Local hidden variables are ruled out by experiment (Bell). Non-local ones are not excluded though.
Are there experiments thinkable to discern if they really exist or if reality is intrinsically indeterministic, i.e, irreducibly stochastic? For example, the measurement of the electric field around a hydrogen atom? If the wavefunction corresponds to a real structure surrounding the electron in the atom, there would exist a rapidly fluctuating dipole moment around it.
