## Why Does E=mc^2 Imply Creation of Particles?

Many references of quantum field theory begin with an explanation of the necessity of a field theory as opposed to a single particle theory. Sometimes they use the argument that E=mc^2 implies particle creation.
For example, in Peskin "the Einstein relation E=mc^2 allows for the creation of particle-antiparticle pairs" (page 13).

How does Einstein's relation imply the possibility of creation of particles? Seems to me that you might as well say that the kinetic energy formula Ek=(1/2)mv^2 implies creation of particles.

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 Mentor E=mc^2 (or, better, ##E^2=(mc^2)^2 + (pc)^2##) alone does not show that particle creation is possible. It just shows that mass has a corresponding energy, and indicates that it might be possible to get particles if you have that energy available.
 I don't think that at first that was considered. Attention focussed on the possibility of obtaining energy from mass. (Energy from KE is a no-brainer) Of course, experiments rapidly threw up the fact of matter/energy conversion both ways. Then it becomes somewhat obvious with hindsight that E= etc. implies creation.

Recognitions:

## Why Does E=mc^2 Imply Creation of Particles?

It's a really sloppy statement. E²=p²c²+(mc²)² is where you get Dirac equation from, but even that merely predicts existence of anti-particles. Not of creation/annihilation process. You can only get pair creation/annihilation once you consider field theory. The motivation for that has to come from experiment.

I'm not really sure why Peskin and Shroeder put it that way. I thought there might be some context loss, but no, that's all they say on the matter.

 Tags einstein's formula, particles, qft