Hidden Variables Theorems with Fewer Measurements

T. E. Phipps

Bart Jongejan

Einstein, Podolsky and Rosen (EPR) showed that it is possible to predict with certainty the value of a property without disturbing the object in question. In contrast, Quantum Mechanics (QM) holds that if different measurement setups cannot coexist, then predictions about those can neither. Using an EPR-inspired experiment with distantly separated measurements on pairs of entangled spinning particles, Bell proved that no local hidden variable (HV) theory can describe reality in more detail than QM. However, it is possible to conceive a viable HV theory based on the assumption that the perceived structure of spacetime is emergent from a hidden curved spacetime. According to this theory, locality can be maintained for each of the measurements while what is perceived as non-locality can be ascribed to the emergence of spacetime correlations between the instruments of the two parties. The theory predicts correlations that agree with QM, provided that the hidden spacetime has three spatial dimensions. If it had fewer than three dimensions, the CHSH inequality would not be violated and if more, Tsirelson's bound would be violated. According to this HV theory, the laboratory frame of reference is a corollary of correlations of the type that are the subject of Bell's thought experiment.

F.J. Duarte

Andreas R. Blass, Yuri G. Gurevich

Hidden-variable (HV) theories allege that a quantum state describes an ensemble of systems distinguished by the values of hidden variables. No-go theorems assert that HV theories cannot match the predictions of quantum theory. The present work started with repairing flaws in the literature on no-go theorems asserting that HV theories cannot predict the expectation values of measurements. That literature gives one an impression that expectation no-go theorems subsume the time-honored no-go theorems asserting that HV theories cannot predict the possible values of measurements. But the two approaches speak about different kinds of measurement. This hinders comparing them to each other. Only projection measurements are common to both. Here, we sharpen the results of both approaches so that only projection measurements are used. This allows us to clarify the similarities and differences between the two approaches. Neither one dominates the other.

Andreas R. Blass, Yuri G. Gurevich

Hidden-variable (HV) theories allege that a quantum state describes an ensemble of systems distinguished by the values of hidden variables. No-go theorems assert that HV theories cannot match the predictions of quantum theory. The present work started with repairing flaws in the literature on no-go theorems asserting that HV theories cannot predict the expectation values of measurements. That literature gives one an impression that expectation no-go theorems subsume the time-honored no-go theorems asserting that HV theories cannot predict the possible values of measurements. But the two approaches speak about different kinds of measurement. This hinders comparing them to each other. Only projection measurements are common to both. Here, we sharpen the results of both approaches so that only projection measurements are used. This allows us to clarify the similarities and differences between the two approaches. Neither one dominates the other.