- #36
PAllen
Science Advisor
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You are missing a subtlety of the history of GR. In the modern view, GR is the theory of curved spacetime, SR the theory of flat spacetime that (only) is locally true in GR. However, Einstein had a different way of looking at it, which (to the best of my knowledge) he never abandoned. In his view, the derivation of the properties of non-inertial frames in SR was part of GR, which also extended this to cover significant mass with curved spacetime. Thus, he is using the features of accelerated coordinates in SR displaying a position dependent potential (which you can see in the Rindler metric - to which I believe I referred you earlier), all derived for flat spacetime (no Einstein field equations of GR involved). Einstein just viewed this physics as special case of GR rather than part of SR.CKH said:Try that explanation on your grandmother. ;)
While it's true that he does not present the detailed calculations, a careful reading makes it obvious what he's trying to do.
I'm surprised that you don't see the circularity. Einstein argues that he can view the accelerating traveler as stationary in a uniform gravitational field (by applying the equivalence principle). He then applies the physical laws of a gravitational field (that presumably come from GR) to the problem .
The circularity is that these physical laws of a gravitation field were not independently derived. They were derived directly from the physics of uniform acceleration in SR. The physics of uniform acceleration were transported to apply to a gravitational field (by invoking the equivalence principle) in the first place. That is, the gravitational law is founded on uniform acceleration in SR.
So by invoking a gravitation field, Einstein has added nothing to the analysis already done using acceleration alone in SR. In other words, the impression that he is applying something new that comes from GR is an illusion. Perhaps he had a sly smile on his face when answering his critics in this way?
Thus, with Einstein's packaging, there is no circularity.
It seems you have still not fully grappled with my posts #5 and #11. Especially the point that in the non-inertial coordinates in which the metric shows a potential, the traveling twin is not accelerating. It is the home twin that is accelerating in these coordinate, and that acceleration plays no role in the clock rate of the home twin.