 'resolved', but for the wrong reason.
Because he then writes (para 5): "In view of this dilemna 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. Those of you who have carefully followed the preceding discussion are almost sure to expect that we should retain the principle of relativity, which appeals so convincingly to the intellect because it is so natural and simple. The law of the propagation of light in vacuo would then have to be replaced by a more complicated law conformable to the principle of relativity.
That is, one of these variables cannot co-exist, assuming they are invoked properly and dimension alteration is a physical fact (leaving aside that the effect is being explained in terms of time variance).
And then he writes (para 6): At this juncture the theory of relativity entered the arena. As a result of an analysis of the physical conceptions of time and space, it became evident that in reality there is not the least incompatibilitiy between the principle of relativity and the law of propagation of light, and that by systematically holding fast to both these laws a logically rigid theory could be arrived at. This theory has been called the special theory of relativity to distinguish it from the extended theory, with which we shall deal later. In the following pages we shall present the fundamental ideas of the special theory of relativity.
That is, a special theoretical circumstance is invoked. Where, because of the circumstance invoked, everything can, by definition, co-exist, as defined. It proves nothing, and is a tautology. Neither is it the circumstance of 1905. It is also 'disconnected' from GR, ie that is not developed from it. GR is really the only theory.
Einstein defines SR as:
Einstein Foundation of GR 1916, section A, sub sec 1:
"We call this postulate "The Special Relativity Principle." By the word special, it is signified that the principle is limited to the case, when K' has uniform translatory motion with reference to K, but the equivalence of K and K' does not extend to the case of non-uniform motion of K' relative to K. The special theory of relativity does not depart from classical mechanics through the postulate of relativity, but through the postulate of the constancy of the velocity of light in vacuo."
"According to the special relativity theory, the theorems of geometry are to be looked upon as the laws about any possible relative positions of solid bodies at rest."
Einstein Foundation of GR 1916, section A, sub sec 3:
"the case of special relativity appearing as a limiting case when there is no gravitation."
Einstein SR & GR 1916, section 28:
"The special theory of relativity has reference to Galileian domains, ie to those in which no gravitational field exists."
"In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity."
Einstein SR & GR 1916, section 18:
"the special principle of relativity, i.e. the principle of the physical relativity of all uniform motion. Let us once more analyse its meaning carefully. It was at all times clear that, from the point of view of the idea it conveys to us, every motion must only be considered as a relative motion."
"If it is simply a question of detecting or of describing the motion involved, it is in principle immaterial to what reference-body we refer the motion. As already mentioned, this is self-evident, but it must not be confused with the much more comprehensive statement called "the principle of relativity,""
"we started out from the assumption that there exists a reference-body K, whose condition of motion is such that the Galileian law holds with respect to it: A particle left to itself and sufficiently far removed from all other particles moves uniformly in a straight line."
"provided that they are in a state of uniform rectilinear and non-rotary motion with respect to K; all these bodies of reference are to be regarded as Galileian reference-bodies. The validity of the principle of relativity was assumed only for these reference-bodies, but not for others (e.g. those possessing motion of a different kind). In this sense we speak of the special principle of relativity, or special theory of relativity. In contrast to this we wish to understand by the "general principle of relativity" the following statement: All bodies of reference are equivalent for the description of natural phenomena (formulation of the general laws of nature), whatever may be their state of motion."
So SR, as defined by Einstein, involves:
-no gravitation
-only motion that is uniform rectilinear and non-rotary (which is in effect, stillness)
-fixed shape bodies at rest (no dimension alteration)
-light which travels in straight lines at a constant speed
When gravity is present, then the condition of in vacuo, which was invoked in 1905, is withdrawn. In other words, light and matter co-exist in the same condition, ie a real world where they are subjected to common forces. Light is therefore affected, as Einstein states. One example being:
Einstein SR & GR 1916, section 22:
"However, we obtain a new result of fundamental importance when we carry out the analogous consideration for a ray of light. With respect to the Galileian reference-body K, such a ray of light is transmitted rectilinearly with the velocity c. It can easily be shown that the path of the same ray of light is no longer a straight line when we consider it with reference to the accelerated chest (reference-body K'). From this we conclude, that, in general, rays of light are propagated curvilinearly in gravitational fields. In two respects this result is of great importance...... In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)."
