I've just recently heard of Positronium, an "element" with interesting properties formed by an electron and positron, and I was shocked to hear that physicists were actually working with this element, even if for a very short lifetime. I was always under the impression that matter and antimatter annihilated when they came even remotely close to each other, which is apparently not the case.
How do these two particles combine to form an element if they're oppositely charged and roughly the same mass? What kind of interactions could possibly take place before they're pulled together and annihilated?
Answer
As you've noticed, it's not automatically true that a particle and its antiparticle will annihilate each other when they get close to each other. In fact, no interaction between particles is really certain to happen. Quantum mechanics (and at a higher level, quantum field theory) tells you that all these interactions happen with certain probabilities. So for instance, when a particle and its antiparticle come into close proximity, there is only a chance that they will interact within any given amount of time.
However, the longer the particles remain together, the greater the probability that they will interact and annihilate each other. This is responsible for the 142 ns lifetime of positronium as reported in the Wikipedia article: the probability of annihilation increases with time in such a way that the average lifetime of an "atom" of positronium is 142 ns.
As Cedric said, as long as the positron and electron don't annihilate each other (and remember, there is only a limited chance of that happening in any given time), they can interact in much the same way as any other charged particles, such as the proton and electron. Being bound together by the electromagnetic interaction, as in a hydrogen atom or a positronium "atom," is just one example.
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