Pilot-Wave Theory, Bohmian Metaphysics, and the Foundations of Quantum Mechanics Lecture 6 Calculating Things with Quantum Trajectories
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Arxiv:1911.07386V2 [Quant-Ph] 25 Nov 2019
Ideas Abandoned en Route to QBism Blake C. Stacey1 1Physics Department, University of Massachusetts Boston (Dated: November 26, 2019) The interpretation of quantum mechanics known as QBism developed out of efforts to understand the probabilities arising in quantum physics as Bayesian in character. But this development was neither easy nor without casualties. Many ideas voiced, and even committed to print, during earlier stages of Quantum Bayesianism turn out to be quite fallacious when seen from the vantage point of QBism. If the profession of science history needed a motto, a good candidate would be, “I think you’ll find it’s a bit more complicated than that.” This essay explores a particular application of that catechism, in the generally inconclusive and dubiously reputable area known as quantum foundations. QBism is a research program that can briefly be defined as an interpretation of quantum mechanics in which the ideas of agent and ex- perience are fundamental. A “quantum measurement” is an act that an agent performs on the external world. A “quantum state” is an agent’s encoding of her own personal expectations for what she might experience as a consequence of her actions. Moreover, each measurement outcome is a personal event, an expe- rience specific to the agent who incites it. Subjective judgments thus comprise much of the quantum machinery, but the formalism of the theory establishes the standard to which agents should strive to hold their expectations, and that standard for the relations among beliefs is as objective as any other physical theory [1]. The first use of the term QBism itself in the literature was by Fuchs and Schack in June 2009 [2]. -
The Theory of (Exclusively) Local Beables
The Theory of (Exclusively) Local Beables Travis Norsen Marlboro College Marlboro, VT 05344 (Dated: June 17, 2010) Abstract It is shown how, starting with the de Broglie - Bohm pilot-wave theory, one can construct a new theory of the sort envisioned by several of QM’s founders: a Theory of Exclusively Local Beables (TELB). In particular, the usual quantum mechanical wave function (a function on a high-dimensional configuration space) is not among the beables posited by the new theory. Instead, each particle has an associated “pilot- wave” field (living in physical space). A number of additional fields (also fields on physical space) maintain what is described, in ordinary quantum theory, as “entanglement.” The theory allows some interesting new perspective on the kind of causation involved in pilot-wave theories in general. And it provides also a concrete example of an empirically viable quantum theory in whose formulation the wave function (on configuration space) does not appear – i.e., it is a theory according to which nothing corresponding to the configuration space wave function need actually exist. That is the theory’s raison d’etre and perhaps its only virtue. Its vices include the fact that it only reproduces the empirical predictions of the ordinary pilot-wave theory (equivalent, of course, to the predictions of ordinary quantum theory) for spinless non-relativistic particles, and only then for wave functions that are everywhere analytic. The goal is thus not to recommend the TELB proposed here as a replacement for ordinary pilot-wave theory (or ordinary quantum theory), but is rather to illustrate (with a crude first stab) that it might be possible to construct a plausible, empirically arXiv:0909.4553v3 [quant-ph] 17 Jun 2010 viable TELB, and to recommend this as an interesting and perhaps-fruitful program for future research. -
On the Foundations of Eurhythmic Physics: a Brief Non Technical Survey
International Journal of Philosophy 2017; 5(6): 50-53 http://www.sciencepublishinggroup.com/j/ijp doi: 10.11648/j.ijp.20170506.11 ISSN: 2330-7439 (Print); ISSN: 2330-7455 (Online) On the Foundations of Eurhythmic Physics: A Brief Non Technical Survey Paulo Castro 1, José Ramalho Croca 1, 2, Rui Moreira 1, Mário Gatta 1, 3 1Center for Philosophy of Sciences of the University of Lisbon (CFCUL), Lisbon, Portugal 2Department of Physics, University of Lisbon, Lisbon, Portugal 3Centro de Investigação Naval (CINAV), Portuguese Naval Academy, Almada, Portugal Email address: To cite this article: Paulo Castro, José Ramalho Croca, Rui Moreira, Mário Gatta. On the Foundations of Eurhythmic Physics: A Brief Non Technical Survey. International Journal of Philosophy . Vol. 5, No. 6, 2017, pp. 50-53. doi: 10.11648/j.ijp.20170506.11 Received : October 9, 2017; Accepted : November 13, 2017; Published : February 3, 2018 Abstract: Eurhythmic Physics is a new approach to describe physical systems, where the concepts of rhythm, synchronization, inter-relational influence and non-linear emergence stand out as major concepts. The theory, still under development, is based on the Principle of Eurhythmy, the assertion that all systems follow, on average, the behaviors that extend their existence, preserving and reinforcing their structural stability. The Principle of Eurhythmy implies that all systems in Nature tend to harmonize or cooperate between themselves in order to persist, giving rise to more complex structures. This paper provides a brief non-technical introduction to the subject. Keywords: Eurhythmic Physics, Principle of Eurhythmy, Non-Linearity, Emergence, Complex Systems, Cooperative Evolution among a wider range of interactions. -
The Quantum Epoché
Accepted Manuscript The quantum epoché Paavo Pylkkänen PII: S0079-6107(15)00127-3 DOI: 10.1016/j.pbiomolbio.2015.08.014 Reference: JPBM 1064 To appear in: Progress in Biophysics and Molecular Biology Please cite this article as: Pylkkänen, P., The quantum epoché, Progress in Biophysics and Molecular Biology (2015), doi: 10.1016/j.pbiomolbio.2015.08.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT The quantum epoché Paavo Pylkkänen Department of Philosophy, History, Culture and Art Studies & the Academy of Finland Center of Excellence in the Philosophy of the Social Sciences (TINT), P.O. Box 24, FI-00014 University of Helsinki, Finland. and Department of Cognitive Neuroscience and Philosophy, School of Biosciences, University of Skövde, P.O. Box 408, SE-541 28 Skövde, Sweden [email protected] Abstract. The theme of phenomenology and quantum physics is here tackled by examining some basic interpretational issues in quantum physics. One key issue in quantum theory from the very beginning has been whether it is possible to provide a quantum ontology of particles in motion in the same way as in classical physics, or whether we are restricted to stay within a more limited view of quantum systems, in terms of complementary but mutually exclusiveMANUSCRIPT phenomena. -
Pilot-Wave Hydrodynamics
FL47CH12-Bush ARI 1 December 2014 20:26 Pilot-Wave Hydrodynamics John W.M. Bush Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; email: [email protected] Annu. Rev. Fluid Mech. 2015. 47:269–92 Keywords First published online as a Review in Advance on walking drops, Faraday waves, quantum analogs September 10, 2014 The Annual Review of Fluid Mechanics is online at Abstract fluid.annualreviews.org Yves Couder, Emmanuel Fort, and coworkers recently discovered that a This article’s doi: millimetric droplet sustained on the surface of a vibrating fluid bath may 10.1146/annurev-fluid-010814-014506 self-propel through a resonant interaction with its own wave field. This ar- Copyright c 2015 by Annual Reviews. ticle reviews experimental evidence indicating that the walking droplets ex- All rights reserved hibit certain features previously thought to be exclusive to the microscopic, Annu. Rev. Fluid Mech. 2015.47:269-292. Downloaded from www.annualreviews.org quantum realm. It then reviews theoretical descriptions of this hydrody- namic pilot-wave system that yield insight into the origins of its quantum- Access provided by Massachusetts Institute of Technology (MIT) on 01/07/15. For personal use only. like behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, and multimodal statistics appear to be a feature of chaotic pilot-wave dynamics. I attempt to assess the po- tential and limitations of this hydrodynamic system as a quantum analog. This fluid system is compared to quantum pilot-wave theories, shown to be markedly different from Bohmian mechanics and more closely related to de Broglie’s original conception of quantum dynamics, his double-solution theory, and its relatively recent extensions through researchers in stochastic electrodynamics. -
Pilot-Wave Theory, Bohmian Metaphysics, and the Foundations of Quantum Mechanics Lecture 8 Bohmian Metaphysics: the Implicate Order and Other Arcana
Pilot-wave theory, Bohmian metaphysics, and the foundations of quantum mechanics Lecture 8 Bohmian metaphysics: the implicate order and other arcana Mike Towler TCM Group, Cavendish Laboratory, University of Cambridge www.tcm.phy.cam.ac.uk/∼mdt26 and www.vallico.net/tti/tti.html [email protected] – Typeset by FoilTEX – 1 Acknowledgements The material in this lecture is largely derived from books and articles by David Bohm, Basil Hiley, Paavo Pylkk¨annen, F. David Peat, Marcello Guarini, Jack Sarfatti, Lee Nichol, Andrew Whitaker, and Constantine Pagonis. The text of an interview between Simeon Alev and Peat is extensively quoted. Other sources used and many other interesting papers are listed on the course web page: www.tcm.phy.cam.ac.uk/∼mdt26/pilot waves.html MDT – Typeset by FoilTEX – 2 More philosophical preliminaries Positivism: Observed phenomena are all that require discussion or scientific analysis; consideration of other questions, such as what the underlying mechanism may be, or what ‘real entities’ produce the phenomena, is dismissed as meaningless. Truth begins in sense experience, but does not end there. Positivism fails to prove that there are not abstract ideas, laws, and principles, beyond particular observable facts and relationships and necessary principles, or that we cannot know them. Nor does it prove that material and corporeal things constitute the whole order of existing beings, and that our knowledge is limited to them. Positivism ignores all humanly significant and interesting problems, citing its refusal to engage in reflection; it gives to a particular methodology an absolutist status and can do this only because it has partly forgotten, partly repressed its knowledge of the roots of this methodology in human concerns. -
Hamiltonian Formulation of the Pilot-Wave Theory Has Also Been Developed by Holland [9]
Hamiltonian Formulation of the Pilot-Wave Theory Dan N. Vollick Irving K. Barber School of Arts and Sciences University of British Columbia Okanagan 3333 University Way Kelowna, B.C. Canada V1V 1V7 Abstract In the pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. The velocity of a particle is deter- mined by the wave function of the system (the guidance equation) and the wave function evolves according to Schrodinger’s equation. In this paper I first construct a Hamiltonian that gives Schrodinger’s equation and the guidance equation for the particle. I then find the Hamiltonian for a relativistic particle in Dirac’s theory and for a quantum scalar field. arXiv:2101.10117v1 [quant-ph] 21 Jan 2021 1 1 Introduction In the standard approach to quantum mechanics the wave function provides a complete description of any system and is used to calculate probability distributions for observ- ables associated with the system. In the pilot-wave theory pioneered by de Broglie [1, 2] in the 1920’s, particles have definite positions and velocities and are “guided” by the wave function, which satisfies Schrodinger’s equation. A similar approach was developed by Bohm [3, 4] in the early 1950’s (see [5] and [6] for extensive reviews). For a single particle in the non-relativistic theory the velocity of the particle is given by dX~ = J~(X,~ t) , (1) dt where X~ is the particle’s position and h¯ J~ = ψ∗ ~ ψ ψ ~ ψ∗ . (2) 2im ψ 2 ∇ − ∇ | | h i Particle trajectories are, therefore, integral curves to the vector field J~. -
Consciousness, the Unconscious and Mathematical Modeling of Thinking
entropy Article On “Decisions and Revisions Which a Minute Will Reverse”: Consciousness, The Unconscious and Mathematical Modeling of Thinking Arkady Plotnitsky Literature, Theory and Cultural Studies Program, Philosophy and Literature Program, Purdue University, West Lafayette, IN 47907, USA; [email protected] Abstract: This article considers a partly philosophical question: What are the ontological and epistemological reasons for using quantum-like models or theories (models and theories based on the mathematical formalism of quantum theory) vs. classical-like ones (based on the mathematics of classical physics), in considering human thinking and decision making? This question is only partly philosophical because it also concerns the scientific understanding of the phenomena considered by the theories that use mathematical models of either type, just as in physics itself, where this question also arises as a physical question. This is because this question is in effect: What are the physical reasons for using, even if not requiring, these types of theories in considering quantum phenomena, which these theories predict fully in accord with the experiment? This is clearly also a physical, rather than only philosophical, question and so is, accordingly, the question of whether one needs classical-like or quantum-like theories or both (just as in physics we use both classical and quantum theories) in considering human thinking in psychology and related fields, such as decision Citation: Plotnitsky, A. On science. It comes as no surprise that many of these reasons are parallel to those that are responsible “Decisions and Revisions Which a for the use of QM and QFT in the case of quantum phenomena. -
On the Interpretation of the Quantum Wave Function
On the interpretation of the quantum wave function Master's thesis Physics and Astronomy Radboud University Nijmegen Supervisors: Prof. R.H.P. Kleiss and H.C. Donker Second corrector: Assoc. Prof. F. Filthaut Han van der Pluijm August 26, 2016 Contents Introduction 3 1 The wave function and its relation to the real world: Ontic and epistemic interpretations of the wave function 5 1.1 Classical states . .6 1.2 A classical particle in phase space . .7 1.3 Example of an incomplete ontic state . 10 1.4 Quantum states . 11 1.4.1 Epistemic and ontic states in quantum theory . 12 2 Ontological models and the PBR no-go theorem 14 2.1 Ontological models . 15 2.2 The structure of PBR's no-go theorem . 16 2.3 Assumptions . 17 2.3.1 Mathematical equivalents . 18 2.4 The proof . 19 3 Spekkens Toy Theory 23 3.1 The knowledge balance principle . 24 3.2 Spekkens' Toy Bit . 26 3.3 Multiple bits . 31 3.4 Parallels with quantum theory . 33 3.4.1 Convex combinations . 33 3.4.2 Coherent superpositions . 34 3.4.3 Interference . 35 4 Mach-Zehnder interferometer in Spekkens toy theory 36 4.1 Setup of the Mach-Zehnder interferometer . 36 4.2 Quantum behaviour . 38 4.3 States of the MZI in Spekkens' toy theory . 41 4.4 Future prospects . 44 5 Conclusion and discussion 45 Bibliography 47 1 Preface The reason I choose to study physics was twofold. On the one hand I was looking for a challenge and on the other hand I wanted to under- stand the world truly. -
Hydrodynamic Quantum Field Theory: the Free Particle
Comptes Rendus Mécanique Yuval Dagan and John W. M. Bush Hydrodynamic quantum field theory: the free particle Volume 348, issue 6-7 (2020), p. 555-571. <https://doi.org/10.5802/crmeca.34> Part of the Thematic Issue: Tribute to an exemplary man: Yves Couder Guest editors: Martine Ben Amar (Paris Sciences & Lettres, LPENS, Paris, France), Laurent Limat (Paris-Diderot University, CNRS, MSC, Paris, France), Olivier Pouliquen (Aix-Marseille Université, CNRS, IUSTI, Marseille, France) and Emmanuel Villermaux (Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE, Marseille, France) © Académie des sciences, Paris and the authors, 2020. Some rights reserved. This article is licensed under the Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0/ Les Comptes Rendus. Mécanique sont membres du Centre Mersenne pour l’édition scientifique ouverte www.centre-mersenne.org Comptes Rendus Mécanique 2020, 348, nO 6-7, p. 555-571 https://doi.org/10.5802/crmeca.34 Tribute to an exemplary man: Yves Couder Bouncing drops, memory / Bouncing drops, memory Hydrodynamic quantum field theory: the free particle a b,* Yuval Dagan and John W. M. Bush a Faculty of Aerospace Engineering, Technion - Israel Institute of Technology, Haifa, Israel b Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA E-mails: [email protected] (Y. Dagan), [email protected] (J. W. M. Bush) Abstract. We revisit de Broglie’s double-solution pilot-wave theory in light of insights gained from the hy- drodynamic pilot-wave system discovered by Couder and Fort [1]. de Broglie proposed that quantum parti- cles are characterized by an internal oscillation at the Compton frequency, at which rest mass energy is ex- changed with field energy. -
Violation of Bell Inequalities: Mapping the Conceptual Implications
International Journal of Quantum Foundations 7 (2021) 47-78 Original Paper Violation of Bell Inequalities: Mapping the Conceptual Implications Brian Drummond Edinburgh, Scotland. E-mail: [email protected] Received: 10 April 2021 / Accepted: 14 June 2021 / Published: 30 June 2021 Abstract: This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical balance and entanglement, (b) the thinking that led to the derivation of the original Bell inequality, and (c) the range of claimed implications, including realism, locality and others which attract less attention. The main conclusion is that violation of Bell inequalities appears to have some implications for the nature of physical reality, but that none of these are definite. The violations constrain possible prequantum (underlying) theories, but do not rule out the possibility that such theories might reconcile at least one understanding of locality and realism to quantum mechanical predictions. Violation might reflect, at least partly, failure to acknowledge the contextuality of quantum mechanics, or that data from different probability spaces have been inappropriately combined. Many claims that there are definite implications reflect one or more of (i) imprecise non-mathematical language, (ii) assumptions inappropriate in quantum mechanics, (iii) inadequate treatment of measurement statistics and (iv) underlying philosophical assumptions. Keywords: Bell inequalities; statistical balance; entanglement; realism; locality; prequantum theories; contextuality; probability space; conceptual; philosophical International Journal of Quantum Foundations 7 (2021) 48 1. Introduction and Overview (Area Mapped and Mapping Methods) Concepts are an important part of physics [1, § 2][2][3, § 1.2][4, § 1][5, p. -
Quantum Retrodiction: Foundations and Controversies
S S symmetry Article Quantum Retrodiction: Foundations and Controversies Stephen M. Barnett 1,* , John Jeffers 2 and David T. Pegg 3 1 School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK 2 Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK; [email protected] 3 Centre for Quantum Dynamics, School of Science, Griffith University, Nathan 4111, Australia; d.pegg@griffith.edu.au * Correspondence: [email protected] Abstract: Prediction is the making of statements, usually probabilistic, about future events based on current information. Retrodiction is the making of statements about past events based on cur- rent information. We present the foundations of quantum retrodiction and highlight its intimate connection with the Bayesian interpretation of probability. The close link with Bayesian methods enables us to explore controversies and misunderstandings about retrodiction that have appeared in the literature. To be clear, quantum retrodiction is universally applicable and draws its validity directly from conventional predictive quantum theory coupled with Bayes’ theorem. Keywords: quantum foundations; bayesian inference; time reversal 1. Introduction Quantum theory is usually presented as a predictive theory, with statements made concerning the probabilities for measurement outcomes based upon earlier preparation events. In retrodictive quantum theory this order is reversed and we seek to use the Citation: Barnett, S.M.; Jeffers, J.; outcome of a measurement to make probabilistic statements concerning earlier events [1–6]. Pegg, D.T. Quantum Retrodiction: The theory was first presented within the context of time-reversal symmetry [1–3] but, more Foundations and Controversies. recently, has been developed into a practical tool for analysing experiments in quantum Symmetry 2021, 13, 586.