A Suggested Answer To Wallstrom's Criticism: Zitterbewegung Stochastic Mechanics II

Derakhshani, Maaneli

doi:10.48550/arxiv.1607.08838

Cited by 2 publications

(2 citation statements)

References 67 publications

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“…Such an assumption must be made ad hoc, since the wave function is not a fundamental object in the theory. Several responses against this criticism have been given, such as for example the incorporation of zitterbewegung [47,48], adding a postulate regarding the boundedness of the Laplace operator acting on the probability density [49] or by adding the assumption of unitarity of superpositions of wave functions [34]. It is also worth mentioning that on nodal manifolds winding numbers lead to a periodicity factor in the wave function [11], which could resolve Wallstrom's criticism.…”

Section: Criticism On Stochastic Quantizationmentioning

confidence: 99%

Stochastic Quantization on Lorentzian Manifolds

Kuipers

2021

Preprint

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We embed Nelson's stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of quantum mechanics on (pseudo)-Riemannian manifolds. Within this approach, we derive stochastic differential equations for massive spin-0 test particles charged under scalar potentials, vector potentials and gravity. Furthermore, we derive the associated Schrödinger equation. The resulting equations show that massive scalar particles must be conformally coupled to gravity in a theory of quantum gravity. We conclude with a discussion of some prospects of the stochastic framework.

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Section: Criticism On Stochastic Quantizationmentioning

confidence: 99%

Stochastic Quantization on Lorentzian Manifolds

Kuipers

2021

Preprint

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“…Goldstein also independently commented on multi-valued wave functions in stochastic mechanics [23]. Derakhshani has recently suggested an interesting explanation for the single-valued constraint based on zitterbewegung [17,18]. Smolin has also considered this issue [65].…”

Section: Introductionmentioning

confidence: 99%

Multi-valued vortex solutions to the Schrödinger equation and radiation

Davidson

2019

Preprint

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This paper addresses the single-valued requirement for quantum wave functions when they are analytically continued in the spatial coordinates. This is particularly relevant for de Broglie-Bohm, hydrodynamic, or stochastic models of quantum mechanics where the physical basis for singlevaluedness has been questioned. It first constructs a large class of multivalued wave functions based on knotted vortex filaments familiar in fluid mechanics, and then it argues that for free particles, these systems will likely radiate electromagnetic radiation if they are charged or have multipolar moments, and only if they are single-valued will they definitely be radiationless. Thus, it is proposed that electromagnetic radiation is possibly the mechanism that causes quantum wave functions to relax to states of single-valuedness, and that multi-valued states might possibly exist in nature for transient periods of time. If true, this would be a modification to the standard quantum mechanical formalism. A prediction is made that electrons in vector Aharonov-Bohm experiments should radiate energy at a rate dependent on the solenoid's magnetic flux.

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A Suggested Answer To Wallstrom's Criticism: Zitterbewegung Stochastic Mechanics II

Cited by 2 publications

References 67 publications

Stochastic Quantization on Lorentzian Manifolds

Stochastic Quantization on Lorentzian Manifolds

Multi-valued vortex solutions to the Schrödinger equation and radiation

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