A Footnote to Nelson's Interpretation of the Two-Slit Experiment

Pavon, Michele

doi:10.1142/s0217979204024367

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…For a list of further "successes", as well as failures, of Nelson's stochastic mechanics see [62]. Among the successes, it might be worthwhile quoting from [62] the little known: "A stochastic picture of the two-slit experiment, explaining how particles have trajectories going through just one slit or the other, but nevertheless produce a probability density as for interfering waves; see [61,Section 17]", see also [69].…”

Section: B Remarks On Stochastic Mechanicsmentioning

confidence: 99%

Extremal flows on Wasserstein space

Conforti¹,

Pavon²

2017

Preprint

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We develop an intrinsic geometric approach to calculus of variations on Wasserstein space. We show that the flows associated to the Schrödinger bridge with general prior, to Optimal Mass Transport and to the Madelung fluid can all be characterized as annihilating the first variation of a suitable action. We then discuss the implications of this unified framework for stochastic mechanics: It entails, in particular, a sort of fluid-dynamic reconciliation between Bohm's and Nelson's stochastic mechanics.

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Section: B Remarks On Stochastic Mechanicsmentioning

confidence: 99%

Extremal flows on Wasserstein space

Conforti¹,

Pavon²

2017

Preprint

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“…We shall show elsewhere [49] that the variational principle of section 5 may be replaced by two stochastic differential games with real velocities with an appealing classical interpretation. We shall also show that, using Nelson's observation in [38,15] and this variational principle, it is possible to obtain a completely satisfactory classical probabilistic description of the two-slit experiment.…”

Section: Discussionmentioning

confidence: 99%

Quantum Schrödinger Bridges

Pavon

Directions in Mathematical Systems Theory and Optimization

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Elaborating on M. Pavon, J. Math. Phys. 40 (1999), 5565-5577, we develop a simplified version of a variational principle within Nelson stochastic mechanics that produces the von Neumann wave packet reduction after a position measurement. This stochastic control problem parallels, with a different kinematics, the problem of the Schrödinger bridge. This gives a profound meaning to what was observed by Schrödinger in 1931 concerning Schrödinger bridges: "Merkwürdige Analogien zur Quantenmechanik, die mir sehr des Hindenkens wert erscheinen".

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Extremal flows in Wasserstein space

Conforti

Pavon

2018

Journal of Mathematical Physics

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We develop an intrinsic geometric approach to the calculus of variations in the Wasserstein space. We show that the flows associated with the Schrödinger bridge with general prior, with optimal mass transport, and with the Madelung fluid can all be characterized as annihilating the first variation of a suitable action. We then discuss the implications of this unified framework for stochastic mechanics: It entails, in particular, a sort of fluid-dynamic reconciliation between Bohm’s and Nelson’s stochastic mechanics.

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A Footnote to Nelson's Interpretation of the Two-Slit Experiment

Cited by 3 publications

References 18 publications

Extremal flows on Wasserstein space

Extremal flows on Wasserstein space

Quantum Schrödinger Bridges

Extremal flows in Wasserstein space

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