In quantum field theory, gravity arises from the exchange of gravitons. However, to an observer in a local inertial reference frame, there is no gravity. How can a particle that exists in one reference frame vanish in another?
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5$\begingroup$ Not only is it possible, it happens for all kinds of particles when you change between frames with relative acceleration -- that's the Unruh effect. The issue here is that different reference frames come with different natural definitions of what particles are. $\endgroup$– knzhouCommented May 1, 2020 at 3:49
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$\begingroup$ This is not just a matter of definition. If gravitons can impart energy and/or momentum to other particles, that would be an effect independent of the reference frame in which it is observed. $\endgroup$– Steve StahlerCommented May 2, 2020 at 18:19
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2$\begingroup$ Yeah, that's the objection that everybody makes when they first learn about this. But actually it works out, because what looks like absorption of a particle in one frame can look like emission in the other. $\endgroup$– knzhouCommented May 2, 2020 at 18:21
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$\begingroup$ Good question; this is just to say knzhou is telling you the right answer but it would take time to expound this more fully. $\endgroup$– Andrew SteaneCommented May 2, 2020 at 19:03
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$\begingroup$ Yes, knzhou (and Unruh) have reminded me that particle number is not conserved. But how does it come about, that in a freely falling reference frame, the exchange of gravitons is strictly forbidden? What, in the QFT version of GR, guarantees that? $\endgroup$– Steve StahlerCommented May 3, 2020 at 22:21
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2 Answers
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Gravitational tidal forces do not vanish in a local inertial reference frame. You cannot transform away spacetime curvature. You can make the metric locally flat to first order in the coordinates, but not to higher order. Putting it another way, by choosing suitable coordinates you can make the Christoffel symbols vanish, but not the Riemann curvature tensor.
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$\begingroup$ This is great- now I know the difference between the Christoffel symbols and the Riemann curvature tensor! $\endgroup$ Commented May 1, 2020 at 6:45
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$\begingroup$ Your answer would be perfectly adequate if the OP were talking about Classical (ie. non quantum) gravity. But he is not. He is talking about gravitons as if they were bullets flying around. If you see them in one frame, how is it possible you do not see them in another frame? I think the ideal answer should explain what are "particles" ; that we are talking about "virtual particles" (I think); how these particles transform from one frame to another,ect. Unfortunately I know too little Quantum Field Theory to answer this myself, that's why I am eagerly waithing for a QFT oriented answer. $\endgroup$– magmaCommented May 1, 2020 at 14:54
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I have had several interesting answers, but none that satisfy me. Yes, I am talking about a local inertial frame, so that gravity does not (and generally cannot) vanish globally. As I responded to knzhou, the paradox is deepened if gravitons can impart energy and/or momentum to other particles. Magma's comment suggests they cannot, since they are virtual particles. We both await clarification.
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1$\begingroup$ Where do you get the idea that virtual particles can't impart energy or momentum? That happens in almost every nontrivial interaction; for example, in generic tree-level electromagnetic scattering, a virtual photon is emitted from one charged particle (taking some energy and momentum from that particle) and imparts energy and momentum to another charged particle. $\endgroup$ Commented May 2, 2020 at 18:35
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$\begingroup$ That sounds correct. But I thought the essence of "virtual" is that the particle exists for such a brief time that its true energy is poorly determined. Are gravitons virtual in that sense? $\endgroup$ Commented May 3, 2020 at 22:27