Directly observing relativistic Bohmian mechanics

Abstract: Bohmian mechanics, also referred to as the de Broglie-Bohm pilot-wave theory, represents a deterministic and nonlocal interpretation of quantum mechanics. Since its origination in 1927, despite many attempts, reconciling it with relativistic theory and verification of its relativistic effects have remained elusive. Here, we report a direct observation of relativistic characteristics of Bohmian mechanics. We reconstruct the relativistic Bohmian trajectories of single photons utilizing weak measurement techniques in a double-slit interferometer, unveiling a fundamental aspect of relativistic Bohmian mechanics. We investigate the effective squared mass density of single photons, revealing its negative values in the destructive regions -- a phenomenon directly links to the tachyonic behavior in relativistic Bohmian mechanics. The continuity equations given by both the Klein-Gordon equation and Schr\"{o}dinger's equation are experimentally examined. Our result indicates that within the framework of relativity, the conservation of energy holds true, whereas the conservation of particle number for a free scalar field no longer holds. The emergence of previously unobserved phenomena in the extensively studied double-slit experiment are enabled by Bohmian mechanics, while conversely, these experimental outcomes offer unambiguous evidence of the long-sought-after relativistic features within Bohmian mechanics.