Q:

What are the problems in trying to interpret the Klein-Gordon equation as a single particle equation?

What is the problem if we try to interpret KG equation as a single-particle equation? Also, I wish to know whether the born interpretation of wavefunction is applicable in relativistic quantum mechanics.

A:

There is no part of the physics involved that requires particle number to be conserved. Combine this with $E=mc^2$, which allows for energy to be converted into particle-antiparticle pairs, even when there is not enough energy to create such a pair, virtual particles allow for the temporary appearance of particles in a system that doesn't have sufficient energy for them. As such we cannot treat relativistic quantum equations as being based on particles, instead we treat them as fields with a certain energy, and assume the particle number of this field to not be constant.

