preprints.org > physical sciences > quantum science and technology > 202105.0097.v1

Working Paper Article Version 1 This version is not peer-reviewed

Version 1 : Received: 4 May 2021 / Approved: 6 May 2021 / Online: 6 May 2021 (15:06:38 CEST)

It is claimed that classical mechanics (CM) in terms of its equivalent Koopman-von Neumann formulation (KvN) is indeed a ’real’ quantum theory since the formalism of quantum mechanics (FQM) does not, nor need it, exclude it as a such. This claim is made manifest by suggesting a common structure of which both KvN and ordinary quantum mechanics (OQM) correspond to unitary representations of, although unitarily inequivalent such. It is shown that OQM is obtained by enforcing the extra physical condition of quantized energy levels, which by itself does not constitute the ’quantum mystery’. It is furthermore shown that KvN in a physically realizable sense contain the hallmark quantum behavior of quantum interference. It is hence concluded that both CM and OQM are subjected to the same foundational issues. As the central part of both KvN and OQM is the introduction of probabilities via FQM it is suggested that the foundational issues regarding FQM are less about FQM itself and more about the concept of probability.

The Koopman-von Neumann formulation of classical mechanics; THe measurement problem; Bell’s theorem; The EPR paradox; Schrödinger’s cat; The double-slit experiment; quantum interference; Probability theory

Physical Sciences, Quantum Science and Technology

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