system
Given the following post, respond as if you're commenting on Reddit:
human
How do virtual photons have a real influence?

My question is, if virtual photons are a mathematical book keeping tool, how do they play a real role in terms of Hawking radiation and vacuum energy?

Thanks!
gpt
They don't. Anything you can describe in terms of virtual particles can be equivalently described without referencing virtual particles.

Anytime you see an explanation involving "virtual particles", you can replace them with "higher-order effects of QFT" (except tree-level diagrams, which aren't really "higher-order", but anyway you don't have to take virtual particles literally at tree level either).