matter anti-matter annihilation

[Perpetual Student]

As everyone knows, when a particle of matter encounters a particle of ant-matter the result is mutual annihilation. So, why is that? Why can't an electron and a positron cozy up and form a nice mutually revolving pair? What is it about this situation that requires annihilation into photons?

Ancillary question: how close do these two particles have to get to annihilate? Do they have to touch?

[Mr.D]

As everyone knows, when a particle of matter encounters a particle of ant-matter the result is mutual annihilation. So, why is that? Why can't an electron and a positron cozy up and form a nice mutually revolving pair? What is it about this situation that requires annihilation into photons?


Hmmm. Fun!

Try this thought experiment: (Stick to the simplified classical/Bohr model and electrostatics for now) Consider a positron and electron pair rotating about each other - ie. in the same orbit about the center of mass of the system.

a) Sketch it out with vector arrows for the velocity of each particle and the electrostatic forces and gravitational between them.

b) Now answer this: What happens to accelerating charges? What does the answer imply for the stability of this state?

And just for fun: Assume such a pair rotating about each other 1 Angstrom apart (ie atomic scales). How fast do the particles have to be rotating about each other for this system to be "stable"?

[ben m]

As everyone knows, when a particle of matter encounters a particle of ant-matter the result is mutual annihilation. So, why is that? Why can't an electron and a positron cozy up and form a nice mutually revolving pair? What is it about this situation that requires annihilation into photons?

They do form a pair; it's called "positronium" and it has all of the properties of an atom---orbitals, excitations, etc.---until it annihilates.

Why does it annihilate? Because there's nothing stopping it, in some sense. More technically: in quantum field theory, there's an electron-photon coupling constant which is not zero. This constant means that electrons can scatter photons, positrons can scatter photons, two photons can collide and make e+ e-, and e+ e- can collide and make two photons. These are all just four sides of the same coin.

Another way to spin your question: why doesn't a hydrogen atom annihilate the same way? They might---it might just take so long that no one, not even the dedicated multi-year search for such things in thousands of tonnes of matter. The stability of ordinary electron+proton atoms tells us that, if there's an annihilation coupling constant at all, it must be very, very, very small.

[Dilb]

b) Now answer this: What happens to accelerating charges? What does the answer imply for the stability of this state?

Acceleration has nothing to do with it. An electron and a positron can, and will, pair up to form a hydrogen-like atom. A reduced-mass treatment of the Bohr atom predicts the approximate energy levels, which are around half the energy levels of the hydrogen atom.

A similar situation happens with electrons and holes in semiconductors. The positive hole and negative electron will form an exciton, which like the electron-positron pair, will be atom-like for a short time, and then decay into photons. Of course, in a crystal other things like phonons can also be created.

In this sort of picture, a positron is like a 'perfect' hole in the electron field, so positron-electron annihilation is like the electron dropping into the hole, where it stops being observable. This implies there are an infinite number of electrons already filling up these holes, which is why we can't feel any electric field from them, which is a bit of a problem. Even so, Dirac used this sort of thinking to predict negatively charged electron-like particles should exist. After figuring out that it wouldn't be the proton, it was found to predict the positron.

Basically, it happens because it can happen: if a reaction is not forbidden for violating energy conservation, momentum conservation, charge conservation, etc., it occurs. After the photons have been produced, they move apart, and you no longer have the energy. If the photons were trapped in a cavity of some sort, you'd wind up with the electron-positron decaying into photons, and the photons recombining into an electron-positron pair. Since the photons would have an energy of 511 keV, the cavity would need to be about 2.4 picometres wide. As this is much smaller than atoms, there's no way to make a cavity like that, so the process is irreversible for practical purposes.

Naturally, if you go back to the electron-hole pair, you can use a cavity around 1 micrometre to trap the emitted photons, so it's fairly simple to observe the electron-hole pair being destroyed and created again.

I don't think there's any absolute requirement for the electron and positron to have overlapping wavefunctions, but being as close to each other as possible will make the reaction go faster.

[Singularitarian]

Good old Hardy's paradox. It is possible to have a particle and its antipartner to even come in contact but not annihilate. As what has been mentioned, the positronium is a special case where two entangled particles do not annihilate until they are changed in some way.

But why do they annihilate? Quite simple really. It's actually a type of decay process which is also itself a conservation of energies. They annihilate because they contain information which either cancels their current independant structures, or you can say their contact and annililation is preserving the energy required to make them. It's all conservation.