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I recently asked this question: How close does a particle-antiparticle pair need to be for annihilation to happen?

And that received a good answer. But there was a second part to my question that was not addressed, and so I'm posting it here for more direct attention.

When an annihilation event occurs, how fast does it occur, and can the release of energy somehow be moderated (in a similar manner in which a fission reaction is moderated)? Or is it all or nothing?

With charged pairs I would think the task of moderating the reaction might be difficult since the two particles would be strongly attracted to one another. But then for a neutral particle pair (e.g. neutron and anti-neutron) there might be hope?

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Within current quantum field theory, it does not make sense to ask "how long" a particular process takes to occur. There is a certain probability that a particle and its antiparticle annihilate. But there is no concept of a "process of annihilation".

There's the in-state (particle and anti-particle) and the out-state (products of the annihilation, usually photons), which are assumed to lie in the infinite past and future where no interaction is possible (since there is no notion of "particles" in the interacting case), and there's the probability to get the out-state from the in-state. Quantum field theory offers no description of "how" the in-state is converted into the out-state, except that it's unitary time evolution. You can expand the amplitude in Feynman graphs and think of the individual graphs as possible "processes" producing the out-state, but this is not rigorously meaningful. In particular, you can't tell which one of those processes produced the out-state, so the notion that a specific one of them did is not meaningful.

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  • $\begingroup$ So then is that just a 'missing piece' of QFT? To me, and using an analogy of classical mechanics it's like knowing statics and being oblivious and unable to conceive the existence of dynamics in looking at the world. I've often heard QM is weird, but guess I haven't really grasped how weird just yet! $\endgroup$
    – docscience
    Commented Oct 28, 2015 at 21:24
  • $\begingroup$ @docscience: It's a missing piece in the sense that we can't solve the description of the interaction, not that it isn't there. In principle, QFT has a time evolution operator that you can use to timestep your way through an annihilation process, seeing what intermediate states the in-state goes through to become the out-state. However, since this is in the interacting regime, it's so far technically infeasible to do that, and the states in the interacting theory would not be particles at all, so it would be very unlike what we think of when we think of the "process" turning 'in' into 'out'. $\endgroup$
    – ACuriousMind ♦
    Commented Oct 28, 2015 at 21:30
  • $\begingroup$ This is not that unique to QFT, it also happens in standard quantum mechanics: If you detect a particle at one position and later at another, you might be tempted to ask "which path did it take to get there?", but that's not a sensible question - the intermediate states were not localized at all, they were smeared out and look nothing like a well-defined particle moving from one position to the other. In the same way, you should not expect to find a description of the in-state turning into the out-state in terms of particles. $\endgroup$
    – ACuriousMind ♦
    Commented Oct 28, 2015 at 21:32
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in a similar manner in which a fission reaction is moderated

I think you are confusing ideas here, and it is leading you to ask a somewhat nonsensical question. The individual nuclear fission events don't change at all in a moderated nuclear pile. What does change is

  • the odds of a neutron from one causing another and
  • how long it take for that neutron to find the next target and
  • how much energy that neutron has when it gets there.

That is, you moderate the chain reaction rather than doing anything to fission per se.

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  • $\begingroup$ Thanks - that does make sense. My thinking (and understanding I might be fully wrong) was that by bringing a neutral particle close to its antiparticle - rather than very close proximity - that the energy and particle annihilation might be 'slowed' in some fashion. But I'm beginning to believe now the event is either all or nothing. So if you wanted to design an antiparticle reactor (to harvest energy) you would rather need to design mechanisms that would separately feed normal matter and antimatter together at some reaction location. And the rate at which you feed would be the means of.. $\endgroup$
    – docscience
    Commented Oct 28, 2015 at 21:15
  • $\begingroup$ .. moderation... $\endgroup$
    – docscience
    Commented Oct 28, 2015 at 21:15

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