Reading List on Philosophy of Quantum Mechanics David Wallace, June 2018
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On the Lattice Structure of Quantum Logic
BULL. AUSTRAL. MATH. SOC. MOS 8106, *8IOI, 0242 VOL. I (1969), 333-340 On the lattice structure of quantum logic P. D. Finch A weak logical structure is defined as a set of boolean propositional logics in which one can define common operations of negation and implication. The set union of the boolean components of a weak logical structure is a logic of propositions which is an orthocomplemented poset, where orthocomplementation is interpreted as negation and the partial order as implication. It is shown that if one can define on this logic an operation of logical conjunction which has certain plausible properties, then the logic has the structure of an orthomodular lattice. Conversely, if the logic is an orthomodular lattice then the conjunction operation may be defined on it. 1. Introduction The axiomatic development of non-relativistic quantum mechanics leads to a quantum logic which has the structure of an orthomodular poset. Such a structure can be derived from physical considerations in a number of ways, for example, as in Gunson [7], Mackey [77], Piron [72], Varadarajan [73] and Zierler [74]. Mackey [77] has given heuristic arguments indicating that this quantum logic is, in fact, not just a poset but a lattice and that, in particular, it is isomorphic to the lattice of closed subspaces of a separable infinite dimensional Hilbert space. If one assumes that the quantum logic does have the structure of a lattice, and not just that of a poset, it is not difficult to ascertain what sort of further assumptions lead to a "coordinatisation" of the logic as the lattice of closed subspaces of Hilbert space, details will be found in Jauch [8], Piron [72], Varadarajan [73] and Zierler [74], Received 13 May 1969. -
Relational Quantum Mechanics
Relational Quantum Mechanics Matteo Smerlak† September 17, 2006 †Ecole normale sup´erieure de Lyon, F-69364 Lyon, EU E-mail: [email protected] Abstract In this internship report, we present Carlo Rovelli’s relational interpretation of quantum mechanics, focusing on its historical and conceptual roots. A critical analysis of the Einstein-Podolsky-Rosen argument is then put forward, which suggests that the phenomenon of ‘quantum non-locality’ is an artifact of the orthodox interpretation, and not a physical effect. A speculative discussion of the potential import of the relational view for quantum-logic is finally proposed. Figure 0.1: Composition X, W. Kandinski (1939) 1 Acknowledgements Beyond its strictly scientific value, this Master 1 internship has been rich of encounters. Let me express hereupon my gratitude to the great people I have met. First, and foremost, I want to thank Carlo Rovelli1 for his warm welcome in Marseille, and for the unexpected trust he showed me during these six months. Thanks to his rare openness, I have had the opportunity to humbly but truly take part in active research and, what is more, to glimpse the vivid landscape of scientific creativity. One more thing: I have an immense respect for Carlo’s plainness, unaltered in spite of his renown achievements in physics. I am very grateful to Antony Valentini2, who invited me, together with Frank Hellmann, to the Perimeter Institute for Theoretical Physics, in Canada. We spent there an incredible week, meeting world-class physicists such as Lee Smolin, Jeffrey Bub or John Baez, and enthusiastic postdocs such as Etera Livine or Simone Speziale. -
Philosophy of Science and Philosophy of Chemistry
Philosophy of Science and Philosophy of Chemistry Jaap van Brakel Abstract: In this paper I assess the relation between philosophy of chemistry and (general) philosophy of science, focusing on those themes in the philoso- phy of chemistry that may bring about major revisions or extensions of cur- rent philosophy of science. Three themes can claim to make a unique contri- bution to philosophy of science: first, the variety of materials in the (natural and artificial) world; second, extending the world by making new stuff; and, third, specific features of the relations between chemistry and physics. Keywords : philosophy of science, philosophy of chemistry, interdiscourse relations, making stuff, variety of substances . 1. Introduction Chemistry is unique and distinguishes itself from all other sciences, with respect to three broad issues: • A (variety of) stuff perspective, requiring conceptual analysis of the notion of stuff or material (Sections 4 and 5). • A making stuff perspective: the transformation of stuff by chemical reaction or phase transition (Section 6). • The pivotal role of the relations between chemistry and physics in connection with the question how everything fits together (Section 7). All themes in the philosophy of chemistry can be classified in one of these three clusters or make contributions to general philosophy of science that, as yet , are not particularly different from similar contributions from other sci- ences (Section 3). I do not exclude the possibility of there being more than three clusters of philosophical issues unique to philosophy of chemistry, but I am not aware of any as yet. Moreover, highlighting the issues discussed in Sections 5-7 does not mean that issues reviewed in Section 3 are less im- portant in revising the philosophy of science. -
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]. -
International Centre for Theoretical Physics
XA<? 6 H 0 <! W IC/95/320 INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS BOHM'S THEORY VERSUS DYNAMICAL REDUCTION G.C. Ghirardi and INTERNATIONAL ATOMIC ENERGY R. Grassi AGENCY UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION MIRAMARE-TRIESTE VQL 'l 7 Ha ° 7 IC/95/320 ABSTRACT International Atomic Energy Agency and United Nations Educational scientific and Cultural Organization made that theories which exhibit parameter , INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS BOHM'S THEORY VERSUS DYNAMICAL REDUCTION1 1. Introduction. We share today's widespread opinion that Standard Quantum Mechanics (SQM), in spite of its enormous successes, has failed in giving a G.C. Ghirardi satisfactory picture of the world, as we perceive it. The difficulties about International Centre for Theoretical Physics, Trieste, Italy, the conceptual foundations of the theory arising, as is well known, from and the so-called objectification problem, have stimulated various attempts to Department of Theoretical Physics. University di Trieste, Trieste, Italy overcome them. Among these one should mention the search for a and deterministic completion of the theory, the many worlds and many minds intepretations, the so called environment induced superselection rules, the R. Grassi quantum histories approach and the dynamical reduction program. In this Department of Civil Engineering, University of Udine, Udine, Italy. paper we will focus our attention on the only available and precisely formulated examples of a deterministic completion and of a stochastic and nonlinear modification of SQM, i.e., Bohm's theory and the spontaneous reduction models, respectively. It is useful to stress that while the first theory is fully equivalent, from a predictive point of view, to SQM, the second one qualifies itself as a rival of SQM but with empirical divergence so small that it can claim all the same experimental support. -
Quantum Theory Cannot Consistently Describe the Use of Itself
ARTICLE DOI: 10.1038/s41467-018-05739-8 OPEN Quantum theory cannot consistently describe the use of itself Daniela Frauchiger1 & Renato Renner1 Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here, we propose a Gedankenexperiment 1234567890():,; to investigate the question whether quantum theory can, in principle, have universal validity. The idea is that, if the answer was yes, it must be possible to employ quantum theory to model complex systems that include agents who are themselves using quantum theory. Analysing the experiment under this presumption, we find that one agent, upon observing a particular measurement outcome, must conclude that another agent has predicted the opposite outcome with certainty. The agents’ conclusions, although all derived within quantum theory, are thus inconsistent. This indicates that quantum theory cannot be extrapolated to complex systems, at least not in a straightforward manner. 1 Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland. Correspondence and requests for materials should be addressed to R.R. (email: [email protected]) NATURE COMMUNICATIONS | (2018) 9:3711 | DOI: 10.1038/s41467-018-05739-8 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-05739-8 “ 1”〉 “ 1”〉 irect experimental tests of quantum theory are mostly Here, | z ¼À2 D and | z ¼þ2 D denote states of D depending restricted to microscopic domains. Nevertheless, quantum on the measurement outcome z shown by the devices within the D “ψ ”〉 “ψ ”〉 theory is commonly regarded as being (almost) uni- lab. -
Arxiv:2004.01992V2 [Quant-Ph] 31 Jan 2021 Ity [6–20]
Hidden Variable Model for Universal Quantum Computation with Magic States on Qubits Michael Zurel,1, 2, ∗ Cihan Okay,1, 2, ∗ and Robert Raussendorf1, 2 1Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada 2Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada (Dated: February 2, 2021) We show that every quantum computation can be described by a probabilistic update of a proba- bility distribution on a finite phase space. Negativity in a quasiprobability function is not required in states or operations. Our result is consistent with Gleason's Theorem and the Pusey-Barrett- Rudolph theorem. It is often pointed out that the fundamental objects In Theorem 2, we apply this to quantum computation in quantum mechanics are amplitudes, not probabilities with magic states, showing that universal quantum com- [1, 2]. This fact notwithstanding, here we construct a de- putation can be classically simulated by the probabilistic scription of universal quantum computation|and hence update of a probability distribution. of all quantum mechanics in finite-dimensional Hilbert This looks all very classical, and therein lies a puzzle. spaces|in terms of a probabilistic update of a probabil- In fact, our Theorem 2 is running up against a number ity distribution. In this formulation, quantum algorithms of no-go theorems: Theorem 2 in [23] and the Pusey- look structurally akin to classical diffusion problems. Barrett-Rudolph (PBR) theorem [24] say that probabil- While this seems implausible, there exists a well-known ity representations for quantum mechanics do not exist, special instance of it: quantum computation with magic and [9{13] show that negativity in certain Wigner func- states (QCM) [3] on a single qubit. -
Introduction to Copyright and Licensing in an Open Access Environment
IOP publications Frequently asked questions Glossary Frequently asked questions Creative Commons Moral rights Creative Commons Assignment Open access Dealing with copyright works Introduction to copyright copyright.iop.org Introduction to Introduction open access environment access open copyright and licensing in an in licensing and copyright Introduction to copyright to Introduction works copyright with Dealing access Open Assignment Commons Creative Commons Creative questions asked Frequently Glossary questions asked Frequently publications IOP Moral rights rights Moral What is copyright? As soon as an idea is expressed in a physical medium, such as writing a paper, it qualifies for copyright protection. Copyright is a legal right that gives the copyright holder exclusive rights over how others use their work. The level and type of protection offered by copyright varies between countries. A form of intellectual property, copyright can be dealt with like other types of property – it can be acquired, disposed of or licensed. Copyright is time-limited. The period of protection varies, but in most countries a journal article created at the present time will be protected for between 50 and 70 years from the death of the last surviving author. By means of a number of local and international laws and conventions, copyright which arises in one country is recognised and protected in many others. Treatment of copyright in the digital environment is evolving at an unprecedented rate. Copyright exists to protect the rights of an owner of an original piece of work by imposing restrictions on reuse but it does not always fit well with how we use and share information in the digital sphere. -
Arxiv:2002.00255V3 [Quant-Ph] 13 Feb 2021 Lem (BVP)
A Path Integral approach to Quantum Fluid Dynamics Sagnik Ghosh Indian Institute of Science Education and Research, Pune-411008, India Swapan K Ghosh UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Kalina, Santacruz, Mumbai-400098, India ∗ (Dated: February 16, 2021) In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of non-linear, coupled partial differential equations (PDEs) simultaneously. We opt for a fundamentally different route. We first derive a general closed form expression for the Path Integral propagator valid for any general potential as a functional of the corresponding classical path. The method is exact and is applicable in many dimensions as well as multi-particle cases. This, then, is used to compute the Quantum Potential (QP), which, in turn, can generate the Quantum Trajectories. For cases, where closed form solution is not possible, the problem is formally boiled down to solving the classical path as a boundary value problem. The work formally bridges the Path Integral approach with Quantum Fluid Dynamics. As a model application to illustrate the method, we work out a toy model viz. the double-well potential, where the boundary value problem for the classical path has been computed perturbatively, but the Quantum part is left exact. Using this we delve into seeking insight in one of the long standing debates with regard to Quantum Tunneling. Keywords: Path Integral, Quantum Fluid Dynamics, Analytical Solution, Quantum Potential, Quantum Tunneling, Quantum Trajectories Submitted to: J. -
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. -
Arxiv:1909.06771V2 [Quant-Ph] 19 Sep 2019
Quantum PBR Theorem as a Monty Hall Game Del Rajan ID and Matt Visser ID School of Mathematics and Statistics, Victoria University of Wellington, Wellington 6140, New Zealand. (Dated: LATEX-ed September 20, 2019) The quantum Pusey{Barrett{Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a -ontic model (system's physical state) or to a -epistemic model (observer's knowledge about the system). We reformulate the PBR theorem as a Monty Hall game, and show that winning probabilities, for switching doors in the game, depend whether it is a -ontic or -epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved to quantum teleportation, in particular for improving reliability. Introduction: No-go theorems in quantum foundations Furthermore, concepts involved in the PBR proof have are vitally important for our understanding of quantum been used for a particular guessing game [43]. physics. Bell's theorem [1] exemplifies this by showing In this Letter, we reformulate the PBR theorem into that locally realistic models must contradict the experi- a Monty Hall game. This particular gamification of the mental predictions of quantum theory. theorem highlights that winning probabilities, for switch- There are various ways of viewing Bell's theorem ing doors in the game, depend on whether it is a -ontic through the framework of game theory [2]. These are or -epistemic game; we also show that in certain - commonly referred to as nonlocal games, and the best epistemic games switching doors provides no advantage. known example is the CHSH game; in this scenario the This may have consequences for an alternative experi- participants can win the game at a higher probability mental test of the PBR theorem. -
151545957.Pdf
Universit´ede Montr´eal Towards a Philosophical Reconstruction of the Dialogue between Modern Physics and Advaita Ved¯anta: An Inquiry into the Concepts of ¯ak¯a´sa, Vacuum and Reality par Jonathan Duquette Facult´ede th´eologie et de sciences des religions Th`ese pr´esent´ee `ala Facult´edes ´etudes sup´erieures en vue de l’obtention du grade de Philosophiae Doctor (Ph.D.) en sciences des religions Septembre 2010 c Jonathan Duquette, 2010 Universit´ede Montr´eal Facult´edes ´etudes sup´erieures et postdoctorales Cette th`ese intitul´ee: Towards A Philosophical Reconstruction of the Dialogue between Modern Physics and Advaita Ved¯anta: An Inquiry into the Concepts of ¯ak¯a´sa, Vacuum and Reality pr´esent´ee par: Jonathan Duquette a ´et´e´evalu´ee par un jury compos´edes personnes suivantes: Patrice Brodeur, pr´esident-rapporteur Trichur S. Rukmani, directrice de recherche Normand Mousseau, codirecteur de recherche Solange Lefebvre, membre du jury Varadaraja Raman, examinateur externe Karine Bates, repr´esentante du doyen de la FESP ii Abstract Toward the end of the 19th century, the Hindu monk and reformer Swami Vivekananda claimed that modern science was inevitably converging towards Advaita Ved¯anta, an important philosophico-religious system in Hinduism. In the decades that followed, in the midst of the revolution occasioned by the emergence of Einstein’s relativity and quantum physics, a growing number of authors claimed to discover striking “par- allels” between Advaita Ved¯anta and modern physics. Such claims of convergence have continued to the present day, especially in relation to quantum physics. In this dissertation, an attempt is made to critically examine such claims by engaging a de- tailed comparative analysis of two concepts: ¯ak¯a´sa in Advaita Ved¯anta and vacuum in quantum physics.