Logical Requirements for Resolution of the Quantum Measurement Problem

Summary

There are two quantum measurement problems that arose historically [1]. The first measurement problem can be resolved via an a posteriori interpretation, which assumes that a measurement has already occurred. In this case, the problem can be solved by providing an explanation or interpretation of how the result of the measurement came about, but with knowledge that a measurement has already occurred.  One does not need to provide an explanation of why the measurement occurred or the conditions for which measurement occurs. The second problem found by Schrödinger in 1935 [2] is that entanglement is predicted during the interaction between measuring device and system by Schrödinger’s equation.  The entangled state that is predicted appears to be in contradiction to the state that results under measurement. In this paper, the logical requirements for resolution of these two historical measurement problems is examined. If one believes that one can go no further than these two postulates to provide the maximum predictive power that a theory can provide, than this first measurement problem can largely be resolved by providing an interpretation given the knowledge that a measurement has already occurred a posteriori. However, from a scientific standpoint the second problem cannot be resolved by providing an interpretation with a posteriori knowledge that a measurement has occurred. In this latter problem, the predictions of the quantum state evolution are different and contradictory, where the amount of the contradiction is independent of the number of particles that compose the device [3, Ch. 3].  In the second problem, one cannot presuppose knowledge that a measurement has or has not occurred, if the theory is to be considered complete.  We show in this paper that logically, the theory can only be concluded to be incomplete and more investigation is required that explains in more detail the circumstances for which measurement occurs. Specific scientific requirements are proposed for the resolution of the second quantum measurement problem. 

[1] M. Steiner and R. Rendell, “Two Historical Problems in Quantum Measurement,” 2022.
[2] E. Schrödinger, “The present situation in quantum mechanics,” Naturwissenshaften (English translation in Proceedings of the American Philosophical Society vol 124), vol. 23, pp. 802–812, 1935.
[3] M. Steiner and R. Rendell, The Quantum Measurement Problem. Inspire Institute, 2018.