The Road to Heisenberg Quantum Mechanics

Peña, Luis de la; Cetto, Ana Marı́a; Hernández, Andrea Valdés

doi:10.1007/978-3-319-07893-9_5

Cited by 4 publications

(6 citation statements)

References 12 publications

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“…The relation of the ED formalism to quantum theory can made explicit by making a canonical transformation (often called a Madelung transformation) from the dynamical variables ρ and Φ into a pair of complex variables 15 ,…”

Section: The Local-time Schrödinger Functional Equationmentioning

confidence: 99%

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Entropic dynamics: reconstructing quantum field theory in curved space-time

Ipek

Abedi

Caticha

2019

Class. Quantum Grav.

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The Entropic Dynamics reconstruction of quantum mechanics is extended to the quantum theory of scalar fields in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is combined with the covariant methods of Dirac, Hojman, Kuchař, and Teitelboim, which they used to develop a framework for classical covariant Hamiltonian theories. The goal is to formulate an information-based alternative to current approaches based on algebraic quantum field theory. One key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces. The resulting dynamics is a non-dissipative diffusion that is constrained by the requirements of foliation invariance and incorporates the necessary local quantum potentials. As applications of the formalism we derive the Ehrenfest relations for fields in curved-spacetime and briefly discuss the nature of divergences in quantum field theory.

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Section: The Local-time Schrödinger Functional Equationmentioning

confidence: 99%

“…[9][10][11]) culminating in a variety of proposals for the reconstruction of quantum mechanics (see e.g. [12][13][14][15][16][17][18]). Notable among the latter are proposals that seek a deeper foundation based on information theory (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Entropic dynamics: reconstructing quantum field theory in curved space-time

Ipek

Abedi

Caticha

2019

Class. Quantum Grav.

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“…While claims of single-particle diffraction and interference [6] have been contested [7], tunneling [8,9], orbital quantization in both a rotating frame [10][11][12] and harmonic potential [13,14], and wavelike statistics in confined geometries [15][16][17][18] are all robust quantumlike phenomena. This hydrodynamic pilot-wave system and its relation to realist quantum theories, specifically, de Broglie's double-solution pilot-wave theory [19] and its modern extensions [20], were recently reviewed by Bush [21,22].…”

Section: Introductionmentioning

confidence: 99%

Simulations of pilot-wave dynamics in a simple harmonic potential

2017

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We present the results of a numerical investigation of droplets walking in a harmonic potential on a vibrating fluid bath. The droplet's trajectory is described by an integrodifferential equation, which is simulated numerically in various parameter regimes. We produce a regime diagram that summarizes the dependence of the walker's behavior on the system parameters for a droplet of fixed size. At relatively low vibrational forcing, a number of periodic and quasiperiodic trajectories emerge. In the limit of large vibrational forcing, the walker's trajectory becomes chaotic, but the resulting trajectories can be decomposed into portions of unstable quasiperiodic states.

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“…We also wish to thank Lev Vaidman and several other colleagues for stimulating discussions. We thank the latter for the exchange of viewpoints sometimes closely related to our approach, as they also become apparent in their respective works: Herman Batelaan [ 34 ], Ana María Cetto and Luis de la Peña [ 35 ], Hans-Thomas Elze [ 36 ], Basil Hiley [ 37 ], Tim Maudlin [ 38 ], Travis Norsen [ 39 ], Garnet Ord [ 40 ], and Louis Vervoort [ 41 ].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Vacuum Landscaping: Cause of Nonlocal Influences without Signaling

Groessing

Fussy

Pascasio

et al. 2018

Entropy

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In the quest for an understanding of nonlocality with respect to an appropriate ontology, we propose a "cosmological solution". We assume that from the beginning of the universe each point in space has been the location of a scalar field representing a zero-point vacuum energy that nonlocally vibrates at a vast range of different frequencies across the whole universe. A quantum, then, is a nonequilibrium steady state in the form of a "bouncer" coupled resonantly to one of those (particle type dependent) frequencies, in remote analogy to the bouncing oil drops on an oscillating oil bath as in Couder's experiments. A major difference to the latter analogy is given by the nonlocal nature of the vacuum oscillations.We show with the examples of double-and n-slit interference that the assumed nonlocality of the distribution functions alone suffices to derive the de˜Broglie--Bohm guiding equation for N particles with otherwise purely classical means. In our model, no influences from configuration space are required, as everything can be described in 3-space. Importantly, the setting up of an experimental arrangement limits and shapes the forward and osmotic contributions and is described as vacuum landscaping. * Corresponding author: ains@chello.at; http://www.nonlinearstudies.at arXiv:1806.05466v2 [quant-ph]

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The Road to Heisenberg Quantum Mechanics

Cited by 4 publications

References 12 publications

Entropic dynamics: reconstructing quantum field theory in curved space-time

Entropic dynamics: reconstructing quantum field theory in curved space-time

Simulations of pilot-wave dynamics in a simple harmonic potential

Vacuum Landscaping: Cause of Nonlocal Influences without Signaling

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