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The Conceptual Foundations of Quantum Mechanics

Oxford, UK: Oxford University Press (2019)

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  1. Everettian Mechanics with Hyperfinitely Many Worlds.Jeffrey Barrett & Isaac Goldbring - 2022 - Erkenntnis 89 (4):1-20.
    The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.
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  • Spin and Contextuality in Extended de Broglie-Bohm-Bell Quantum Mechanics.Jeroen C. Vink - 2022 - Foundations of Physics 52 (5):1-27.
    This paper introduces an extension of the de Broglie-Bohm-Bell formulation of quantum mechanics, which includes intrinsic particle degrees of freedom, such as spin, as elements of reality. To evade constraints from the Kochen-Specker theorem the discrete spin values refer to a specific basis – i.e., a single spin vector orientation for each particle; these spin orientations are, however, not predetermined, but dynamic and guided by the wave function of the system, which is conditional on the realized location values of the (...)
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  • Quantum Equilibrium in Stochastic de Broglie–Bohm–Bell Quantum Mechanics.Jeroen C. Vink - 2023 - Foundations of Physics 53 (1):1-19.
    This paper investigates dynamical relaxation to quantum equilibrium in the stochastic de Broglie–Bohm–Bell formulation of quantum mechanics. The time-dependent probability distributions are computed as in a Markov process with slowly varying transition matrices. Numerical simulations, supported by exact results for the large-time behavior of sequences of (slowly varying) transition matrices, confirm previous findings that indicate that de Broglie–Bohm–Bell dynamics allows an arbitrary initial probability distribution to relax to quantum equilibrium; i.e., there is no need to make the ad-hoc assumption that (...)
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  • One world is (probably) just as good as many.Jer Steeger - 2022 - Synthese 200 (97):1-32.
    One of our most sophisticated accounts of objective chance in quantum mechanics involves the Deutsch-Wallace theorem, which uses state-space symmetries to justify agents’ use of the Born rule when the quantum state is known. But Wallace argues that this theorem requires an Everettian approach to measurement. I find that this argument is unsound. I demonstrate a counter-example by applying the Deutsch-Wallace theorem to the de Broglie-Bohm pilot-wave theory.
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  • Particles, fields, and the measurement of electron spin.Charles T. Sebens - 2020 - Synthese 198 (12):11943-11975.
    This article compares treatments of the Stern–Gerlach experiment across different physical theories, building up to a novel analysis of electron spin measurement in the context of classical Dirac field theory. Modeling the electron as a classical rigid body or point particle, we can explain why the entire electron is always found at just one location on the detector but we cannot explain why there are only two locations where the electron is ever found. Using non-relativistic or relativistic quantum mechanics, we (...)
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  • Quantum mechanics.Jenann Ismael - 2008 - Stanford Encyclopedia of Philosophy.
    Quantum mechanics is, at least at first glance and at least in part, a mathematical machine for predicting the behaviors of microscopic particles — or, at least, of the measuring instruments we use to explore those behaviors — and in that capacity, it is spectacularly successful: in terms of power and precision, head and shoulders above any theory we have ever had. Mathematically, the theory is well understood; we know what its parts are, how they are put together, and why, (...)
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