This replaces my post of 11 July 20.14 (ie it is a better version). In effect it is a supplementary, substantiating what had to be virtually a 'throwaway' line in the essay, and a point that keeps coming up in other blogs.
Einstein and an urban myth
Introduction
1 It is commonly assumed that Special Relativity (SR) is that which was written in 1905. This is not so. In propounding General Relativity (GR), Einstein had to resolve the significance of light, and specified what constituted SR in doing so.
The original hypothesis: dimension alteration
2 The original start point concerned the expected calibrated speed of light, given earth movement, the transparency of matter, and ether. For example: Michelson 1881: "Assuming then that the ether is at rest, the earth moving through it, the time required for light to pass from one point to another on the earth's surface, would depend on the direction in which it travels". Further on Michelson writes: "If, therefore, an apparatus is so constructed as to permit two pencils of light, which have traveled over paths at right angles to each other, to interfere, the pencil which has traveled in the direction of the earth's motion, will in reality travel 4/100 of a wave-length farther than it would have done, were the earth at rest".
3 The perceived results of his experiments prompted the hypothesis by Lorentz and Fitzgerald that matter altered in dimension whilst it endured an imbalance of forces (subsequently deemed to be gravitational forces), which also caused a change in momentum. This was to reconcile the fact that the expected differential in light speed was not, apparently, demonstrated, but nevertheless still held to be true. These alterations continue whilst the imbalance persists, ie when the forces incurred are again in equilibrium then dimension returns to its rest/normal state, and momentum becomes constant. An imbalance effectively means that a force (ie the differential) is being applied. This is a similar concept to movement, where since everything is moving, movement effectively refers to a differential.
4 Which part of this combination of assumptions, relationships and results was incorrect (if any), is irrelevant, in the sense that the hypothesis of dimension alteration was deemed to occur physically, and never retracted subsequently. For example:
4.1 Lorentz 1892: "It consists of the assumption, that the line joining two points of a solid body doesn't conserve its length, when it is once in motion parallel to the direction of motion of Earth, and afterwards it is brought normal to it...Such a change in length of the arms in Michelson's first experiment, and in the size of the stone plate in the second, is really not inconceivable as it seems to me. Indeed, what determines the size and shape of a solid body? Apparently the intensity of molecular forces; any cause that could modify it, could modify the shape and size as well".
4.2 Lorentz 1895: "Thus from a theoretical perspective there is no objection to the hypothesis. As regards the experimental confirmation, it is to be noticed at first, that the relevant elongations and contractions are extremely small... it would cause a contraction in the direction of motion in the ratio of 1 to √(1-p2/V2). In reality the molecules of a body are not at rest, but there exists a stationary motion in every "equilibrium state".
4.3 Einstein 1916: "For this reason non-rigid reference bodies are used, which are as a whole not only moving in any way whatsoever, but which also suffer alterations in form during their motion".
4.4 Einstein (Foundation) 1916: "The unit measuring rod appears, when referred to the co-ordinate-system, shortened by the calculated magnitude [equation (71)] through the presence of the gravitational field, when we place it radially in the field. The gravitational field has no influence upon the length of the rod, when we put it tangentially in the field [equation (71a)]...But a glance at (70a) and (69) shows that the expected difference is much too small to be noticeable in the measurement of earth's surface"
5 Concern therefore began to revolve around the electrodynamics of this supposed effect. The expanation as to how it worked changed over the years, the final one before the Einstein 1905 paper being thought to involve electrons becoming flattened ellipsoids (Lorentz 1904). Indeed, in response to criticism of this mechanism, Poincaré (July 1905) had "to suppose a special force which explains at the same time the contraction and the constancy of two of the axes" in order to keep the proposal intact.
6 Before proceeding further, a logical point should be noted here. If there is a dimensional affect on 'objects' due to some form of atomic disturbance caused by a force, then that equally affects an oberver, in that he/she is an object, and clocks. Also, it has to be assumed until proven otherwise, that light must similarly be affected in some way.
The 1905 reconciliation problem
7 But, in 1905 there is a combination of alteration consequent upon forces, with an 'unaffected' light, ie it is in vacuo and therefore not subject to these forces. There must be one common condition for these to co-exist.
8 There are two key words in 1905. When stating the two postulates, Einstein 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, non controversial, statements in their own right. Yet he is already aware of a potential conflict (ie they cannot co-exist, as stated).
9 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, ie that existence occurs and has certain properties, irrespective of the calibration of them, which can only be effected with a reference. Use of phrases such as 'frame of reference' have nothing to do with observation and light, per se, they are about referencing. That is, as there is no known absolute, everything must be deemed in terms of its relativity, ie difference when compared to another. Then, in order 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 actual physically existent state does not alter.
10 The interest in light stems back to a consideration of it which sparked this whole train of thought, including the M&M experiments, and then its use as a substitute for the distance variable in a flawed equation (see other supplementary essay).
11 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 still a physical entity. And as such, it will continue to travel at that start speed, just like any other physical entity, unless impeded in some way. Impediment does not occur in vacuo, by definition, a condition stipulated in 1905.
The resolution of the recinciliation problem
12 The resolution of the 'apparent irreconcilability' was pursued by Einstein in section 7 of SR & GR 1916. The explanatory example used is incorrect, the ray of light and man walking are not equivalent (to be precise, given his definition of the circumstance, the man is of the earth system, the ray of light is not). 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 therefore be a function of that reference. However, a flaw in the explanation of a circumstance, does not mean that the underlying hypothesis is incorrect.
13 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".
14 That is, one of these factors cannot co-exist, assuming they have been invoked properly and dimension alteration is a physical fact. That is, there is variability somewhere, even if it is wrongly attributed. So, the fact that this dimensional effect is being misrepresented by 1916, ie it has become associated with timing differences (which originates with Poincaré and then Minkowski spacetime), is irrelevant to this context. Which again raises the point that a flaw in explanation, does not necessarily mean that the underlying hypothesis is incorrect.
15 He then 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".
16 That is, a special theoretical circumstance is invoked. One where everything can, by definition, co-exist. It proves nothing, and is a tautology. Neither is it the circumstance described in 1905. It is also 'disconnected' from GR, ie that is not developed from it. GR is the only theory.
17 This is proven when it is established what Einstein himself defines SR as. Some quotes follow:
17.1 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."
17.2 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."
17.3 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."
17.4 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."
18 So, SR, as defined by Einstein, involves:
-no gravitational forces
-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 (no curvature)
19 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 a common force (ie gravity). Light is therefore affected now, as Einstein states. One example being:
19.1 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)."
Conclusion
20 In 1905 the factors involved are not all subject to the same condition, so they cannot co-exist. And Einstein knew this at the time of writing because of the phrase "only apparently irreconcilable". By 1916 this had been reconciled with the propounding of a theoretical circumstance, ie a "limiting case" where light was still in the same condition as 1905, but the other factors were too. It was called, SR. The factor which was different was that there was no gravity, hence the title, 'special'. So SR is not 1905. In GR, all factors are subject to the same condition, ie gravitational forces, hence the title GR. The theory is concerned with the electrodynamics of moving bodies. Moving being altering momentum, because everything is in motion, but a differential (movement) is only noticeable, by comparison, when something is not in constant motion (alternatively referred to as "at rest" or "in equilibrium"). The theory was not about the observation of this electrodynamics. Consideration of light speed prompted the train of thought. And light, and its speed, took on a significance that is not physically substantiated with it being used as a surrogate for distance in a flawed equation which misconceptualised timing.
