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An electron and a positron annihilate in pure energy.

What is the mechanism by which an electron and a positron annihilate each other, losing their mass and their electric and magnetic field? Especially, does the charge and by this the fields vanish instantaneous or during some time period? The same for the mass.

Qmechanic
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HolgerFiedler
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  • Well, the net charge of the system remains constant since the positron has the exact opposite of the electron and the resulting particle, a photon, has no charge. The net mass is certainly lost but in our current understanding of physics is the mass-energy that has to be constant and here, this variable is preserved. For the magnetic field I would say that this is only a property of electric charges in motion and it can all be eliminated by having a frame of reference that moves with the charges, I don't see why it should be conserved if you can change the values even by changing perspective. – Swike Jun 26 '20 at 11:20
  • @Swike Well, not the main point. Anyway, to think about the magnetic field at equal rights with the electric is poor established, partially due to the time of discovery and partially due to the teaching. On the other hand, after annihilation, which fields the EM radiation carries? How permanent magnet is what it is? The imagination about revolving and rotating charges is over or not? About the main question, I gave a comment here https://physics.stackexchange.com/questions/561969/what-makes-an-electron-proton-barrier?rq=1 – HolgerFiedler Jun 26 '20 at 11:37
  • What level do you want this answered at? Would a heavily mathematical answer in terms if Quantum Field Theory be useful for you? BTW, you may find this of interest: https://en.wikipedia.org/wiki/Positronium – PM 2Ring Jun 26 '20 at 11:39
  • @PM2Ring Im not enough educated for QFT. An explanation of how and why QFT do something is the right answer. BTW, reading again and again brings always new facets. About Pisitronium:“ the two particles annihilate each other to predominantly produce two or three gamma-rays, depending on the relative spin states. ” Why? But this is another question :-) – HolgerFiedler Jun 26 '20 at 12:00
  • Ok, you need to add that info about QFT to your question so people know how to answer it, and to prevent the question being closed as a duplicate of questions that focus on the maths without giving the physical motivation for the maths. – PM 2Ring Jun 26 '20 at 12:08
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    Isolated ortho-positronium has to decay to an odd number of photons to preserve angular momentum, aka spin. It can't decay to 1 photon because that doesn't preserve linear momentum. – PM 2Ring Jun 26 '20 at 12:10
  • @PM2Ring Of course two but sometimes three photons. Interesting. – HolgerFiedler Jun 26 '20 at 12:37

2 Answers2

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The main mechanism is the scattering process $e^-+e^+\to 2\gamma$ admitted by quantum electrodynamics (QED).. Higher order process also contribute but much less. The process is not instantaneous. Since it is calculated as a scattering process, it is defined strictly speaking between times $-\infty$ and $+\infty$, but for practical purposes - like in any scattering calculation - any mesoscopic time scale suffices.

Arnold Neumaier
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You say in a comment

Im not enough educated for QFT.

but you ask

An electron and a positron annihilate in pure energy.

An electron and a positron are quantum mechanical entities, and their behavior can only be described using quantum mechanics, and special relativity, in addition to momentum energy and angular momentum absolute conservation laws.

What is the mechanism by which an electron and a positron annihilate each other,

When a particle (electron in this case) and its antiparticle(positron) trajectories meet in space time, by definition all the quantum numbers may add up to zero within a volume in phase space where there is a quantum mechanical probability for the pure energy of the two particles to manifest in possible new particles that also add up to zero quantum numbers. This probability can be calculated using Quantum Electrodynamics, QED,

losing their mass and their electric and magnetic field?

The probability can be calculated using QED, yes , the charges and magnetic moments also have to add up to zero for the probability of the annihilation to be measurable in a phase space volume.

Especially, does the charge and by this the fields vanish instantaneous or during some time period? The same for the mass.

Again this is a quantum mechanical interaction controlled by quantum mechanical probabilities that can be calculated using QED. There will be an interval of time delta(t) where the probability of annihilation is measurable, depending on the experimental accuracies.

anna v
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