Complex numbers have a real component, say 6, and an imaginary component, say √-1. So it is 6+√-1. In a recent math flap, someone claimed that complex numbers don’t really exist and others claim, yes, they do.

Sabine Hossenfelder thinks they do exist, at least for quantum physics. Discussing the “yes, they do” camp, she explains:

The question which they look at in the new paper is then whether there are ways to entangle particles in the normal, complex quantum mechanics that you cannot build up from particles that are described entirely by real valued functions. Previous calculation showed that this could always be done if the particles came from a single source. But in the new paper they look at particles from two independent sources, and claim that there are cases which you cannot reproduce with real numbers only. They also propose a way to experimentally measure this specific entanglement.

I have to warn you that this paper has not yet been peer reviewed, so maybe someone finds a flaw in their proof. But assuming their result holds up, this means if the experiment which they propose finds the specific entanglement predicted by complex quantum mechanics, then you know you can’t describe observations with real numbers. It would then be fair to say that complex numbers exist. So, this is why it’s cool. They’ve figured out a way to experimentally test if complex numbers exist!

Sabine Hossenfelder, “Do Complex Numbers Exist?” atBackRe(Action)

But, she warns, if they are right,

This conclusion only applies if you want the purely real-valued theory to work the same way as normal quantum mechanics. If you are willing to alter quantum mechanics, so that it becomes even more non-local than it already is, then you can still create the necessary entanglement with real valued numbers.

Sabine Hossenfelder, “Do Complex Numbers Exist?” atBackRe(Action)

The people who don’t think complex numbers really exist would probably not be happy with quantum mechanics being even more non-local without them. But of course, if complex numbers really do exist, then immaterial things really exist. Not a good time to be a hard core materialist.