# Particle annihilation in quantum vacuum

1. May 3, 2014

### pabloxd43

Well this is a doubt that comes from some time ago and I haven't found the answer on the net. Quantum fluctuations in quantum vacuum create particle-antiparticle pairs for very short periods of time satisfying ΔEΔt≥$\frac{\hslash}{2}$ It is very well known that when a pair particle-antiparticle come together annihilate and emite two photons. What happens exactly in quantum foam, why does't this happen. Do they disappear too fast for even annihilating?

By the way sorry for my english I'm from Spain :D

2. May 4, 2014

### abitslow

ΔEΔt ≥ ½ℏ is not correct, although is often stated as fact. Given two observables A and E, where E is the system's energy and A,E are non-commuting. The "spread" of the observable can be characterized by its standard deviation σ. Hence σe * σa/|(d<A>/dt)| ≥ ½ℏ for non-relativistic Quantum Mechanics. The equivalent expression which you have learned as Δxᵢ* Δpᵢ ≥ ½ℏ is actually σxᵢ * σpᵢ ≥ ½ℏ, so as long as you accept the idea that 'uncertainty' equals the standard deviation, the position (x) momentum (p) uncertainty principle holds. It is not equivalent with time, however.
"It is very well known that when a pair particle-antiparticle come together annihilate and emit two photons."
This is one of many possibilities, any pair of particle+antiparticle can be emitted iff the annihilation contains enough energy to make the rest mass of the pair. This means that while massless particles (such as the photon) are 'easiest' to make, as the annihilating pair get more massive (or more energetic), it becomes possible to create neutrino-antineutrino pairs, electron-positron pairs, and even proton-antiproton pairs (etc.).
Quantum foam is much much smaller than collision cross-sections, what leads you to believe it doesn't happen at that scale? see http://en.wikipedia.org/wiki/Quantum_foam where annihilation is discussed in the foam.

3. May 4, 2014

### pabloxd43

Thanks a lot for answering. I'm still introducing myself into physics, I'm only 15 years old, so I didn't catch most of the things you said so I will reread it again ;)

I wrote it a little bit fast last night and I'm new to this blog so I'm not very used to formalism. Could you recommend me a good book which explains all this?