A model for the stochastic origins of Schrödinger’s equation

Davidson, Mark P.

doi:10.1063/1.524304

Cited by 37 publications

(30 citation statements)

References 21 publications

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“…(see [6][7][8][9][10] for discussions) various attempts to go beyond QM have been done during last 80 years. We can mention De Broglies' theory of double solution which was later elaborated in Bohmian mechanics, stochastic electrodynamics (SED), semiclassical model for quantum optics, Nelson's stochastic QM and its generalization by Davidson and, recently, 't Hooft's model, see, e.g., [2,3,[11][12][13][14][15][16][17][18], also cf. V.I.…”

Section: Introductionmentioning

confidence: 99%

Detection Model Based on Representation of Quantum Particles by Classical Random Fields: Born’s Rule and Beyond

Khrennikov

2009

Found Phys

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Recently a new attempt to go beyond quantum mechanics (QM) was presented in the form of so called prequantum classical statistical field theory (PCSFT). Its main experimental prediction is violation of Born's rule which provides only an approximative description of real probabilities. We expect that it will be possible to design numerous experiments demonstrating violation of Born's rule. Moreover, recently the first experimental evidence of violation was found in the triple slit interference experiment, see Sinha, et al. (Foundations of Probability and Physics-5. . Although this experimental test was motivated by another prequantum model, it can be definitely considered as at least preliminary confirmation of the main prediction of PCSFT. In our approach quantum particles are just symbolic representations of "prequantum random fields," e.g., "electron-field" or "neutron-field"; photon is associated with classical random electromagnetic field. Such prequantum fields fluctuate on time and space scales which are essentially finer than scales of QM, cf. 't Hooft's attempt to go beyond QM (see 't Hooft arXiv:hep-th/0105105, 2001; arXiv:quant-ph/0212095, 2002; arXiv:quant-ph/0701097, 2007). In this paper we elaborate a detection model in the PCSFT-framework. In this model classical random fields (corresponding to "quantum particles") interact with detectors inducing probabilities which match with Born's rule only approximately. Thus QM arises from PCSFT as an approximative theory. New tests of violation of Born's rule are proposed.

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Section: Introductionmentioning

confidence: 99%

Detection Model Based on Representation of Quantum Particles by Classical Random Fields: Born’s Rule and Beyond

Khrennikov

2009

Found Phys

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“…Several models have been proposed [15]- [19]. Although the definitive explanation has not yet been found, one possibility seems to stand out: quantum mechanics may arise out of the interaction of charged particles with random forces in the vacuum, and with radiative forces playing an important role.…”

Section: Resultsmentioning

confidence: 99%

The Formulation of Quantum Mechanics

Ballentine¹

1998

Quantum Mechanics

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Abstract. The origin of the algebra of the non-commuting operators of quantum mechanics is explained in the general Fényes-Nelson stochastic models in which the diffusion constant is a free parameter. This is achieved by continuing the diffusion constant to imaginary values, a continuation which destroys the physical interpretation, but does not affect experimental predictions. This continuation leads to great mathematical simplification in the stochastic theory, and to an understanding of the entire mathematical formalism of quantum mechanics. It is more than a formal construction because the diffusion parameter is not an observable in these theories.

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“…It is the author's opinion that this extra term may be related to radiation reaction effects. The only derivation he is aware of for this strange type of force was given in [58], and it involved a radiative reactive force in thermal equilibrium with a statistical medium like our present fluid in spectral truncation and exhibiting ergodic behavior. Here is another reason that suggests there is a connection with radiation.…”

Section: Quantizationmentioning

confidence: 99%

The quark-gluon plasma and the stochastic interpretation of quantum mechanics

Davidson¹

2010

Physica E: Low-dimensional Systems and Nanostructures

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Quark-gluon plasmas formed in heavy ion collisions at high energies are well described by ideal classical fluid equations with nearly zero viscosity. It is believed that a similar fluid permeated the entire universe at about three microseconds after the big bang. The estimated Reynolds number for this quark-gluon plasma at 3 microseconds is approximately 10^19. The possibility that quantum mechanics may be an emergent property of a turbulent proto-fluid is tentatively explored. A simple relativistic fluid equation which is consistent with general relativity and is based on a cosmic dust model is studied. A proper time transformation transforms it into an inviscid Burgers equation. This is analyzed numerically using a spectral method. Soliton-like solutions are demonstrated for this system, and these interact with the known ergodic behavior of the fluid to yield a stochastic and chaotic system which is time reversible. Various similarities to quantum mechanics are explored.

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A model for the stochastic origins of Schrödinger’s equation

Cited by 37 publications

References 21 publications

Detection Model Based on Representation of Quantum Particles by Classical Random Fields: Born’s Rule and Beyond

Detection Model Based on Representation of Quantum Particles by Classical Random Fields: Born’s Rule and Beyond

The Formulation of Quantum Mechanics

The quark-gluon plasma and the stochastic interpretation of quantum mechanics

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