I asked a question here about path integrals and QFT. I just want to confirm something. Is the path integral in quantum field theory a mathematical tool only? I thought the path integral meant that particles literally do take all paths as stated by Victor Stenger and Stephen Hawking in their interpretation of what happens in reality? If particles are field excitations, as QFT says, does that mean Stenger and Hawking's interpretation is right and in reality particles do take all paths (sum over histories)?
[Physics] the path integral exactly
path-integralquantum mechanicsquantum-field-theory
Best Answer
I would say that it's only a poetic description of a mathematical device, not a literal description of physical reality. We don't actually get to observe what the particle is doing when we aren't looking at it, so it's not really meaningful to say that it's doing this or that.
If you're reading about path integrals at the popular science level, you should strongly consider reading Feynman's little book QED: The Strange Theory of Light & Matter. It contains a remarkably accurate and BS free popular explanation of how path integrals work. (A small caveat: Feynman's description of renormalization in the last chapter is a bit antiquated. Unfortunately, as far as I know there's not any good explanations of renormalization in the popular science literature. The best thing I can recommend is Wilson's Nobel lecture.)