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On the falsification of the pilot-wave interpretation of quantum mechanics

Jakub M. Ratajczak

Published Aug 26, 2020• 0 citations
OpenAlex

Abstract

Quantum mechanics has lacked a widely recognized interpretation since its birth. Many interpretations are under consideration because they are difficult to disprove experimentally. In this paper, we show that the results of a recent experiment go against one of them: the pilot-wave interpretation. This is because the key assumption of this interpretation, particle locality, contradicts the assumption of wave function nonlocality on which the experiment is founded. This is a rare example of a quantum model and an experiment not indifferent to the interpretation of quantum mechanics.

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Quantum mechanics has lacked a widely recognized interpretation since its birth. Many interpretations are under consideration because they are difficult to disprove experimentally. In this paper, we show that the results of a recent experiment go against one of them: the pilot-wave interpretation. This is because the key assumption of this interpretation, particle locality, contradicts the assumption of wave function nonlocality on which the experiment is founded. This is a rare example of a quantum model and an experiment not indifferent to the interpretation of quantum mechanics.
Abstract We consider the interpretation of quantum mechanics on the basis of the so-called ‘pilot-wave’ concept from the point of view of its adequacy in the light of both already-realized and possible and gedanken experiments, including those that involve photons. It is shown that this concept, despite undoubtedly being useful, can hardly ensure compliance of quantum-theory predictions with the postulate that particle coordinates and velocities objectively exist, while splitting the wave function into empty and nonempty wave packets seems to contradict to the results of feasible experiments and their interpretations.
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical dependence, however it necessitates the existence of "ghost waves". This manuscript develops a deterministic dynamical system with local interactions. The aggregate behavior of the trajectories are reminiscent of a quantum particle evolving under the Schrödinger equation and reminiscent of Feynman's path integral interpretation in three canonical examples: motion in free space, double slit diffraction, and superluminal barrier traversal. Moreover, the system bifurcates into various dynamical regimes including a classical limit. These results illustrate a deterministic alternative to probabilistic interpretations and aims to shed light on the transition from quantum to classical mechanics.