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"Einstein continues by pointing out how things fare better in GR:
By the way, physical space possesses reality according to the general theory of relativity, too, but not an independent one; for its properties are completely determined by matter. Space is incorporated into the causal nexus without playing a one-sided role in the causal chain.
The second half of the first sentence is also striking, as Einstein had previously recognised that Mach’s principle only holds for certain solutions of the Einstein field equations, not for all of them — but of course, at the time he considered those solutions for which it held as the only physically relevant ones. At any rate, we here see the complete position which would first be presented in the 1921 Princeton lectures: in Newtonian mechanics space acts without being acted upon, while in general relativity it interacts."
For twenty years I have made the same point for quantum theory.
Signal nonlocality happens when the matter beables and their quantum information mental pilot waves obey the very same AR action reaction principle. This opens Pandora's Box.
See Lecture 8 of http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html
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"As we mentioned in section 3.3 above, Norton argued in 1999 that AR was in the back of Einstein’s mind well before 1920, and indeed formed the stimulus of his original Machian tendencies. Here is a further quote from Norton’s study:
This view of the deficiency of earlier theories [their violating the action–reaction principle] and general relativity’s achievement is not one that grew in the wake of Einstein’s disenchantment with Mach’s principle. Rather, it was present even in his earliest writings beneath the concerns for the relative motion of bodies and the observability of causes.78
Next year the eclipse is supposed to show whether light rays are bent by the sun, whether, in other words, the fundamental assumption of the equivalence between ac- celeration of the frame of reference on the one hand and the gravitational field on the
79Einstein , p.1260-1261.
80It is true that Einstein rejected his own 1912 scalar field theory (mentioned footnote 32 above) when he discovered that it failed to satisfy Newton’s third law of motion concerning action–reaction. But this is a case of the existence of both action and reaction, which happen not to be equal and opposite, thus giving rise to an unacceptable force-free accelerative phenomenon. As we stressed in section 2, AR is not be to be conflated with Newton’s third law, which is a much stronger constraint on the way bodies act on each other.
Einstein is explicit in regard to the claim that gravitation is an interaction, with the clarification that the interaction is said to be mediated by gμν. The outcome, incidentally, is a revised description of the 1916 thought experiment of the two rotating spheres:
'Mr. Reichenb ̈acher misunderstood my considerations regarding two celestial bodies rotating with respect to one another. One of these bodies is rotating in the sense of Newtonian Mechanics, and thus flattened by centrifugal effects, the other is not. This is what the inhabitants would measure with rigid rods, tell each other about it, and then ask themselves about the real cause of the different behaviour of the celestial bodies. (This has nothing to do with Lorentz contraction.) Newton answered this question by declaring absolute space real, with respect to which one but not the other allegedly rotates. I myself am of the Machian opinion, which in the language of relativity theory can be put in the following way: All masses of the world together determine the gμν- field, which is, judged from the first celestial body, a different one than judged from the second one; for the motion of the masses producing the gμν-field differ significantly. Inertia is, in my opinion, a (mediated) interaction between the masses of the world in the same sense as those effects which in Newtonian theory are considered as gravitational effects.'
To summarise, it seems fair to say that Einstein did not need a variant of the action–reaction principle as a reason to adopt the relativity of inertia in 1913. His strong belief in the equivalence between gravity and inertia, together with his retention of the Newtonian tenet that gravity is an interaction between bodies, could be seen as reason enough.85 Furthermore, it is the pairing of the equivalence principle and the principle of the relativity of inertia, together with the principle of relativity, that Einstein mentions repeatedly up until 1920 as the cornerstones of GR, whereas AR only really takes centre stage in 1920 in the correspondence with Schlick and in subsequent publications. For these reasons, we are inclined to believe that the 1920 correspondence brought out a watershed in Einstein’s thinking, marking an unprecedented shift in Einstein’s interpretation of the superiority of GR over preceding theories of space-time: its superiority now rested on satisfaction of the action–reaction principle, rather than implementation of Mach’s original analysis of inertia.
Einstein’s frequent references to GR’s vindication of the action–reaction principle in the years following his 1921 Princeton lectures have been noted in a number of studies.86 A particularly telling quotation is from a letter Einstein wrote a year before his death to Georg Jaffe:
'You consider the transition to special relativity as the most essential thought of relativity, not the transition to general relativity. I consider the reverse to be correct. I see the most essential thing in the overcoming of the inertial system, a thing which acts upon all processes, but undergoes no reaction. The concept is in principle no better than that of the centre of the universe in Aristotelian physics.87'
For Einstein, the glory of GR rested partly on its alleged superiority to preceding theories of space-time which involve absolute structure. His 1924 essay “On the ether” contains a particularly clear denunciation of Newtonian mechanics in terms of its violation of AR.88 But caution should be exercised when extrapolating backwards, as it were, in the history of physics. It doesn’t automatically follow from the fact that GR satisfies AR, that NM and SR don’t, as we mentioned in section 1 above. To repeat, Einstein was content in his 1905 development of SR to explicitly borrow the inertial frames from NM, without any fretting about the correct metaphysics of action. Of course, if AR is to be respected in these theories, inertia must be taken as a brute fact, a position advocated, in different ways, by Schlick and others, as we have seen. Such a position is surely defensible in the context of these theories.
The two epigrammatic Einstein quotations cited at the beginning of this essay underscore how Einstein’s thinking changed between 1905 and 1913, and again between 1913 and 1924. In the years 1912 and 1913, when Mach’s influence on him may have been greatest, Einstein had convinced himself that the phenomenon of inertia required a causal explanation, while regarding as absurd the notion of immaterial space acting as such a cause. By 1924, he was stressing that the metric field in GR is as real and efficacious as the electromagnetic field, and in particular could indeed be seen as the origin of inertia. (But it is worth stressing here that Einstein did not view GR as furnishing a geometric explanation of gravitational phenomena; he continued to reject the notion of space, or space-time, as providing the cause of inertia.89)
Nowadays, acceptance of Einstein’s 1924 claim should be seen to rest not simply on the nature of gμν and its geodesics, but rather on the so-called geodesic theorem, which demonstrates that the form of Einstein’s field equations, along, it must be noted, with other plausible universal assumptions about matter fields, imply that the world-lines of test particles are time-like geodesics as defined by the metric field.90 Note that the theorem deals with an idealisation; it states that extended, but truly freely-falling bodies only approximately move inertially.91 In fact, it is a subject worthy of investigation as to whether the details of the theorem are strictly consistent with Einstein’s insistence that a violation of AR holds in theories with absolute space-time structure.92 But such an investigation must be pursued elsewhere. It is our hope that in the present essay, some further light has been shed on the circumstances which led Einstein to bring to the fore the role of the action–reaction principle in his new theory of gravity.
84Einstein  p. 12 see also Vol.7, Doc. 31 CPAE for a similar statement from December 1919 / January 1920. 85Compare Norton [1989b], p. 24: “[I]t was natural for expect that the extended theory, which dealt with general gravitational effects, would explain the observed disposition of inertial frames of reference in terms of the matter distribution of the universe. For the structure that determined this disposition would behave in many aspects like a traditional gravitational field and therefore be strongly influenced by any motion of its sources, the masses of the universe.”
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