Relativistic Bohmian trajectories of photons via weak measurements.
Nat Commun 2022;
13:4002. [PMID:
35821022 PMCID:
PMC9276825 DOI:
10.1038/s41467-022-31608-6]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 06/17/2022] [Indexed: 11/21/2022] Open
Abstract
Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has mainly been restricted to nonrelativistic regimes due to the widely held belief that the theory is incompatible with special relativity. Here, we present an approach for constructing the relativistic Bohmian-type velocity field of single particles. The advantage of our proposal is that it is operational in nature, grounded in weak measurements of the particle’s momentum and energy. We apply our weak measurement formalism to obtain the relativistic spacetime trajectories of photons in a Michelson–Sagnac interferometer. The trajectories satisfy quantum-mechanical continuity and the relativistic velocity addition rule. We propose a modified Alcubierre metric which could give rise to these trajectories within the paradigm of general relativity.
Making Bohmian mechanics fully compatible with special relativity is still an ongoing challenge. Here, the authors make a further step in this direction by providing a way of constructing the relativistic Bohmian-type velocity field of single photons which is operationally based on weak measurements.
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