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About Einstein's Leyden lecture
#1
(05-19-2016, 07:41 PM)John Duffield Wrote: NB: perhaps you have the wrong idea about ether? See Einstein talking about it here in 1920.

Einstein's Leyden lecture Ether and the theory of relativity is, of course, a very interesting document.

I like it also because it is a rare place where Einstein has made an error - even if only a minor one:
Quote:But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time.
A minor on, "is in general relativity not thought of" would have been correct. But a "may not be thought of" contains, I would say, more. It excludes also, I would say, interpretations of the Einstein equations of GR which endow the gravitational field with this characteristic of ponderable media.

And this is quite simple. First of all, we endow the harmonic coordinates with the status of being preferred coordinates. Then, in these preferred harmonic coordinates, we endow \(\rho = g^{00}\sqrt{-g}\) with the meaning of a density, and \(v^i=g^{0i}/g^{00}\) with the meaning of a velocity field which allows to track parts of the ether through time. If time is harmonic, this leads to the continuity equation \(\partial_t \rho + \partial_i (\rho v^i) = 0\), and if time is time-like, this gives \(\rho>0\).
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