John von Neumann published a proof that no hidden variable theory could be made consistent with the prediction of quantum mechanics. This proof was accepted for some time, but was eventually found to be in error. The current status of hidden variable theories is framed by an influential paper by John Bell, which acknowledges that hidden variable theories are possible, but only if the theories are nonlocal, meaning that changes in the quantum system are conveyed from place to place faster than the speed of light, in violation of Einstein's special relativity theory. Coupled Particles Bell's work addressed the case of coupled particles, first used by Einstein, Podolsky, and Rosen to argue that quantum mechanics must be an incomplete theory. Consider an atomic process that produces two photons of light, emitted in opposite directions, but with the same polarization.
Polarization is measured by passing the photon through a polarizer.
If the polarizer is oriented parallel to the polarization of the photon, the photon passes through unimpeded. If it is oriented perpendicular to the polarization of the photon, the photon is absorbed. At an intermediate angle, the photon will have a certain probability of being transmitted. The interesting thing is that there are two photons with the same polarization, moving apart from one another at the speed of light. If the coherence of the system can be maintained, a measurement made at one location will assign a single definite state to the system, which should be verified by any subsequent measurements, no matter where they occur.