Quantum measurement and weak values in entropic dynamics

Vanslette, Kevin; Caticha, Ariel

doi:10.1063/1.4985372

Cited by 11 publications

(18 citation statements)

References 19 publications

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“…The wave function, on the other hand, is a purely epistemic notion and, as it turns out, all other quantities, such as energy or momentum, are epistemic too. They do not reflect properties of the particles but properties of the wave function [ 70 , 71 , 72 ].…”

Section: The Ed Of Short Stepsmentioning

confidence: 99%

“…In contrast, in ED probabilities refer to ontic positions—including the ontic positions of pointer variables. In the end, this is what solves the problem of quantum measurement (see [ 70 , 71 ]).…”

Section: Remarks On Ed and Quantum Bayesianismmentioning

confidence: 99%

“…This paper focuses on the derivation of the Schrödinger equation but the ED approach has been applied to a variety of other topics in quantum theory. These include: the quantum measurement problem [ 70 , 71 ]; momentum and uncertainty relations [ 50 , 72 ] (see also [ 73 , 74 , 75 , 76 ]); the Bohmian limit [ 49 , 50 ] and the classical limit [ 77 ]; extensions to curved spaces [ 78 ]; to relativistic fields [ 79 , 80 ]; and the ED of spin [ 81 ].…”

Section: Introductionmentioning

confidence: 99%

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The Entropic Dynamics Approach to Quantum Mechanics

Caticha

2019

Entropy

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Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The central challenge is to specify how those constraints are themselves updated. In this paper we review and extend the ED framework in several directions. A new version of ED is introduced in which particles follow smooth differentiable Brownian trajectories (as opposed to non-differentiable Brownian paths). To construct ED we make use of the fact that the space of probabilities and phases has a natural symplectic structure (i.e., it is a phase space with Hamiltonian flows and Poisson brackets). Then, using an argument based on information geometry, a metric structure is introduced. It is shown that the ED that preserves the symplectic and metric structures -which is a Hamilton-Killing flow in phase space -is the linear Schrödinger equation. These developments allow us to discuss why wave functions are complex and the connections between the superposition principle, the single-valuedness of wave functions, and the quantization of electric charges. Finally, it is observed that Hilbert spaces are not necessary ingredients in this construction. They are a clever but merely optional trick that turns out to be convenient for practical calculations.4 There exist many different Bayesian interpretations of probability. In section 13 we comment on how ED differs from the frameworks known as Quantum Bayesianism [16]-[18] and its closely related descendant QBism [19][20].5 In both the ES and the OU processes, which were originally meant to model the actual physical Brownian motion, friction and dissipation play essential roles. In contrast, ED is non-dissipative. ED formally resembles Nelson's stochastic mechanics [23] but the conceptual differences are significant. Nelson's mechanics attempted an ontic interpretation of QM as an ES process driven by real stochastic classical forces while ED is a purely epistemic model that does not appeal to an underlying classical mechanics.

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Section: The Ed Of Short Stepsmentioning

confidence: 99%

Section: Remarks On Ed and Quantum Bayesianismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Entropic Dynamics Approach to Quantum Mechanics

Caticha

2019

Entropy

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“…The wave function, on the other hand, is a purely epistemic notion; it defines our epistemic state about the system. All other quantities, such as energy or momentum, are epistemic in that they reflect properties of the wave function, not properties of the particles . These values are not quite “created” by the measurement, but rather inferred from them.…”

Section: The Statistical Modelmentioning

confidence: 99%

“…This paper focuses on the derivation of the Schrödinger equation but the ED approach has been applied to a variety of other topics including the quantum measurement problem; momentum and uncertainty relations; the Bohmian limit and the classical limit; extensions to curved spaces and to relativistic fields are also available.…”

Section: Introductionmentioning

confidence: 99%

Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

Caticha

2018

Annalen der Physik

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Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The epistemic nature of the phase of the wave function is also clear: it controls the flow of probability. The dynamics is driven by entropy subject to constraints that capture the relevant physical information. The central concern is to identify those constraints and how they are updated. After reviewing previous work I describe how considerations from information geometry allow us to derive a phase space geometry that combines Riemannian, symplectic, and complex structures. The ED that preserves these structures is QM. The full equivalence between ED and QM is achieved by taking account of how gauge symmetry and charge quantization are intimately related to quantum phases and the single-valuedness of wave functions.

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