Incompleteness of the Copenhagen Interpretation

Summary

Two distinct measurement problems arose historically [1].  The first to arise in 1926 was due to dual methods of quantum state evolution proposed by Schrödinger and Born. These dual methods were proposed by Bohr to be complementary and both methods proposed to be necessary for a complete description of Nature.  The second measurement problem was found in 1935 by Schrödinger [2]. Schrödinger showed that applying his equation to the interaction of a quantum system and a measurement device results in the prediction of entanglement between system and device.  This second problem is much more serious than the first problem.  Firstly, it appears to imply that Schrödinger’s equation does not suffice to provide the information needed to predict a particular outcome of a measurement.  Secondly, it was shown explicitly in [3, Ch. 3] that assuming two separated detectors and for which the latency of the detectors is assumed to be independent of the separation between the two detectors, that the contradiction continues undiminished or independently of the number of particles in the detector. Schrödinger’s equation predicts the state evolution is not only different from the product state that is expected by the measurement postulate between system and device, but impossible to reconcile without further investigation. Requirements to resolve the second measurement problem have been recently put forward [4]. In this paper, we examine the implications on the Copenhagen interpretation of the necessity for further investigation to meet the requirements set forth in [4] . We also examine whether or not Bohr expected that one could ultimately develop quantum theory further, or whether no theory can be developed with more predictive power than the two von Neumann postulates of quantum mechanics.

[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.
[4] M. Steiner and R. Rendell, “Logical Requirements for the Resolution of the Quantum Measurement Problem.” Work in Progress, 2022.