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gjm comments on A Roadmap: How to Survive the End of the Universe - Less Wrong Discussion
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Reversing time doesn't swap attraction and repulsion. (One way of seeing that: attraction/repulsion is a matter of the sign of a second derivative, and d^2/dt^2 f(-t) = (d^2f/dt^2)(-t). No sign change.)
The thing I was saying I couldn't see how to make sense of in the GR picture was having "gravity" and "antigravity" be separate phenomena (which I thought you might be proposing), not "antigravity" as such. I don't think there's any fundamental conflict between GR and having things of negative mass.
Wikipedia on the subject. We don't seem to have experimental evidence one way or the other, and reasons to expect either effect (with the consensus favoring normal attraction). In particular, the section on CPT suggests that CPT suggests that matter and antimatter are attracted to each other.