I feel like this question is probably wrong for MO, (too low level, perhaps unclear) but my curiosity has got the better of me:

I hear that the Riemann Zeta Function and its zeros have applications to quantum mechanics, as well as other fields. I do not understand these connections, and because of this the following question came up:

In theory, is it possible through physical experiments (particle experiments) to approximately calculate the first few zeros of the Riemann zeta function?

In other words, (using the explicit formula) could we write down the $n^{th}$ prime number (up to a given margin of error/probability of correctness) only from doing quantum mechanical experiments?

(If there are conjectures/facts that we cannot prove, but would answer the question, I would be happy to hear those too)

Thanks!