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The Intrinsic Structure of Quantum Mechanics

In Essays on the Metaphysics of Quantum Mechanics. New Brunswick, NJ: PhD dissertation, Rutgers University. pp. Chapter 1 (2019)

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  1. Mathematics and Metaphilosophy.Justin Clarke-Doane - 2022 - Cambridge: Cambridge University Press.
    This book discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the problem of explaining the (defeasible) justification of our mathematical beliefs (‘the justificatory challenge’), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the problem of explaining their reliability (‘the reliability challenge’), arises to the extent that we could have easily had different beliefs. The book shows that mathematical facts are not, in general, empirically accessible, contra Quine, (...)
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  • Morality and Mathematics.Justin Clarke-Doane - 2020 - Oxford, England: Oxford University Press.
    To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to (...)
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  • On Absolute Units.Neil Dewar - 2021 - British Journal for the Philosophy of Science.
    How may we characterize the intrinsic structure of physical quantities such as mass, length, or electric charge? This article shows that group-theoretic methods—specifically, the notion of a free and transitive group action—provide an elegant way of characterizing the structure of scalar quantities, and uses this to give an intrinsic treatment of vector quantities. It also gives a general account of how different scalar or vector quantities may be algebraically combined with one another. Finally, it uses this apparatus to give a (...)
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  • Wavefunction realism does not ‘privilege position’.David Schroeren - 2022 - Synthese 200 (1):1-14.
    It is common ground among proponents and detractors of wavefunction realism that the view ‘privileges position’, in the sense that it arbitrarily singles out one among a continuum infinity of wavefunction representations as characterizing the fundamental field: the position representation. This paper shows that, properly understood, wavefunction realism does not involve such an arbitrary choice. First, I argue that, though each wavefunction representation gives rise to a different version of wavefunction realism, the difference between these theories amounts to a mere (...)
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  • Symmetry fundamentalism in quantum mechanics.David Schroeren - 2021 - Philosophical Studies 178 (12):3995-4024.
    Modern particle physics suggests an intriguing vision of physical reality: we are to imagine the symmetries of the world as fundamental, whereas the material constituents of the world are ontologically derivative of them. This paper develops a novel ontology for non-relativistic quantum mechanics which gives precise metaphysical content to this vision.
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  • Symmetry Fundamentalism: A Case Study from Classical Physics.David Schroeren - 2020 - Philosophical Quarterly 71 (2):308-333.
    Physicists have suggested what I call symmetry fundamentalism: the view that symmetries are fundamental aspects of physical reality and that these aspects are more fundamental than what one might ordinarily think of as the fundamental building blocks of the world, such as elementary particles. The goal of this paper is to develop an ontology for classical particle mechanics that provides a precise instance of symmetry fundamentalism.
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  • Multi-field and Bohm’s theory.Davide Romano - 2020 - Synthese (11):29 June 2020.
    In the recent literature, it has been shown that the wave function in the de Broglie–Bohm theory can be regarded as a new kind of field, i.e., a "multi-field", in three-dimensional space. In this paper, I argue that the natural framework for the multi-field is the original second-order Bohm’s theory. In this context, it is possible: i) to construe the multi-field as a real-valued scalar field; ii) to explain the physical interaction between the multi-field and the Bohmian particles; and iii) (...)
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  • Invariance, intrinsicality and perspicuity.Caspar Jacobs - 2022 - Synthese 200 (2):1-17.
    It is now standard to interpret symmetry-related models of physical theories as representing the same state of affairs. Recently, a debate has sprung up around the question when this interpretational move is warranted. In particular, Møller-Nielsen :1253–1264, 2017) has argued that one is only allowed to interpret symmetry-related models as physically equivalent when one has a characterisation of their common content. I disambiguate two versions of this claim. On the first, a perspicuous interpretation is required: an account of the models’ (...)
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  • Hartry Field. Science Without Numbers: A Defense of Nominalism 2nd ed. [REVIEW]Geoffrey Hellman & Mary Leng - 2019 - Philosophia Mathematica 27 (1):139-148.
    FieldHartry. Science Without Numbers: A Defense of Nominalism 2nd ed.Oxford University Press, 2016. ISBN 978-0-19-877792-2. Pp. vi + 56 + vi + 111.
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  • The ethics–mathematics analogy.Justin Clarke-Doane - 2019 - Philosophy Compass 15 (1):e12641.
    Ethics and mathematics have long invited comparisons. On the one hand, both ethical and mathematical propositions can appear to be knowable a priori, if knowable at all. On the other hand, mathematical propositions seem to admit of proof, and to enter into empirical scientific theories, in a way that ethical propositions do not. In this article, I discuss apparent similarities and differences between ethical (i.e., moral) and mathematical knowledge, realistically construed -- i.e., construed as independent of human mind and languages. (...)
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  • Time's arrow and self‐locating probability.Eddy Keming Chen - 2021 - Philosophy and Phenomenological Research 105 (3):533-563.
    One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or the distant ''future''), (...)
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  • Realism about the wave function.Eddy Keming Chen - 2019 - Philosophy Compass 14 (7):e12611.
    A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review (...)
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  • 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 to Wave Function (...)
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  • Quantum Mechanics: Keeping It Real?Craig Callender - 2023 - British Journal for the Philosophy of Science 74 (4):837-851.
    This article is an introduction to and advertisement of Erwin Schrödinger’s little-known real-valued wave equation, the first published time dependent Schrödinger equation. I argue that this equation is not merely a historical curiosity. Not only does it show that quantum mechanics need not be viewed as essentially complex-valued, but the real formalism also provides a deep insight into the puzzling nature of time reversal in a quantum world. It is hoped that this observation will stimulate the discovery of other areas (...)
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  • The Theory of Every Thing: Toward a Symmetry-Based Metaphysics of Matter.David Schroeren - 2020 - Dissertation, Princeton University
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  • Essays on the Metaphysics of Quantum Mechanics.Eddy Keming Chen - 2019 - Dissertation, Rutgers University, New Brunswick
    What is the proper metaphysics of quantum mechanics? In this dissertation, I approach the question from three different but related angles. First, I suggest that the quantum state can be understood intrinsically as relations holding among regions in ordinary space-time, from which we can recover the wave function uniquely up to an equivalence class (by representation and uniqueness theorems). The intrinsic account eliminates certain conventional elements (e.g. overall phase) in the representation of the quantum state. It also dispenses with first-order (...)
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  • Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical Probabilities.Eddy Keming Chen - 2020 - In Valia Allori (ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature. World Scientific. pp. 479–515.
    In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...)
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  • Quantum States of a Time-Asymmetric Universe: Wave Function, Density Matrix, and Empirical Equivalence.Eddy Keming Chen - 2019 - Dissertation, Rutgers University - New Brunswick
    What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function but by a density matrix. I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories with (...)
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