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Say we have an atom on which we shoot a photon. Is the process of absorption the time reversed process of emission? I can't imagine the two processes being the same, although in both cases the photon has the same mean energy. Can we tell, if we "see" a photon coming out of an atom, if time is going forwards, or if it's the time-reversed image of absorption?

In Compton scattering, the two real photons, before and after scattering, have different energies, but still, the process could go as well forward as backwards in time.

On the other hand (say in a hydrogen atom), if we consider the absorbed and emitted photon, they have the same energy (momentum) but I don't think both time directions are the same, like in Compton scattering. So, contrary to Compton scattering, we should be able to see the difference between:

-a photon being absorbed and subsequently emmited spontaneously

and the time-inversed proces:

-the emitted photon becoming the one absorbed, and the absorbed photon the emitted.

Of course, absorption is a reversible process, like opening or shutting a door (you can see a difference though if we "play the film in reverse", so you can tell if time goes forward or backwards. Can we say in which direction the clock ticks if we "look" at an absorption-emission process (unlike the scattering of a photon with an electron)?

MatterGauge
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    I'm off my turf here but I think the only circumstances in which you can "tell" which way time is flowing may be when entropy increases. In any case, we are all on dodgy ground talking about what is going on when we get to photon absorbtion... is it a particle or a wave? – Martin CR Jan 10 '22 at 11:02

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Absorption is a word used somewhat ambiguously. In the case of Compton scattering we are talking about an elementary process, governed by a certain Hamiltonian and reversible equations of motion. So this process is reversible. On the other hand, in case of an emission/absorption by an atom we usually mean it changing irreversibly from one state to another. If we were to treat emission by an atom by exactly solving the Schrödinger equation for an atom coupled to electromagnetic field, the atom would continuously reabsorb and reemit the photon into different modes of the field. In practice this does not happen for the reasons that are usually not discussed in simple treatments of emission and absorption, but do introduce irreversibility: infinite number of the radiation modes, coupling to the environment, finite experiment duration, etc. See, e.g., my posts about what is hidden in Fermi Golden rule (this answer and the answers linked in it).

Remark: Janes-Cummings model is an extreme example where the atom is coupled to only one light mode, and the reversibility (in the form of Rabi oscillations) is manifest.

Book recommendations:

Roger V.
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  • Thanks for your enlightening answer! – MatterGauge Jan 10 '22 at 17:26
  • Maybe a totally different question, but still. Why can't we describe an emission/absorption by QFT? Because the electron is not free? We have a real electron (though coupled to the proton, in hydrogen), and real photon initially (like in Compton scattering. And finally there are (after emission) again an electron and a photon. The both are not the same, but how? Is there no electron in a virtual intermediary state (like in CS)? – MatterGauge Jan 10 '22 at 17:40
  • One can use qft... But for this one has to know the qft. And in many cases the processes are rather simple, so qft doesn't add much. – Roger V. Jan 10 '22 at 19:40
  • I could recommend the books by Loudon and by Cohen-Tannouji on atomic physics. – Roger V. Jan 10 '22 at 19:42
  • Really nice answer. – Árpád Szendrei Jan 18 '22 at 16:28