Relativistic Bohmian trajectories of photons via weak measurements

Foo, Joshua; Asmodelle, Estelle; Lund, Austin P.; Ralph, Timothy C.

doi:10.1038/s41467-022-31608-6

Cited by 11 publications

(5 citation statements)

References 51 publications

(72 reference statements)

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“…De Broglie singularities tunnel quickly through these regions. Such transitions of the Bohmian trajectories are well demonstrated in works [68][69][70].…”

Section: Computation Of the Velocity Variancementioning

confidence: 67%

Louis de Broglie Double Solution Theory Confirms the Wave-Particle Duality Principle

Sbitnev

2023

Preprint

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Louis de Broglie in the beginning 20th century voices his theory of a double solution, according to which a pilot wave accompanies a particle, simulated as a point singularity, along the most optimal path from its creation on a source up to the detection. The pilot wave is a real hidden wave, which is similar to the wave function resulting from the solution of the Schrödinger equation. This theory is in agreement with de Broglie’s postulate about the matter waves. In this article we are based on the Helmholtz decomposition theorem according to which any velocity may be represented as a sum of two velocities – irrotational and solenoidal ones. The first velocity stems from the gradient of the scalar field. The second occurs from a pseudo-vector field. We proclaim that the gradients of the scalar field define guiding paths of the pilot wave. While the pseudo-vector field defines a particle solenoidal filling. We give mathematical models of the irrotational and solenoidal flows simulating the position of a particle in a guiding wave. Modified Navier-Stokes equation in pair with the continuity equation resulting in the Schrödinger equation gives such solutions consisting of superposition of the irrotational and solenoidal flow. It is declared that the guiding wave forms from the irrotational flows. In turn, the solenoidal flows underlie forming particles that travel along optimal paths slave by the guiding wave. There are described mathematical solutions of the spherical particle washed by the superfluid representing the guiding wave along which it travels.

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“…De Broglie singularities tunnel quickly through these regions. Such transitions of the Bohmian trajectories are well demonstrated in works [68][69][70].…”

Section: Computation Of the Velocity Variancementioning

confidence: 67%

Louis de Broglie Double Solution Theory Confirms the Wave-Particle Duality Principle

Sbitnev

2023

Preprint

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“…Due to the non-locality of Bohmian dynamics, there is no obvious and agreed-upon way to achieve a relativistic extension of it, especially for systems with more than one particle [124][125][126] . However, there are various proposals for this purpose 72,[127][128][129][130][131][132] . Therefore, using particles with relativistic speeds, the same kind of experiment could be used to probe these proposals.…”

Section: Discussionmentioning

confidence: 99%

“…Nonetheless, it has been proved that in the quantum equilibrium condition 62,63 , Bohmian mechanics is experimentally equivalent to orthodox quantum mechanics 64,65 insofar as the latter is unambiguous [66][67][68] ; e.g., in usual position or momentum measurements at a specific time. In recent years, Bohmian mechanics has gained renewed interest for various reasons [69][70][71][72] . One of these reasons is the fact that Bohmian trajectories can lead to clear predictions for quantum characteristic times, such as tunneling time duration 52,73,74 and arrival time distribution 24,43,67 .…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Non-local temporal interference

Ayatollah Rafsanjani,

Kazemi,

Hosseinzadeh

et al. 2024

Sci Rep

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Although position and time have different mathematical roles in quantum mechanics, with one being an operator and the other being a parameter, there is a space–time duality in quantum phenomena—a lot of quantum phenomena that were first observed in the spatial domain were later observed in the temporal domain as well. In this context, we propose a modified version of the double-double-slit experiment using entangled atom pairs to observe a non-local interference in the arrival time distribution, which is analogous to the non-local interference observed in the arrival position distribution. However, computing the arrival time distribution in quantum mechanics is a challenging open problem, and so to overcome this problem we employ a Bohmian treatment. Based on this approach, we numerically demonstrate that there is a complementary relationship between the one-particle and two-particle interference visibilities in the arrival time distribution, which is analogous to the complementary relationship observed in the position distribution. These results can be used to test the Bohmian arrival time distribution in a strict manner, i.e., where the semiclassical approximation breaks down. Moreover, our approach to investigating this experiment can be applied to a wide range of phenomena, and it seems that the predicted non-local temporal interference and associated complementary relationship are universal behaviors of entangled quantum systems that may manifest in various phenomena.

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“…In order to specify whether the resulting 'field theory' should be classical or quantum one has to refer to arguments put forth in [1] that ruled out a conventional deterministic theory. Whether the resulting theory can only be quantum field theory or other alternatives are also possible [24][25][26]] is yet to be determined. What remains out of question is that the superluminal extension of special relativity in 1 + 3 spacetime is possible in a fully consistent way.…”

Section: Dynamicsmentioning

confidence: 99%