Could two particles be released in parallel to test if their quantum probability waves interact, showing whether pilot waves exist?

Question

What if you just release two streams of particles next to each other in parallel? Then you don't even need the double slits. See if their waves interact, and you'll know whether pilot waves are real or not, will you not?

If the Copenhagen interpretation is true, and the waves are just abstract values of probability, then they won't interact, and you'll get two areas where the particles are distributed. Otherwise, if the waves interact due to pilot waves (Bohmian mechanics) being more accurate, then you'll get distribution with combined interference from both waves.

Has this been tested before? If not, could it work, and, if so, did it work? What would the results of this experiment mean, or would they mean anything?

Answer 1

Pilot waves cannot be "tested" as far as we know. They are an interpretation of quantum theory, not quantum theory itself, and they do not change the predictive formalism, which is still the usual wave function together with the Born rule statistics. What they do is provide an explanation for why we see a specific outcome after a quantum measurement, out of all the possible ones that could occur.

More specifically, the pilot wave means that we add to the usual quantum theory an extra "hidden" parameter which is the particle's "true position" $x(t)$, and couple it to the usual wave function with a suitable deterministic guiding equation. We assume that statistically this $x(t)$ is distributed according to the Born rule at the beginning of a quantum experiment, and the guiding equation together with the normal evolution of the wave function $[\psi(t)](x)$ ensures it will retain that distribution exactly and eternally. The value of the hidden parameter is revealed when a quantum measurement is performed. There is no variance in experimental predictions because we did not change the predictive source, only added this additional piece that is completely consistent with it to provide an underlying "mechanism" for why we see what we do.

The only way they could be tested is if there were some way the Universe had to allow us access to that information without the measurement. But this would effectively constitute proving quantum mechanics wrong as a fundamental theory of nature as it means we would be seeing a phenomenon that is at variance with the usual quantum theory. Any theory that allows this is not an interpretation of quantum mechanics, but a different physical theory altogether.