We discuss what we take to be three possible misconceptions in the foundations of general relativity, relating to: (a) the interpretation of the *weak equivalence principle* and the relationship between gravity and inertia; (b) the connection between gravitational redshift results and spacetime curvature; and (c) the *Einstein equivalence principle* and the ability to “transform away” gravity in local inertial coordinate systems.

## References

*Principia*, particularly in relation to the discussion of the system of Jupiter and its moons. For a recent discussion, see

*Einstein's strong equivalence principle*. See, e.g., p. 601 of

Though WEP 1 and WEP 2 are both referred to as the “weak” equivalence principle, we stress that we do *not* conflate the two. In fact, in what follows we will argue broadly in favor of WEP 1, and against WEP 2, from the perspective of GR.

*op*.

*cit*.

*et al.*, Ref. 16. In the former, it is argued that despite not relying on the details of the Einstein field equations, the redshift experiment should not be regarded as a “weak test” of GR.

*et al.*, Ref. 16. In fact, this is not an example of a gravitational redshift-type result, but rather of the relativistic Doppler effect. In a correct derivation of Eq. (1), source and accelerator must be considered at rest with respect to one another, but accelerating with respect to an inertial frame.

*A*is the higher sample, then received signals at

*B*will in fact be

*blueshifted*. If the positions of emitter and receiver are swapped, then the situation resembles the original Pound–Rebka experiment;

*et al.*, Ref. 16.

*et al.*, Ref. 16.

In what follows, we use the Einstein summation convention, with Greek indices ranging from 0 to 3.

*et al.*, Ref. 16;

The arguments leading to our Eq. (8) above are essentially those given by Thorne and Will, Ref. 30, pp. 602–603; the analysis there is given in the context of a curved spacetime geometry, however, with the curvature playing no part in the analysis. Given Hartle's claim above that redshift is ultimately connected to spacetime curvature, it is striking that in Problem 6, p. 132 (*op. cit.*), Hartle uses the transformations to accelerating coordinates to conclude that accelerating clocks in special relativity are affected in accordance with our Eq. (8), but leaves how this is related to “the equivalence principle idea” as a question. Exercise 5.1 in the Poisson-Will textbook (p. 285, *op. cit.*) almost exactly reproduces Hartle's Problem 6, even repeating the same question. This section of the present paper can be read as an attempt to answer this question.

**8**, 28 (1963).

*et al.*, Ref. 16;

Similar considerations hold for the “proper distance” read off by accelerating rigid rulers. For further discussion of the role of rods and clocks in GR, see Harvey R. Brown, “The behavior of rods and clocks in general relativity, and the meaning of the metric field,” forthcoming in the Einstein Studies Series, e-print arXiv: 0911.4440.

The metric is of course also surveyed by the proper distance read off by rigid rulers.

*c*; whether it is photons which instantiate this speed is a separate question; recently circumstances in which the group velocity of light

*in vacuo*is slightly less than

*c*were demonstrated experimentally. See

Nomenclature varies here considerably; for example, EEP is related to the “medium strong equivalence principle” in Sec. 3.2.4 of Ciufolini and Wheeler, Ref. 10. In the philosophical literature, it is frequently referred to as the strong equivalence principle.

*et al.*, Ref. 16.

*et al.*, Ref. 16.

*et al.*, Ref. 16.

*et al.*, Ref. 16.

*et al.*, Ref. 16;

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