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Consider that a low energy electron and positron annihilate creating two 511keV photons with no other particles around. To time reverse this process, we send two 511eV photons to collide hoping that they would produce an electron/positron pair.

However photons don’t interact with each other, at least not at such low energies. Instead of colliding, they just ignore each other and move on.

The picture changes when other particles are involved, but then it would not be the exact time reversal of the annihilation described above, but a time reversal of a different process involving other particles.

If I cross electron and positron beams, I’d have fireworks with likely most particles annihilating to gamma rays. Yet if I cross two beams of 511keV gamma rays in vacuum, nothing happens. They just pass through each other with no interaction whatsoever. Not a single electron/positron pair would be created to detect.

So is annihilation time reversible? If yes, then how? If no, then would it not violate some fundamental symmetry of nature?

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@anna 's answer is spot on: in a level playing field, we'd expect a complete and unequivocal time reversal.

I cannot explain adequately why "direct production is hard", as invited, because it is really an experimental question, not an issue of principle: it is extremely hard to produce 0.51 MeV photon beams, but I don't have a global grasp of the beam physics issues.

On the theory side, it is normally assumed that QED, which is T invariant, holds, and there has been nothing for over 70 years now to suggest otherwise; and not for people not trying hard enough! As noted, all indirect experiments to determine the $\sigma_{γγ\to e^+e^-}$ cross section agree as expected with the theoretical QED predictions at high energy. The colliding protons do not really mar the vacuum, they are just distant sinks of momentum needed in the production of single photons, so expediters in the production of the colliding γs.

Quasi-real photons can also be emitted by both protons, with a variety of final states produced. In these processes the pp collision can be then considered as a photon–photon (γγ) collision.

At those high energies (s) where the electron mass does not much matter, this cross section is close to the time reversed one, eqn (48.8) of the PDG, $$ \frac{d\sigma_{e^+e^-\to γγ }}{d\Omega}= \frac{\alpha^2 (u^2+t^2)}{2stu}. $$ But these are High energies, effectively hundreds of thousand times higher than the threshold reaction you are visualizing; and, predictably, much rarer by about the square of that, since the cross section is inversely proportional to s. The astro paper anna cites, eqns (5,6), appears to roughly comport with this, although I haven't checked every minute conversion to the PDG conventions, and cross section phase-space normalizations. (The phase space factors ensure you are slamming as many e+e- pairs together as γγ s, otherwise you'd have a T-asymmetric statistics issue, call it entropy if you wish, and hence not a level playing field. The crucial point is that the microscopic QED amplitudes are completely, unequivocally, unquestionably T-symmetric.)

So, to sum up, you'd expect equal numbers of such reactions, if only you could produce clean comparable photon density beams colliding against each other. Producing controlled high energy pure photon beams is extremely hard, but I understand they are getting there; anna's photon collider reference suggests $E_γ$ peak anticipated at 200 GeV. It is only a matter of time and funding. However, as apologized for, I am the wrong person to ask about these practical issues...

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    $\begingroup$ Thanks for your insight! +1 $\endgroup$
    – safesphere
    Aug 9, 2021 at 19:37
  • $\begingroup$ Aside from purely practical reasons, isn’t there a theoretical justification for why gamma colliders are so enormously harder to make that no production has been ever observed? Earlier you mentioned the phase space. Others did too. If it is the reason, then why is it so different upon time reversal? $\endgroup$
    – safesphere
    Aug 9, 2021 at 20:01
  • $\begingroup$ No theoretical reason I can think of, except that photons are hard to accelerate--you may accelerate the charged articles that produce them. By phase space, I meant the density of energetic photons available to collide... perhaps I should have said luminosity of the beams or effective beams, instead. $\endgroup$ Aug 9, 2021 at 20:15
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    $\begingroup$ While this answer may not resolve all concerns, it is helpful, so I am accepting it. Thanks again! :) $\endgroup$
    – safesphere
    Jul 5, 2022 at 4:12
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However photons don’t interact with each other, at least not at such low energies.

Half an Mev photon is a gamma ray, and you are asking about the crossection of gamma gamma scattering.

In this paper the reverse reaction is considered to use in astrophysics obsvervations.

Instead of colliding, they just ignore each other and move on.

This is true for low energy photons. It has to do with coupling constants and quantum number conservation but the time reversed diagrams mathematicaly work .

They are considering gamma gamma colliders.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – ACuriousMind
    Aug 9, 2021 at 15:30

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