Quantum Mechanics as Classical Physics

Sebens, Charles T.

doi:10.1086/680190

Cited by 30 publications

(54 citation statements)

References 34 publications

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“…Our interest in studying the explicit model (1.1) is that rigorous investigation of its limiting behavior becomes feasible. Both Hall et al (2014) and Sebens (2014) noted the ontological difficulty of a continuum of worlds, a feature of an earlier but closely related hydrodynamical approach due to Holland (2005), Poirier (2010) and Schiff and Poirier (2012).…”

Section: Introductionmentioning

confidence: 95%

“…As far as we know, however, a formal proof of convergence is not yet available. Sebens (2014) independently proposed a similar many-interacting-worlds interpretation, called Newtonian quantum mechanics, although no explicit example was provided. Our interest in studying the explicit model (1.1) is that rigorous investigation of its limiting behavior becomes feasible.…”

Section: Introductionmentioning

confidence: 99%

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Convergence of empirical distributions in an interpretation of quantum mechanics

McKeague¹,

Levin²

2016

Ann. Appl. Probab.

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From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the interaction of finitely many classical “worlds.” The wave function is then recovered (as a secondary object) from observations of particles in these worlds, without knowing the world from which any particular observation originates. Hall, Deckert and Wiseman [Physical Review X 4 (2014) 041013] have introduced an explicit many-interacting-worlds harmonic oscillator model to provide support for this approach. In this note we provide a proof of their claim that the particle configuration is asymptotically Gaussian, thus matching the stationary ground-state solution of Schrödinger’s equation when the number of worlds goes to infinity. We also construct a Markov chain based on resampling from the particle configuration and show that it converges to an Ornstein–Uhlenbeck process, matching the time-dependent solution as well.

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Convergence of empirical distributions in an interpretation of quantum mechanics

McKeague¹,

Levin²

2016

Ann. Appl. Probab.

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“…7;Wallstrom, 1994;Sebens, 2015, sec. 6): Integrating the momenta of the particles along any closed loop in configuration space gives a multiple of Planck's constant, h = 2π ,…”

Section: 2)mentioning

confidence: 99%

“…Here I examine the problem of explaining the symmetry dichotomy within two interpretations of quantum mechanics which clarify the connection between particles and the wave function by including particles following definite trajectories through space in addition to, or in lieu of, the wave function: (1) Bohmian mechanics and (2) a hydrodynamic interpretation that posits a multitude of quantum worlds interacting with one another, which I have called "Newtonian quantum mechanics" (Hall et al , 2014 have called this kind of approach "many interacting worlds"). Versions of this second interpretation have recently been put forward by Tipler (2006); Poirier (2010); Schiff & Poirier (2012); Boström (2012); Boström (2015); Hall et al (2014); Sebens (2015); it builds on the hydrodynamic approach to quantum mechanics (see Madelung, 1927;Wyatt, 2005;Holland, 2005). Bohmian mechanics and Newtonian quantum mechanics are often called "interpretations"…”

Section: Introductionmentioning

confidence: 99%

Constructing and constraining wave functions for identical quantum particles

Sebens

2016

Studies in History and Philosophy of Science Part B: Studies in

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I address the problem of explaining why wave functions for identical particles must be either symmetric or antisymmetric (the symmetry dichotomy) within two interpretations of quantum mechanics which include particles following definite trajectories in addition to, or in lieu of, the wave function: Bohmian mechanics and Newtonian quantum mechanics (a.k.a. many interacting worlds). In both cases I argue that, if the interpretation is formulated properly, the symmetry dichotomy can be derived and need not be postulated.

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“…The wavefunction in my approach is a generating function of, and thus a mathematical representative for, a continuum of trajectories identified as worlds, and so it has its own justification to remain within the theory. I will discuss the approach by Poirier and Schiff in some more detail in the last section, along with related approaches by Tipler (2006), Hall et al (2014), and Sebens (2014).…”

Section: Introductionmentioning

confidence: 99%

Quantum mechanics as a deterministic theory of a continuum of worlds

Boström

2015

Quantum Stud.: Math. Found.

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A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points, both "time" and "world" are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of Everett's many-worlds interpretation, it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett's approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random "collapse of the wavefunction" caused by the measurement, while still being an objectively deterministic theory.Comment: fourth and final revision, this paper is a thoroughly reworked and enhanced formulation of ideas originally published in 2012 as a preprint in arXiv1208.5632, it has been published as a regular article in 2015 in Quantum Studies: Mathematics and Foundation

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Quantum Mechanics as Classical Physics

Cited by 30 publications

References 34 publications

Convergence of empirical distributions in an interpretation of quantum mechanics

Convergence of empirical distributions in an interpretation of quantum mechanics

Constructing and constraining wave functions for identical quantum particles

Quantum mechanics as a deterministic theory of a continuum of worlds

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