Results for 'quantum mechanics Quantenmechanik'

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  1.  24
    Email: Unruh@ physics. Ubc. ca.is Quantum Mechanics Non-Local - 2002 - In T. Placek & J. Butterfield (eds.), Non-Locality and Modality. Kluwer Academic Publishers.
  2. Studien zum wissenschaftlichen Determinismus vor der Entstehung der Quantenmechanik. Von der klassischen Mechanik zur Philosophie Edgar Zilsels (“Studies in the history of scientific determinism before quantum mechanics. From classical mechanics to the philosophy of Edgar Zilsel”).Donata Romizi - 2013 - Dissertation, University of Vienna
  3.  95
    Quantum mechanics and macroscopic quantum phenomena: The case of superconductivity and superfluidity.Kostas Gavroglu & Yorgos Goudaroulis - 1989 - Zeitschrift Für Allgemeine Wissenschaftstheorie 20 (2):249-275.
    Supraleitfähigkeit und Superfluidität sind die einzigen bekannten makroskopischen Quantenphänomene. Ihre Untersuchung liefert interessante Hinweise, um einige der Fragen zu verstehen, die mit den Grenzen der Gültigkeit der Quantenmechanik verbunden sind. In diesem Aufsatz wollen wir den Prozeß entzifferen, durch den ein beobachtetes unerwartetes Phänomen in ein physikalisches Problem übergeführt wird, und wir zeigen die kontinuierliche Reinterpretation der Begriffe, um eine zufriedenstellende Erklärung der Supraleitfähigkeit und Superfluidität zu erreichen.
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  4.  38
    Potentiality, Actuality, and Quantum Mechanics.Boris Koznjak - 2007 - Prolegomena 6 (2):223-252.
    In this paper a possible interpretative value of Aristotle’s fundamental ontological doctrine of potentiality and actuality is considered in the context of operationally undoubtedly the most successful but interpretatively still controversial theory of modern physics – quantum mechanics – especially regarding understanding the nature of the world, the phenomena of which it describes and predicts so successfully. In particular, beings of the atomic world are interpreted as real potential beings actualized by the measurement process in appropriate experimental arrangement, (...)
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  5. Zur Quantenmechanik der Stoßvorgänge.Max Born - 1926 - Zeitschrift für Physik 37 (12):863-867.
    Durch eine Untersuchung der Stoßvorgänge wird die Auffassung entwickelt, daß die Quantenmechanik in der Schrödingerschen Form nicht nur die stationären Zustände, sondern auch die Quantensprünge zu beschreiben gestattet.
     
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  6. Quantum Theory: An Appraisal.Bohmian Mechanics - 1995 - Boston Studies in the Philosophy of Science 184.
  7. Gott würfelt nicht. Einsteins immer noch aktuelle Kritik der Quantenmechanik.Gregor Schiemann - 2005 - In J. Renn (ed.), Albert Einstein. Ingenieur des Universums. 100 Autoren für Einstein.
    Kaum eine Äußerung Einsteins ist so bekannt wie sein Wort, dass Gott nicht würfelt. In ähnlicher Weise, wie Einstein dies unerläutert gelassen hat, ist seine gesamte Position zur Quantenmechanik, auf die es sich bezieht, von Uneindeutigkeiten nicht frei geblieben. Für seine Würfelmetapher ergibt sich ein Spielraum von gegensätzlichen Sichtweisen. Sie lässt sich zum einen mit jüngeren Forschungsresultaten verbinden und weist zum anderen auf rückschrittliche Elemente in Einsteins Denken hin. Ich wende mich zuerst diesen Elementen zu und betrachte dann eine (...)
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  8. Warum Gott nicht würfelt: Einstein und die Quantenmechanik im Licht neuerer Forschungen.Gregor Schiemann - 2010 - In R. Breuniger (ed.), Bausteine zur Philosophie. Bd. 27: Einstein.
    Zuerst werden die Argumente rekonstruiert, die dafür sprechen, Einsteins Wort, dass Gott nicht würfelt, als Ausdruck eines überholten deterministischen Weltbildes anzusehen. Anschließend werden Forschungsergebnisse der letzten Jahrzehnte benannt, die für eine Neubewertung seiner Position zur dominanten Interpretation der Quantenmechanik sprechen. Den Abschluß bildet die Diskussion der Möglichkeiten einer Reinterpretation seines Satzes vom nicht würfelnden Gott.
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  9.  65
    Grete Henry-Hermann: Philosophie – Mathematik – Quantenmechanik : Texte Zur Naturphilosophie Und Erkenntnistheorie, Mathematisch-Physikalische Beiträge Sowie Ausgewählte Korrespondenz Aus den Jahren 1925 Bis 1982.Herrmann Kay (ed.) - 2019 - Wiesbaden: Springer Fachmedien Wiesbaden.
    This publication is an appreciation of the natural philosophy and epistemology of the philosopher Grete (Henry-)Hermann. A student of the mathematician Emmy Noether and the philosopher Leonard Nelson, she was one of the early interpreters of quantum mechanics. Werner Heisenberg memorialized her in his book "The Part and the Whole". For the first time, her writings on natural philosophy and epistemology are collected in one volume. An extensive introduction by various authors introduces the work of Grete Henry-Hermann. This (...)
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  10.  21
    Theodizee im Kontext der Quantenmechanik. Ein vielzitiertes Argument auf dem Prfstand.Anna Ijjas - 2011 - Neue Zeitschrift für Systematicsche Theologie Und Religionsphilosophie 53 (4):418-430.
    ZUSAMMENFASSUNGIm religionsphilosophischen Kontext wurde die Quantenmechanik vielfach bemht, das Argument der Willensfreiheit als naturwissenschaftliche Theorie zu sttzen. Der probabilistische Charakter der Theorie schien eine natrliche Basis fr den Indeterminismus und somit fr sittlich relevante Willensfreiheit zu bieten. Dieser Position wurde jedoch des fteren entgegen gehalten, dass erstens nur bestimmte Interpretationen der Quantenmechanik indeterministisch sind. Zweitens sollen mikroskopische Quanten-Effekte die makroskopische Hirndynamik nicht beeinflussen. Inzwischen mutet die Diskussion immer undurchschaubarer und themenspezifischer an, so dass eine sachgerechte Beurteilung geradezu als (...)
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  11.  5
    Quantum physics wthout quantum philosophy.Detlef Dürr - 2013 - New York: Springer. Edited by Sheldon Goldstein & Nino Zanghì.
    It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. (...)
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  12.  37
    Möglichkeit, Wirklichkeit und Quantenmechanik.Boris Koznjak - 2007 - Prolegomena 6 (2):223-252.
    In this paper a possible interpretative value of Aristotle’s fundamental ontological doctrine of potentiality and actuality is considered in the context of operationally undoubtedly the most successful but interpretatively still controversial theory of modern physics – quantum mechanics – especially regarding understanding the nature of the world, the phenomena of which it describes and predicts so successfully. In particular, beings of the atomic world are interpreted as real potential beings actualized by the measurement process in appropriate experimental arrangement, (...)
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  13. Realism in Context: The Examples of Lifeworld and Quantum Physics.Gregor Schiemann - 2009 - Human Affairs 19 (2):211-222.
    Lifeworld realism and quantum-physical realism are taken as experience-dependent conceptions of the world that become objects of explicit reflection when confronted with context-external discourses. After a brief sketch of the two contexts of experience—lifeworld and quantum physics—and their realist interpretations, I will discuss the quantum world from the perspective of lifeworld realism. From this perspective, the quantum world—roughly speaking—has to be either unreal or else constitute a different reality. Then, I invert the perspective and examine the (...)
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  14. Quantum Mechanics, Metaphysics, and Bohm's Implicate Order.George Williams - 2019 - Mind and Matter 2 (17):155-186.
    The persistent interpretation problem for quantum mechanics may indicate an unwillingness to consider unpalatable assumptions that could open the way toward progress. With this in mind, I focus on the work of David Bohm, whose earlier work has been more influential than that of his later. As I’ll discuss, I believe two assumptions play a strong role in explaining the disparity: 1) that theories in physics must be grounded in mathematical structure and 2) that consciousness must supervene on (...)
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  15.  74
    Translation of: W. Heisenberg, ‘Ist eine deterministische Ergänzung der Quantenmechanik möglich?’.Elise Crull & Guido Bacciagaluppi - unknown
    The publication of the EPR paper in 1935 prompted Heisenberg to draft a manuscript on the question of the completability of quantum mechanics. We give here the English translation of this manuscript with a brief introduction and bibliography.
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  16. What is Orthodox Quantum Mechanics?David Wallace - 2019 - In Alberto Cordero (ed.), Philosophers Look at Quantum Mechanics. Springer Verlag.
    What is called ``orthodox'' quantum mechanics, as presented in standard foundational discussions, relies on two substantive assumptions --- the projection postulate and the eigenvalue-eigenvector link --- that do not in fact play any part in practical applications of quantum mechanics. I argue for this conclusion on a number of grounds, but primarily on the grounds that the projection postulate fails correctly to account for repeated, continuous and unsharp measurements and that the eigenvalue-eigenvector link implies that virtually (...)
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  17. Quantum Mechanics and Experience.David Z. Albert - 1992 - Harvard Up.
    Presents a guide to the basics of quantum mechanics and measurement.
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  18.  7
    Quantum Mechanics Based on an Extended Least Action Principle and Information Metrics of Vacuum Fluctuations.Jianhao M. Yang - 2024 - Foundations of Physics 54 (3):1-31.
    We show that the formulations of non-relativistic quantum mechanics can be derived from an extended least action principle. The principle can be considered as an extension of the least action principle from classical mechanics by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a physical system needs to exhibit during its dynamics in order to be observable. Second, there is constant vacuum fluctuation along a classical trajectory. A novel method is introduced (...)
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  19. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?Albert Einstein, Boris Podolsky & Nathan Rosen - 1935 - Physical Review (47):777-780.
  20. Quantum Mechanics on Spacetime I: Spacetime State Realism.David Wallace & Christopher Gordon Timpson - 2010 - British Journal for the Philosophy of Science 61 (4):697-727.
    What ontology does realism about the quantum state suggest? The main extant view in contemporary philosophy of physics is wave-function realism . We elaborate the sense in which wave-function realism does provide an ontological picture, and defend it from certain objections that have been raised against it. However, there are good reasons to be dissatisfied with wave-function realism, as we go on to elaborate. This motivates the development of an opposing picture: what we call spacetime state realism , a (...)
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  21. Quantum Mechanics and 3 N - Dimensional Space.Bradley Monton - 2006 - Philosophy of Science 73 (5):778-789.
    I maintain that quantum mechanics is fundamentally about a system of N particles evolving in three-dimensional space, not the wave function evolving in 3N-dimensional space.
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  22.  24
    The Quantum Mechanics of Minds and Worlds.Jeffrey A. Barrett - 1999 - Oxford, GB: Oxford University Press UK.
    Jeffrey Barrett presents the most comprehensive study yet of a problem that has puzzled physicists and philosophers since the 1930s. Quantum mechanics is in one sense the most successful physical theory ever, accurately predicting the behaviour of the basic constituents of matter. But it has an apparent ambiguity or inconsistency at its heart; Barrett gives a careful, clear, and challenging evaluation of attempts to deal with this problem.
  23.  20
    The Quantum Mechanics of Minds and Worlds.Jeffrey A. Barrett - 1999 - Oxford, GB: Oxford University Press UK.
    Jeffrey Barrett presents the most comprehensive study yet of a problem that has puzzled physicists and philosophers since the 1930s. The standard theory of quantum mechanics is in one sense the most successful physical theory ever, predicting the behaviour of the basic constituents of all physical things; no other theory has ever made such accurate empirical predictions. However, if one tries to understand the theory as providing a complete and accurate framework for the description of the behaviour of (...)
  24. Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State.Eddy Keming Chen - 2021 - British Journal for the Philosophy of Science 72 (4):1155–1183.
    In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast (...)
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  25. Quantum mechanics and consciousness.G. D. Wasserman - 1983 - Nature and System 5 (March-June):3-16.
  26.  86
    Quantum Mechanics Between Ontology and Epistemology.Florian J. Boge - 2018 - Cham: Springer (European Studies in Philosophy of Science).
    This book explores the prospects of rivaling ontological and epistemic interpretations of quantum mechanics (QM). It concludes with a suggestion for how to interpret QM from an epistemological point of view and with a Kantian touch. It thus refines, extends, and combines existing approaches in a similar direction. -/- The author first looks at current, hotly debated ontological interpretations. These include hidden variables-approaches, Bohmian mechanics, collapse interpretations, and the many worlds interpretation. He demonstrates why none of these (...)
  27. Time, quantum mechanics, and tense.Simon Saunders - 1996 - Synthese 107 (1):19 - 53.
    The relational approach to tense holds that the now, passage, and becoming are to be understood in terms of relations between events. The debate over the adequacy of this framework is illustrated by a comparative study of the sense in which physical theories, (in)deterministic and (non)relativistic, can lend expression to the metaphysics at issue. The objective is not to settle the matter, but to clarify the nature of this metaphysics and to establish that the same issues are at stake in (...)
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  28.  84
    Quantum mechanics over sets: a pedagogical model with non-commutative finite probability theory as its quantum probability calculus.David Ellerman - 2017 - Synthese (12):4863-4896.
    This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability (...)
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  29.  73
    Quantum Mechanics: Ontology Without Individuals.Newton da Costa & Olimpia Lombardi - 2014 - Foundations of Physics 44 (12):1246-1257.
    The purpose of the present paper is to consider the traditional interpretive problems of quantum mechanics from the viewpoint of a modal ontology of properties. In particular, we will try to delineate a quantum ontology that (i) is modal, because describes the structure of the realm of possibility, and (ii) lacks the ontological category of individual. The final goal is to supply an adequate account of quantum non-individuality on the basis of this ontology.
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  30. On the quantum mechanics of dreams and the emergence of self-awareness.Fred Alan Wolf - 1996 - In Stuart R. Hameroff, Alfred W. Kaszniak & Alwyn Scott (eds.), Toward a Science of Consciousness: The First Tucson Discussions and Debates. MIT Press.
  31.  8
    Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony.James T. Cushing - 1994 - University of Chicago Press.
    Why does one theory "succeed" while another, possibly clearer interpretation, fails? By exploring two observationally equivalent yet conceptually incompatible views of quantum mechanics, James T. Cushing shows how historical contingency can be crucial to determining a theory's construction and its position among competing views. Since the late 1920s, the theory formulated by Niels Bohr and his colleagues at Copenhagen has been the dominant interpretation of quantum mechanics. Yet an alternative interpretation, rooted in the work of Louis (...)
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  32.  50
    The Quantum Mechanics of Minds and Worlds.Jeffrey Alan Barrett - 1999 - Oxford, GB: Oxford University Press.
    Jeffrey Barrett presents the most comprehensive study yet of a problem that has puzzled physicists and philosophers since the 1930s.
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  33. Quantum Mechanics is About Quantum Information.Jeffrey Bub - 2005 - Foundations of Physics 35 (4):541-560.
    I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive—just as, following Einstein’s special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical primitive in its own right.
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  34.  36
    Emergent quantum mechanics : David Bohm Centennial perspectives.Jan Walleczek, Gerhard Grössing, Paavo Pylkkänen & Basil Hiley - 2019 - Entropy 21 (2).
    Emergent quantum mechanics (EmQM) explores the possibility of an ontology for quantum mechanics. The resurgence of interest in realist approaches to quantum mechanics challenges the standard textbook view, which represents an operationalist approach. The possibility of an ontological, i.e., realist, quantum mechanics was first introduced with the original de Broglie-Bohm theory, which has also been developed in another context as Bohmian mechanics. This Editorial introduces a Special Issue featuring contributions which were (...)
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  35. Relational quantum mechanics and the determinacy problem.Matthew J. Brown - 2009 - British Journal for the Philosophy of Science 60 (4):679-695.
    Carlo Rovelli's relational interpretation of quantum mechanics holds that a system's states or the values of its physical quantities as normally conceived only exist relative to a cut between a system and an observer or measuring instrument. Furthermore, on Rovelli's account, the appearance of determinate observations from pure quantum superpositions happens only relative to the interaction of the system and observer. Jeffrey Barrett ([1999]) has pointed out that certain relational interpretations suffer from what we might call the (...)
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  36. How Quantum Mechanics Can Consistently Describe the Use of Itself.Dustin Lazarovici & Mario Hubert - 2019 - Scientific Reports 470 (9):1-8.
    We discuss the no-go theorem of Frauchiger and Renner based on an "extended Wigner's friend" thought experiment which is supposed to show that any single-world interpretation of quantum mechanics leads to inconsistent predictions if it is applicable on all scales. We show that no such inconsistency occurs if one considers a complete description of the physical situation. We then discuss implications of the thought experiment that have not been clearly addressed in the original paper, including a tension between (...)
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  37. Time, quantum mechanics, and probability.Simon Saunders - 1998 - Synthese 114 (3):373-404.
    A variety of ideas arising in decoherence theory, and in the ongoing debate over Everett's relative-state theory, can be linked to issues in relativity theory and the philosophy of time, specifically the relational theory of tense and of identity over time. These have been systematically presented in companion papers (Saunders 1995; 1996a); in what follows we shall consider the same circle of ideas, but specifically in relation to the interpretation of probability, and its identification with relations in the Hilbert Space (...)
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  38. Quantum Mechanics and Experience.[author unknown] - 1994 - Erkenntnis 40 (3):403-406.
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  39. Quantum mechanics over sets: a pedagogical model with non-commutative finite probability theory as its quantum probability calculus.David Ellerman - 2017 - Synthese (12).
    This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability (...)
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  40.  26
    Relational Quantum Mechanics is About Facts, Not States: A Reply to Pienaar and Brukner.Andrea Di Biagio & Carlo Rovelli - 2022 - Foundations of Physics 52 (3):1-21.
    In recent works, Časlav Brukner and Jacques Pienaar have raised interesting objections to the relational interpretation of quantum mechanics. We answer these objections in detail and show that, far from questioning the viability of the interpretation, they sharpen and clarify it.
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  41. Quantum mechanics and Priority Monism.Claudio Calosi - 2014 - Synthese 191 (5):915-928.
    The paper address the question of whether quantum mechanics (QM) favors Priority Monism, the view according to which the Universe is the only fundamental object. It develops formal frameworks to frame rigorously the question of fundamental mereology and its answers, namely (Priority) Pluralism and Monism. It then reconstructs the quantum mechanical argument in favor of the latter and provides a detailed and thorough criticism of it that sheds furthermore new light on the relation between parthood, composition and (...)
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  42.  98
    Relational quantum mechanics.Federico Laudisa - 2008 - Stanford Encyclopedia of Philosophy.
    Relational quantum mechanics is an interpretation of quantum theory which discards the notions of absolute state of a system, absolute value of its physical quantities, or absolute event. The theory describes only the way systems affect each other in the course of physical interactions. State and physical quantities refer always to the interaction, or the relation, between two systems. Nevertheless, the theory is assumed to be complete. The physical content of quantum theory is understood as expressing (...)
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  43. Quantum Mechanics and Experience.[author unknown] - 1995 - British Journal for the Philosophy of Science 46 (2):253-260.
     
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  44.  87
    Quantum Mechanics and Fundamentality: Naturalizing Quantum Theory between Scientific Realism and Ontological Indeterminacy.Valia Allori (ed.) - 2022 - Cham: Springer.
    This edited collection provides new perspectives on some metaphysical questions arising in quantum mechanics. These questions have been long-standing and are of continued interest to researchers and graduate students working in physics, philosophy of physics and metaphysics. It features contributions from a diverse set of researchers, ranging from senior scholars to junior academics, working in varied fields, from physics to philosophy of physics and metaphysics. The contributors reflect on issues about fundamentality (is quantum theory fundamental? If so, (...)
  45.  80
    Quantum mechanical interaction-free measurements.Avshalom C. Elitzur & Lev Vaidman - 1993 - Foundations of Physics 23 (7):987-997.
    A novel manifestation of nonlocality of quantum mechanics is presented. It is shown that it is possible to ascertain the existence of an object in a given region of space without interacting with it. The method might have practical applications for delicate quantum experiments.
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  46.  67
    Quantum mechanics, time, and theology: Indefinite causal order and a new approach to salvation.Emily Qureshi-Hurst & Anna Pearson - 2020 - Zygon 55 (3):663-684.
    Quantum mechanics has recently indicated that, at the fundamental level, temporal order is not fixed. This phenomenon, termed Indefinite Causal Order, is yet to receive metaphysical or theological engagement. We examine Indefinite Causal Order, particularly as it emerges in a 2018 photonic experiment. In this experiment, two operations A and B were shown to be in a superposition with regard to their causal order. Essentially, time, intuitively understood as fixed, flowing, and fundamental, becomes fuzzy. We argue that if (...)
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  47. Quantum mechanics, orthogonality, and counting.Peter J. Lewis - 1997 - British Journal for the Philosophy of Science 48 (3):313-328.
    In quantum mechanics it is usually assumed that mutually exclusives states of affairs must be represented by orthogonal vectors. Recent attempts to solve the measurement problem, most notably the GRW theory, require the relaxation of this assumption. It is shown that a consequence of relaxing this assumption is that arithmatic does not apply to ordinary macroscopic objects. It is argued that such a radical move is unwarranted given the current state of understanding of the foundations of quantum (...)
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  48.  61
    Relativity, Quantum Mechanics and EPR.Robert Clifton, Constantine Pagonis & Itamar Pitowsky - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992 (Volume One: Contributed Papers):114 - 128.
    The Einstein-Podolsky-Rosen argument for the incompleteness of quantum mechanics involves two assumptions: one about locality and the other about when it is legitimate to infer the existence of an element-of-reality. Using one simple thought experiment, we argue that quantum predictions and the relativity of simultaneity require that both these assumptions fail, whether or not quantum mechanics is complete.
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  49. Everettian quantum mechanics without branching time.Alastair Wilson - 2012 - Synthese 188 (1):67-84.
    In this paper I assess the prospects for combining contemporary Everettian quantum mechanics (EQM) with branching-time semantics in the tradition of Kripke, Prior, Thomason and Belnap. I begin by outlining the salient features of ‘decoherence-based’ EQM, and of the ‘consistent histories’ formalism that is particularly apt for conceptual discussions in EQM. This formalism permits of both ‘branching worlds’ and ‘parallel worlds’ interpretations; the metaphysics of EQM is in this sense underdetermined by the physics. A prominent argument due to (...)
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  50. Quantum mechanics in terms of realism.Arthur Jabs - 2017 - arXiv.Org.
    We expound an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new interpretation is formulated in the language of epistemological realism. It involves a change in some basic physical concepts. The ψ function is no longer interpreted as a probability amplitude of the observed behaviour of elementary particles but as an objective physical field representing the particles themselves. The particles are thus extended objects whose extension varies in time (...)
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