Gamma ray photons

Let’s say that a gamma-ray photon has the energy equal to the combined energy-mass of an electron/positron pair. Can such a photon spontaneously tranform into an electron/positron pair in empty space? Or can that only happen if the photon interacts with some other particle?

You need an interaction with some other particle. Think conservation of momentum: There exists some reference frame where your electron-positron pair has zero momentum, but since photons travel at the speed of light, there is not any reference frame where the photon has zero momentum.

Another way to look at it: No matter how high an energy your gamma ray has, in the right reference frame, it’ll have a low energy. In that frame, you would end up seeing a microwave photon, say, split into a couple of particles, which can’t happen.

Toss in another particle, and you’ve got a place to dump the excess momentum, so it all works.