A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II

TLDR

In practice, measurement apparatus disturb the system unpredictably, yielding the uncertainty principle as a practical limitation, though this limitation is not inherent to the interpretation. The paper aims to show how measurement theory can be understood via a hidden‑variable interpretation of quantum mechanics developed in a previous work. The authors propose that by modifying the mathematical formulation of quantum theory at very short distances in ways consistent with the hidden‑variable interpretation, simultaneous position and momentum measurements could achieve unlimited precision. Hidden variables, as defined in this interpretation, determine the exact outcome of each measurement, permit in principle unlimited precision of simultaneous position and momentum measurements through short‑distance modifications of quantum theory, explain EPR correlations, and invalidate von Neumann’s no‑hidden‑variables theorem.

Abstract

In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of "hidden" variables, developed in a previous paper. We find that in principle, these "hidden" variables determine the precise results of each individual measurement process. In practice, however, in measurements that we now know how to carry out, the observing apparatus disturbs the observed system in an unpredictable and uncontrollable way, so that the uncertainty principle is obtained as a practical limitation on the possible precision of measurements. This limitation is not, however, inherent in the conceptual structure of our interpretation. We shall see, for example, that simultaneous measurements of position and momentum having unlimited precision would in principle be possible if, as suggested in the previous paper, the mathematical formulation of the quantum theory needs to be modified at very short distances in certain ways that are consistent with our interpretation but not with the usual interpretation.We give a simple explanation of the origin of quantum-mechanical correlations of distant objects in the hypothetical experiment of Einstein, Podolsky, and Rosen, which was suggested by these authors as a criticism of the usual interpretation.Finally, we show that von Neumann's proof that quantum theory is not consistent with hidden variables does not apply to our interpretation, because the hidden variables contemplated here depend both on the state of the measuring apparatus and the observed system and therefore go beyond certain of von Neumann's assumptions.In two appendixes, we treat the problem of the electromagnetic field in our interpretation and answer certain additional objections which have arisen in the attempt to give a precise description for an individual system at the quantum level.