On the stochastic mechanics of the free relativistic particle

Pavon, Michele

doi:10.1063/1.1401135

Cited by 13 publications

(17 citation statements)

References 17 publications

(25 reference statements)

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“…Is quantum mechanics recovered beyond the non-relativisitic approximation? Nelson's stochastic quantum theory has been extended to relativistic field theory [7], so it is possible that the present results can also be extended.…”

Section: Discussionmentioning

confidence: 83%

Quantum theory from quantum gravity

Markopoulou

Smolin

2004

Phys. Rev. D

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We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model of spacetime, our ansatz is that the microscopic dynamics can be chosen so that 1) the model has a low low energy limit which reproduces the non-relativistic classical dynamics of a system of N particles in flat spacetime, 2) there is a minimum length, and 3) some of the particles are in a thermal bath or otherwise evolve stochastically. We then construct simple functions of the degrees of freedom of the theory and show that their probability distributions evolve according to the Schrödinger equation. The non-local hidden variables required to satisfy the conditions of Bell's theorem are the links in the fundamental graph that connect nodes adjacent in the graph but distant in the approximate metric of the low energy limit. In the presence of these links, distant stochastic fluctuations are transferred into universal quantum fluctuations.

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Section: Discussionmentioning

confidence: 83%

Quantum theory from quantum gravity

Markopoulou

Smolin

2004

Phys. Rev. D

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“…Until now only a few specific bosonic examples have been studied in this framework, see for example refs. [25][26][27][28][29][30][31][32][33], but no general formalism has yet been developed. The embedding of stochastic quantization into second order geometry, as developed in this paper could help guide the way towards such an extension.…”

Section: Discussionmentioning

confidence: 99%

“…refs. [25][26][27][28][29][30][31][32][33]. Furthermore, the notion of spin has been discussed in this framework, cf.…”

Section: Successes Of Stochastic Quantizationmentioning

confidence: 99%

Stochastic quantization on Lorentzian manifolds

Kuipers

2021

J. High Energ. Phys.

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We embed Nelson’s theory of 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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“…(3.25) is appropriate in the nonrelativistic limit, which we have presented for simplicity and because nonrelativistic stochastic mechanics is better established than its relativistic counterpart. Relativistic treatments of stochastic mechanics and stochastic field theory have been presented [29,[50][51][52][53][54][55][56], but the subject is not mature.…”

Section: With One Caveat (See Below For Wallstrom's Objection) Any Somentioning

confidence: 99%

Stochastic emergent quantum gravity

Erlich

2018

Class. Quantum Grav.

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We present a stochastic framework for emergent quantum gravity coupled to matter. The Hamiltonian constraint in diffeomorphism-invariant theories demands the identification of a clock relative to which dynamics may be defined, and other degrees of freedom can play the role of rulers. However, a global system of clock and rulers is generally not available. We provide evidence that stochasticity associated with critical points of clock and ruler fields can be related to the emergence of both a probabilistic description consistent with ordinary quantum theory, and gravitation described by general relativity at long distances. We propose a procedure for embedding any Lorentz-invariant field theory, including the Standard Model and its Lorentz-invariant extensions, in this framework. * erlich@physics.wm.edu 1 arXiv:1807.07083v1 [gr-qc]

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On the stochastic mechanics of the free relativistic particle

Cited by 13 publications

References 17 publications

Quantum theory from quantum gravity

Quantum theory from quantum gravity

Stochastic quantization on Lorentzian manifolds

Stochastic emergent quantum gravity

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