Is it possible that in a theory of gravitons, i.e., a quantum field theory of gravitation, general relativity's principle of the equivalence of gravitational mass and inertial mass, no longer holds?

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    You'll need to clarify what you are asking. The graviton is the gauge boson associated with a quantum field theory description of gravity (though we don't know if such a description makes physical sense). You could for example ask if the equivalence principle is fully respected by all the QFT theories (there are several) of gravity. As it stands, just asking if gravitons break the equivalence principle is meaningless. – John Rennie Jul 10 '15 at 5:07
  • Well said John. – John Duffield Jul 10 '15 at 12:28
  • Let's say maybe, but in that case it would be only a temporary effect (whatever it might be at that level of abstraction) and in its classical limit they should be the same. – gox Jul 24 '15 at 21:26

On the contrary Deser and others [1, and refs therein] have argued that trying to construct a theory of a graviton, that is, a massless spin-2 field in a flat background, consistent with special relativity, then "[c]onsistency [leads] us to universal coupling, which implies the equivalence principle" [1]. The argument is summarized by MTW [2, Box 17.2.5, see also Box 18.2, and refs therein]. More concretely, the conclusion is that the field equations for the graviton field must be the Einstein field equations with the source being the stress-energy tensor.

References

  1. Deser, S. (1970). Self-interaction and gauge invariance. General Relativity and gravitation, 1(1), 9-18.
  2. Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. Macmillan.
  • The trouble with that is that "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". See The Foundation of the General Theory of Relativity. And that energy has a mass-equivalence. The field is not massless. – John Duffield Jul 10 '15 at 12:27
  • @JohnDuffield: A massless field in the quantum field theoretic sense is one without a mass term in the Lagrangian (sometimes protected from acquiring a mass term by gauge invariance). The classical mass-energy equivalence has nothing to do with it. – ACuriousMind Jul 10 '15 at 22:48
  • @ACuriousMind : thanks for the info. But are you saying that we then have a massless field which has mass? – John Duffield Jul 11 '15 at 6:15

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