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These comments seem to say gravitational redshift experiments would only verify theories that obey the equivalence principle (ep), not specifically general relativity: https://arxiv.org/abs/0806.0528 (see 2nd paragraph p.16) and this (by one of the same authors) seems to show even the ep is not needed to explain the shift: https://arxiv.org/abs/gr-qc/0403082

But this paper (published in Nature, 2011): https://arxiv.org/abs/1109.6571 (see p.8 for key graph) says the TeVeS theory is "inadequate" based on gravitational redshift measurements. I only have a vague understanding of the ep and have not studied general relativity or TeVeS but I have read that TeVeS is meant to obey the ep. So do the "comments" and experimental paper not contradict each other? Should gravitational redshift be considered a central test of general relativity or the ep or neither?

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  • $\begingroup$ The gravitational redshift around planets and starts is a property of the Schwarzschild metric. This metric can be viewed as a solution of the GR equations or of some other equations. because different equations can produce the same solution. Friedrich Kottler derived this metric without GR equations in 1918 and there are other examples. So gravitational redshift, at least for planets and stars, is not a proof of GR only. However other theories also must involve the EP, at least to some extent, because the EP is an experimental result (also to some extent). I will defer details to GR experts. $\endgroup$
    – safesphere
    Commented Oct 17, 2019 at 19:10

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It's a test of the equivalence principle. Tensor-scalar theories such as Brans-Dicke and TeVeS do violate the e.p.

I have read that TeVeS is meant to obey the ep.

This seems odd to me. I'm not claiming that this is a totally airtight argument, but basically when we augment the metric with other properties of space such as scalar or tensor fields, we expect the e.p. to be violated for the following reason. The e.p. says that locally, special relativity always applies. SR says that the only built-in structure of spacetime is the metric (which can be made trivial in SR through an appropriate choice of coordinates).

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  • $\begingroup$ I read that "TeVeS...obeys the Einstein equivalence principle..." in another paper (sciencedirect.com/science/article/pii/S0370269314004419). I hadn't realised there were 3 e.ps but then on a wiki page I read that "Other tests of the Einstein equivalence principle are gravitational redshift experiments" (en.wikipedia.org/wiki/…). So I'm still not sure what to think. Do you disagree that it obeys the EEP? Because if it does it's predictions of grav redshift should be right according to the wiki pg. Is the EEP even legit? $\endgroup$
    – Confused
    Commented Oct 17, 2019 at 23:05

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