Why are we even wondering?:
The researchers stressed, however, that their experiment only rules out theories that forgo imaginary numbers if the reigning conventions of quantum mechanics are correct. Most scientists are very confident that this is the case, but this is an important caveat nonetheless.
The result suggests that the possible ways we can describe the universe with math are actually much more constrained than we might have thought, Renou said.Ben Turner, “Imaginary numbers could be needed to describe reality, new studies find” at Live Science (December 21, 2021)