- #26

Avodyne

Science Advisor

- 1,396

- 88

Suppose a particle goes from point x1 at time t1 to point x2 at time t2. If the points have a "timelike separation", (x2-x1)^2 < c^2 (t2-t1)^2, this is classically allowed; if the points have a "spacelike separation", (x2-x1)^2 > c^2 (t2-t1)^2, it is classically disallowed; the particle would have to move faster than light.

But in quantum mechanics, all paths make a contribution to the probability amplitude, and so these paths contribute.

For points that are spacelike separated, their temporal order (that is, whether t1 > t2 or t2 > t1) is frame dependent, and can be different for different inertial observers. So, a process that looks to one observer like a particle going from x1 to x2, looks to another like a particle going from x2 to x1. (Again, this only happens for non-classical, faster-than-light paths). But, if the particle carries a charge (say +1), then to the first observer, the charge decreases at x1 when the particle leaves, but to the second observer, it looks like the charge increases at x1 when the particle

*arrives*. This is inconsistent, so it must be that the second observer sees a particle arriving with charge -1. Obviously this can only happen if such a particle exists, and so there must be antiparticles.