# Experimental Comparison of Bohm-like Theories with Different Primary Ontologies

Arthur O. T. Pang1, Hugo Ferretti1, Noah Lupu-Gladstein1, Weng-Kian Tham1, Aharon Brodutch1, Kent Bonsma-Fisher1,2, J. E. Sipe1, and Aephraim M. Steinberg1,3

1Department of Physics and Centre for Quantum Information Quantum Control, University of Toronto, 60 St George St, Toronto, Ontario, M5S 1A7, Canada
2National Research Council of Canada, 100 Sussex Dr, Ottawa, Ontario, K1A 0R6, Canada
3Canadian Institute for Advanced Research, Toronto, Ontario, M5G 1M1, Canada

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### Abstract

The de Broglie-Bohm theory is a hidden-variable interpretation of quantum mechanics which involves particles moving through space along deterministic trajectories. This theory singles out position as the primary ontological variable. Mathematically, it is possible to construct a similar theory where particles are moving through momentum-space, and momentum is singled out as the primary ontological variable. In this paper, we construct the putative particle trajectories for a two-slit experiment in both the position and momentum-space theories by simulating particle dynamics with coherent light. Using a method for constructing trajectories in the primary and non-primary spaces, we compare the phase-space dynamics offered by the two theories and show that they do not agree. This contradictory behaviour underscores the difficulty of selecting one picture of reality from the infinite number of possibilities offered by Bohm-like theories.

In this paper, we construct the putative particle trajectories for a two-slit experiment in the de Broglie-Bohm theory and a similar theory with momentum as the primary ontological variable. We compare the phase-space dynamics offered by the two theories and show that they do not agree. This contradictory behaviour underscores the difficulty of selecting one picture of reality from the infinite number of possibilities offered by Bohm-like theories.

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### Cited by

[1] Devashish Pandey, Rui Sampaio, Tapio Ala-Nissila, Guillermo Albareda, and Xavier Oriols, "Identifying weak values with intrinsic dynamical properties in modal theories", Physical Review A 103 5, 052219 (2021).

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