symmetry - When is it useful to distinguish between vectors and pseudovectors in experimental & theoretical physics?

My understanding of pseudovectors vs vectors is pretty basic. Both transform in the same way under a rotation, but differently upon reflection. I might even be able to summarize that using an equation, but that's about it.

Similarly, I can follow arguments that pseudovectors behave differently in "mirrors" than vectors. But my response to this is always: Okay, so what? When would I ever "do physics" in a mirror?

The usefulness eludes me. I'd like to gain a better understanding of the importance of this difference.

• When is it useful for an experimental physicist to distinguish between the two?


• When is it useful for a theoretical physicist to distinguish between the two?

I believe symmetry is important to at least one of these, but would appreciate a practical rather than abstract argument of when one has to be careful about the distinction.

Answer

Not only can you do physics "in a mirror", but I've been part of an experiment involving exactly that.

The weak interaction is, well, weak. And that makes it very hard to get access to in any physical process which can also proceed through other interactions. So, you can see the weak interaction at work in beta decay, but to leading order you can't see it at work when a electron scatters off of a proton (because the signal from the electromagnetic interaction is about $10^5$ larger).

But there is a caveat.

You see the electromagnetic interaction respects parity at a conserved quantity, and the weak interaction does not. This is equivalent to saying that the electromenetic interaction is represented by a vector and the weak interaction by the sum of a vector and a pseudo vector (though for historical reasons we call it an "axial vector" which is a synonym). All of this means that if you set up a scattering interaction in which the outcome is different when parity is respected and when it is violated then all of the parity violation that you observe can be attributed to the weak interaction.

Enter $G^0$ which measured the form-factors of the proton as seen by the weak interaction (and which I was a part of) and Q-weak which is a fundamental test of the weak interaction.