For example, it would suffice to prove some form of the GUE hypothesis. Recall that GUE stands for Gaussian Unitary Ensemble, just as in Random Matrix theory. Yes folks, that's the same random matrix theory of the matrix models that kneemo was discussing with us a while back. The idea is that the zeroes of the zeta function (rescaled) are distributed like the eigenvalues of large ($N \rightarrow \infty$) random matrices in the ensemble.
In fact, many attempts to prove the Riemann Hypothesis involve matching the zeroes to a physical eigenvalue problem. Now what physical system could possibly have something to say about such a number theoretic problem? One can't help but wonder.