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It is commonly said that one can view anti-matter as 'matter going back in time'. I'm trying to figure out how far this analogy goes.

For an atom, it is well-known how that atom excites absorbing a photon, then emits a photon again.

Now assuming an anti-atom goes back in time, we would have an anti-atom, suddenly emitting a photon to become excited, then returning to normal when the photon arrives. This means the anti-atom reacts to the photon before it arrives, breaking causality.

Therefore my question is: if one where to make an anti-atom and excite it in a controlled way, would they find that the anti-atom emits before absorbing or after?

Also, if the anti-aton emits before, does that imply that the anti-atom truly has negative energy as the emitted photon contains energy and the excited state of a atom contains 'more energy of the same kind'?

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The statement that antimatter is "matter going back in time" is true in some sense and can be heuretically useful in writing Feynman diagrams, but one should not take this too far. Basically, the answer to your (first) question is no. Anti-particles behave just like regular particles: in Feynman diagrams, they look like "normal" particles running backwards in time, but there are several physical laws that prevent them from doing weird things, like energy conservation and the second law of thermodynamics.

You suggested the process of an anti-atom emitting a photon to reabsorb one some time later. This is only consistent with energy conservation if one assumes the antimatter to have negative energy, which can be even lowered by emitting photons. However, as can be shown within QFT, antimatter has positive energy just like "normal" matter, so such a process does not happen. Otherwise, the anti-atom would tend to minimalize its energy by emitting many photons, causing the positron within the anti-atom to be excited to ever higher orbitals before flying off into free space.

The proper microscopic time-reverse of exciting an atom and having it relax into its ground state again would be as follows. First, the anti-atom would absorb a photon arbitrarily flying around that happens to have the right energy to excite it; then, that photon would be pumped out of the anti-atom by the brave experimenter. Such a strange process is possible, but rather unlikely for entropic reasons. Furthermore, there is nothing that limits this process to antimatter: regular atoms would do just fine.

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  • $\begingroup$ I was afraid of a similar answer, if I understand correctly the answer is 'QFT says no'. In that case, are there any assumptions in QFT which, when the other assumptions are dropped, are consistent with true time-reversal, and would the implied model have interesting consequences? Or has this already been studied, with the implied model having clear contradictions with experiments? $\endgroup$ – Pepijn de Maat Sep 6 '18 at 12:45

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