Peter
1 You did not ask what the cause was. I usually state that in a description of dimension alteration. According to them, the cause was a differential in gravitational forces incurred.
2 Now, there is a set of factors involved, with their presumed attributes and interrelationships, and experiments which may or may not have been valid, with their outcomes which needed interpretation. In all this there is: 1) what actually physically occurs, 2) the extent to which their theory is correct for the right reasons, correct for the wrong reasons, or incorrect. There is also mention of 'translation', in addition to (?) transformation, and first and second order effects.
3 Furthermore, since you refer to it. Section 3 1905 follows on with the mistake incurred at the beginning of this paper. Which is explained in my blog post 11/7 19.33. The 'bottom line' in this section being the derivation of lambda, which for want of a better phrase is the 'all purpose differential factor'. That is, there is deemed to be variance in physical reality, which, because of misconceptualisation, is variously attributed amongst some of the factors involved. But, unsurprisingly, the calibrated variation is the same. In other words, one factor becomes a surrogate for another.
4 However, none of the above matters, in the sense that it is the internal logic of what they state which is the point here. They postulate real physical dimension alteration. The electrodynamics of this is first (Lorentz 1904) explained as revolving around the "intervention of the aether" affecting the "intensity of the molecular forces" which "determines the size and shape of a solid body". It is a plausibility argument given how "electric and magnetic forces act", with the caveat that "since we know nothing about the nature of molecular forces, it is impossible to verify the hypothesis".
5 Over the years this 'mechanism' changes until Lorentz (1904) states: "Our assumption amounts to saying that in an electrostatic system, moving with a velocity, all electrons are flattened ellipsoids with their smaller axes in the direction of motion". Although again there is a caveat: "Our assumption about the contraction of the electrons cannot in itself be pronounced to be either plausible or inadmissible. What we know about the nature of electrons is very little". Poincaré has to introduce (July 1905) the 'Poincaré stresses' in response to criticism, as he 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 mechanism 'intact'.
6 [Note the start of section 4 1905 with its reference back to this concept (radius R). That in 1895 Lorentz is referring to 'local time', which derives from Voigt and Doppler. That in 1899 Lorentz is utilising the physically incorrect concept of "only at such small distances, that two particles of matter, acting on each other, may be said to have the same local time". Which was seized on by Poincaré (1904): "Their task was not easy, and if Lorentz has succeeded, it is only by an accumulation of hypotheses. The most ingenious idea is that of local time". Which is then repeated by Einstein in section 1 1905, which is where the explanation, but not necessarily the underlying physics, all goes wrong].
7 The followung quotes from Lorentz (1904) are important:
"The problem of determining the influence exerted on electric and optical phenomena by a translation, such as all systems have in virtue of the Earth's annual motion, admits of a comparatively simple solution, so long as only those terms need be taken into account, which are proportional to the first power of the ratio between the velocity of translation w and the velocity of light c".
"It would be more satisfactory, if it were possible to show, by means of certain fundamental assumptions, and without neglecting terms of one order of magnitude or another, that many electromagnetic actions are entirely independent of the motion of the system. Some years ago, I have already sought to frame a theory of this kind. I believe now to be able to treat the subject with a better result. The only restriction as regards the velocity will be that it be smaller than that of light".
"Thus far we have only used the fundamental equations without any new assumptions. I shall now suppose that the electrons, which I take to be spheres of radius R in the state of rest, have their dimensions changed by the effect of a translation, the dimensions in the direction of motion becoming kl times and those in perpendicular direction l times smaller. In this deformation, which may be represented by... each element of volume is understood to preserve its charge. [This point was subsequently corrected by Poincaré]. Our assumption amounts to saying that in an electrostatic system, moving with a velocity, all electrons are flattened ellipsoids with their smaller axes in the direction of motion".
"Strictly speaking, the formula (28) may only be applied in the case of a uniform rectilinear translation. On account of this circumstance- though (29) is always true- the theory of rapidly varying motions of an electron becomes very complicated, the more so, because the hypothesis of para 8 would imply that the direction and amount of the deformation are continually changing... Nevertheless, provided the changes in the state of motion be sufficiently slow, we shall get a satisfactory approximation by using (28) at every instant. The application of (29) to such a quasi-stationary translation... is a very simple matter...Hence, in phenomena in which there is an acceleration in the direction of motion, the electron behaves as if it had a mass m'"
8 In simple language. Everything is moving, in 'addition', the earth is moving. So even 'at rest' (ie constant motion) wrt earth, there is a level of interaction with the particles which comprise the 'ether' which results, via some mechanism, with some degree of dimension alteration. If entities are caused to 'move more', ie their momentum is changing, then there is a further level of dimension alteration. Lorentz 1895: "In reality the molecules of a body are not at rest, but there exists a stationary motion in every "equilibrium state".
9 Leaving aside how the mechanism works, the next question is, what is causing that. And the answer is a differential in gravitational force, because these forces are ever present, entities thereby having an "equilibrium" state when these forces, as incurred, are counterbalanced. So the (additional) effect only occurs if there is an imbalance in that, and continues whilst that circumstance obtains, ie there is a reversion to the 'normal' state when the balance in forces is re-established.
10 Note:
10.1 There is no other cause mentioned. Interaction with particles in the 'ether' do not suddenly involve a 'step change'. That is just concerned with the mechanism through which the outcome (dimension alteration) occurs, and that 'underlying state' of 'disturbance' (dimension alteration) due to motion. Gravitational forces are involved in the ether.
10.2 SR involves no gravitational forces, GR does. Why, otherwise differentiate a "linmiting case", or "special case", unless the variable that is the ultimate cause is gravitational force.
11 SR. Einstein defines its scope thus:
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."
Einstein SR & GR 1916, section 18: "provided that they are in a state of uniform rectilinear and non-rotary motion...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."
Einstein SR & GR 1916, section 22: "From this we conclude, that, in general, rays of light are propagated curvilinearly in gravitational fields...A curvature of rays of light can only take place when the velocity of propagation of light varies with position...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)."
12 Ether. The important points are:
Einstein (1921) A Brief Outline of the Development of the Theory of Relativity
"The theory [Lorentz] appeared to be unsatisfactory only in one point of fundamental importance. It appeared to give preference to one system of coordinates of a particular state of motion (at rest relative to the aether) as against all other systems of co-ordinates in motion with respect to this one. In this point the theory seemed to stand in direct opposition to classical mechanics, in which all inertial systems which are in uniform motion with respect to each other are equally justifiable as systems of co-ordinates (Special Principle of Relativity)".
"The Special Theory of Relativity owes its origin to this difficulty...This theory originated as the answer to the question: Is the special principle of relativity really contradictory to the field equations of Maxwell for empty space? The answer to this question appeared to be in the affirmative".
"A more searching analysis of the physical significance of space and time rendered it evident that the Galileo transformation is founded on arbitrary assumptions, and in particular on the assumption that the statement of simultaneity has a meaning which is independent of the state of motion of the system of co-ordinates used. It was shown that the field equations for vacuo satisfy the special principle of relativity, provided we make use of the equations of transformation stated below:... [Lorentz]"
"Now in order that the special principle of relativity may hold, it is necessary that all the equations of physics do not alter their form in the transition from one inertial system to another, when we make use of the Lorentz transformation for the calculation of this change. In the language of mathematics, all systems of equations that express physical laws must be co-variant with respect to the Lorentz transformation".
Einstein (1922) Ether and The Theory of Relativity:
"It may be added that the whole change in the conception of the ether which the special theory of relativity brought about, consisted in taking away from the ether its last mechanical quality, namely, its immobility".
"To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view".
"What is fundamentally new in the ether of the general theory of relativity as opposed to the ether of Lorentz consists in this, that the state of the former is at every place determined by connections with the matter and the state of the ether in neighbouring places, which are amenable to law in the form of differential equations; whereas the state of the Lorentzian ether in the absence of electromagnetic fields is conditioned by nothing outside itself, and is everywhere the same. The ether of the general theory of relativity is transmuted conceptually into the ether of Lorentz if we substitute constants for the functions of space which describe the former, disregarding the causes which condition its state. Thus we may also say, I think, that the ether of the general theory of relativity is the outcome of the Lorentzian ether, through relativation".
13 In simple language. Through the misconceptualisation of time, a non-existent variance was introduced which was then used to resolve the "unsatisfactory" aspect, whereby "It [Lorentz theory] appeared to give preference to one system of coordinates of a particular state of motion (at rest relative to the aether) as against all other systems of co-ordinates in motion with respect to this one". That is, it was deemed that the "apparent preference" was just that, apparent. It being no more than a reflection of the differential in 'local time'. And was resolved so long as the Lorentz transformations were applied.
Paul
