About this topic
Summary All approaches to quantum theory need to make sense of the objective probabilities which apparently correspond to the square of the amplitudes of components of the quantum state.
Key works The Born rule connecting probabilities and squared-amplitudes was first formulated in Born 1926. The interpretation of probabilities varies widely across different approaches to quantum mechanics: as ever, Bell 1987 is indispensable in setting out the main options. Wallace 2012 provides an authoritative treatment of probability in Everettian QM.
Introductions Dickson 2011
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  1. Feyerabend on the Quantum Theory of Measurement: A Reassessment.Daniel Kuby & Patrick Fraser - 2022 - International Studies in the Philosophy of Science 35 (1):23-49.
    In 1957, Feyerabend delivered a paper titled ‘On the Quantum-Theory of Measurement’ at the Colston Research Symposium in Bristol to sketch a completion of von Neumann's measurement scheme without collapse, using only unitary quantum dynamics and well-motivated statistical assumptions about macroscopic quantum systems. Feyerabend's paper has been recognised as an early contribution to quantum measurement, anticipating certain aspects of decoherence. Our paper reassesses the physical and philosophical content of Feyerabend's contribution, detailing the technical steps as well as its overall philosophical (...)
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  2. The Stochastic-Quantum Correspondence.Jacob A. Barandes - manuscript
    This paper introduces an exact correspondence between a general class of stochastic systems and quantum theory. This correspondence provides a new framework for using Hilbert-space methods to formulate highly generic, non-Markovian types of stochastic dynamics, with potential applications throughout the sciences. This paper also uses the correspondence in the other direction to reconstruct quantum theory from physical models that consist of trajectories in configuration spaces undergoing stochastic dynamics. The correspondence thereby yields a new formulation of quantum theory, alongside the Hilbert-space, (...)
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  3. The Open Systems View.Michael E. Cuffaro & Stephan Hartmann - manuscript
    There is a deeply entrenched view in philosophy and physics, the closed systems view, according to which isolated systems are conceived of as fundamental. On this view, when a system is under the influence of its environment this is described in terms of a coupling between it and a separate system which taken together are isolated. We argue against this view, and in favor of the alternative open systems view, for which systems interacting with their environment are conceived of as (...)
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  4. Probabilities in deBroglie-Bohm Theory: Towards a Stochastic Alternative (Version 0.1 beta).Patrick Dürr & Alexander Ehmann - manuscript
    We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed. The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find it (...)
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  5. On classical finite probability theory as a quantum probability calculus.David Ellerman - manuscript
    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 are two parts. The notion of an "event" is reinterpreted from being an epistemological state of indefiniteness to being an objective state of indefiniteness. And the mathematical framework of finite probability theory is recast as the quantum probability calculus for QM/sets. The point is not to (...)
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  6. Does Protective Measurement Tell us Anything about Quantum Reality?Amit Hagar - manuscript
    An analysis of the two routes through which one may disentangle a quantum system from a measuring apparatus, hence protect the state vector of a single quantum system from being disturbed by the measurement, reveals several loopholes in the argument from protective measurement to the reality of the state vector of a single quantum system.
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  7. Principles of physical time directionality and fallacies of the conventional philosophy.Andrew Holster - manuscript
    These are the first two chapters from a monograph (The Time Flow Manifesto, Holster, 2013-14; unpublished), defending the concepts of time directionality and time flow in physics and naturalistic metaphysics, against long-standing attacks from the ‘conventional philosophy of physical time’. This monograph sets out to disprove twelve specific “fallacies of the conventional philosophy”, stated in the first section below. These are the foundational principles of the conventional philosophy, which developed in the mid-C20th from positivist-inspired studies. The first chapter begins by (...)
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  8. Putting probabilities first. How Hilbert space generates and constrains them.Michael Janas, Michael Cuffaro & Michel Janssen - manuscript
    We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of arbitrary (...)
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  9. The concept of probability in physics: an analytic version of von Mises’ interpretation.Louis Vervoort - manuscript
    In the following we will investigate whether von Mises’ frequency interpretation of probability can be modified to make it philosophically acceptable. We will reject certain elements of von Mises’ theory, but retain others. In the interpretation we propose we do not use von Mises’ often criticized ‘infinite collectives’ but we retain two essential claims of his interpretation, stating that probability can only be defined for events that can be repeated in similar conditions, and that exhibit frequency stabilization. The central idea (...)
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  10. QBism, the Perimeter of Quantum Bayesianism.Christopher A. Fuchs - 2010
    This article summarizes the Quantum Bayesian point of view of quantum mechanics, with special emphasis on the view's outer edges---dubbed QBism. QBism has its roots in personalist Bayesian probability theory, is crucially dependent upon the tools of quantum information theory, and most recently, has set out to investigate whether the physical world might be of a type sketched by some false-started philosophies of 100 years ago (pragmatism, pluralism, nonreductionism, and meliorism). Beyond conceptual issues, work at Perimeter Institute is focused on (...)
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  11. Quantum probability and decision theory, revisited [2002 online-only paper].David Wallace - 2002
    An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented which are based upon different decision theories and upon Gleason's Theorem. It is argued that decision theory gives Everettians most or all of what they need from `probability'. Contact is made with Lewis's Principal Principle linking subjective credence with objective chance: an Everettian Principal Principle is (...)
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  12. Causal potency of consciousness in the physical world.Danko D. Georgiev - forthcoming - International Journal of Modern Physics B:2450256.
    The evolution of the human mind through natural selection mandates that our conscious experiences are causally potent in order to leave a tangible impact upon the surrounding physical world. Any attempt to construct a functional theory of the conscious mind within the framework of classical physics, however, inevitably leads to causally impotent conscious experiences in direct contradiction to evolution theory. Here, we derive several rigorous theorems that identify the origin of the latter impasse in the mathematical properties of ordinary differential (...)
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  13. EPR, Bell and quantum probability.S. Gudder - forthcoming - Foundations of Physics.
  14. Conquering Mount Everett: Branch-Counting Versus the Born Rule.Jake Khawaja - forthcoming - British Journal for the Philosophy of Science.
    Abstract: This paper develops and advocates a rule for assigning self-locating credences in quantum branching scenarios, called Indexed Branch-Counting. It is argued that Indexed Branch-Counting can be justified on both accuracy-theoretic grounds and on the grounds that it satisfies a requirement of exchangeability for probability assignments. Since Indexed Branch-Counting diverges from the Born Rule, this poses trouble for Everettian approaches to probability. The paper also addresses a common argument against branch-counting, namely that the rule is incoherent in light of putative (...)
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  15. Negative-Energy Matter and the Direction of Time.J. C. Lindner - forthcoming
    This report offers a modern perspective on the problem of negative energy, based on a reexamination of the concept of time direction as it arises in a classical and quantum-mechanical context. From this analysis emerges an improved understanding of the general-relativistic stress-energy of matter as being a manifestation of local variations in the energy density of zero-point vacuum fluctuations. Based on those developments, a set of axioms is proposed from which are derived generalized gravitational field equations which actually constitute a (...)
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  16. The Measurement Problem is a Feature, Not a Bug – Schematising the Observer and the Concept of an Open System on an Informational, or (neo-)Bohrian, Approach.Michael E. Cuffaro - 2023 - Entropy 25:1410.
    I flesh out the sense in which the informational approach to interpreting quantum mechanics, as defended by Pitowsky and Bub and lately by a number of other authors, is (neo-)Bohrian. I argue that on this approach, quantum mechanics represents what Bohr called a “natural generalisation of the ordinary causal description” in the sense that the idea (which philosophers of science like Stein have argued for on the grounds of practical and epistemic necessity) that understanding a theory as a theory of (...)
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  17. The Physical Foundation of Quantum Theory.Mehran Shaghaghi - 2023 - Foundations of Physics 53 (1):1-36.
    The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems with only one adjustable property cannot carry more than a single message at a time. We demonstrate that this is true for the photons in the double-slit experiment, and that this is what leads to the fundamental limit on measuring the complementary aspect of the photons. Next, we illustrate that systems with a single adjustable property exhibit other quantum (...)
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  18. On quantum probability (о квантовой вероятности).Francois-Igor Pris - 2022 - ФИЛОСОФИЯ НАУКИ 3 (94):46-65.
  19. 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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  20. Is the Reality Criterion Analytic?Florian J. Boge & David Glick - 2021 - Erkenntnis 86 (6):1445-1451.
    Tim Maudlin has claimed that EPR’s Reality Criterion is analytically true. We argue that it is not. Moreover, one may be a subjectivist about quantum probabilities without giving up on objective physical reality. Thus, would-be detractors must reject QBism and other epistemic approaches to quantum theory on other grounds.
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  21. The View from a Wigner Bubble.Eric G. Cavalcanti - 2021 - Foundations of Physics 51 (2):1-31.
    In a recent no-go theorem [Bong et al., Nature Physics (2020)], we proved that the predictions of unitary quantum mechanics for an extended Wigner’s friend scenario are incompatible with any theory satisfying three metaphysical assumptions, the conjunction of which we call “Local Friendliness”: Absoluteness of Observed Events, Locality and No-Superdeterminism. In this paper (based on an invited talk for the QBism jubilee at the 2019 Växjö conference) I discuss the implications of this theorem for QBism, as seen from the point (...)
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  22. Bell’s Theorem, Quantum Probabilities, and Superdeterminism.Eddy Keming Chen - 2021 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. Routledge.
    In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.
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  23. The physics and metaphysics of Tychistic Bohmian Mechanics.Patrick Duerr & Alexander Ehmann - 2021 - Studies in History and Philosophy of Science Part A 90:168-183.
    The paper takes up Bell's “Everett theory” and develops it further. The resulting theory is about the system of all particles in the universe, each located in ordinary, 3-dimensional space. This many-particle system as a whole performs random jumps through 3N-dimensional configuration space – hence “Tychistic Bohmian Mechanics”. The distribution of its spontaneous localisations in configuration space is given by the Born Rule probability measure for the universal wavefunction. Contra Bell, the theory is argued to satisfy the minimal desiderata for (...)
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  24. Information causality, the Tsirelson bound, and the ‘being-thus’ of things.Michael E. Cuffaro - 2020 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 72:266-277.
    The principle of 'information causality' can be used to derive an upper bound---known as the 'Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. In this paper, however, I argue that the principle has not to date been sufficiently motivated to play this role; the motivations that have so far been given are either unsatisfactorily vague or else amount to little more than an appeal to intuition. I then consider how (...)
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  25. Reformulating Bell's theorem: The search for a truly local quantum theory.Mordecai Waegell & Kelvin J. McQueen - 2020 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 70:39-50.
    The apparent nonlocality of quantum theory has been a persistent concern. Einstein et al. and Bell emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this nonlocality, modern variations of the Everett-inspired many worlds interpretation try to circumvent it. In this paper, we review Bell's "no-go" theorem and explain how it rests on three axioms, local causality, no superdeterminism, and one world. Although Bell is often taken to have shown that local causality is ruled out by the (...)
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  26. The Nature of Contingency: Quantum Physics as Modal Realism.Alastair Wilson - 2020 - Oxford, UK: Oxford University Press.
    This book defends a radical new theory of contingency as a physical phenomenon. Drawing on the many-worlds approach to quantum theory and cutting-edge metaphysics and philosophy of science, it argues that quantum theories are best understood as telling us about the space of genuine possibilities, rather than as telling us solely about actuality. When quantum physics is taken seriously in the way first proposed by Hugh Everett III, it provides the resources for a new systematic metaphysical framework encompassing possibility, necessity, (...)
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  27. The best of many worlds, or, is quantum decoherence the manifestation of a disposition?Florian J. Boge - 2019 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 66 (C):135-144.
    In this paper I investigate whether the phenomenon of quantum decoherence, the vanishing of interference and detectable entanglement on quantum systems in virtue of interactions with the environment, can be understood as the manifestation of a disposition. I will highlight the advantages of this approach as a realist interpretation of the quantum formalism, and demonstrate how such an approach can benefit from advances in the metaphysics of dispositions. I will also confront some commonalities with and differences to the many worlds (...)
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  28. Quantum Information Versus Epistemic Logic: An Analysis of the Frauchiger–Renner Theorem.Florian J. Boge - 2019 - Foundations of Physics 49 (10):1143-1165.
    A recent no-go theorem (Frauchiger and Renner in Nat Commun 9(1):3711, 2018) establishes a contradiction from a specific application of quantum theory to a multi- agent setting. The proof of this theorem relies heavily on notions such as ‘knows’ or ‘is certain that’. This has stimulated an analysis of the theorem by Nurgalieva and del Rio (in: Selinger P, Chiribella G (eds) Proceedings of the 15th international conference on quantum physics and logic (QPL 2018). EPTCS 287, Open Publishing Association, Waterloo, (...)
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  29. In defence of the self-location uncertainty account of probability in the many-worlds interpretation.Kelvin J. McQueen & Lev Vaidman - 2019 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 66 (C):14-23.
    We defend the many-worlds interpretation of quantum mechanics against the objection that it cannot explain why measurement outcomes are predicted by the Born probability rule. We understand quantum probabilities in terms of an observer's self-location probabilities. We formulate a probability postulate for the MWI: the probability of self-location in a world with a given set of outcomes is the absolute square of that world's amplitude. We provide a proof of this postulate, which assumes the quantum formalism and two principles concerning (...)
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  30. Reality and the Probability Wave.Daniel Shanahan - 2019 - International Journal of Quantum Foundations 5:51-68.
    Effects associated in quantum mechanics with a divisible probability wave are explained as physically real consequences of the equal but opposite reaction of the apparatus as a particle is measured. Taking as illustration a Mach-Zehnder interferometer operating by refraction, it is shown that this reaction must comprise a fluctuation in the reradiation field of complementary effect to the changes occurring in the photon as it is projected into one or other path. The evolution of this fluctuation through the experiment will (...)
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  31. Reconsidering No-Go Theorems from a Practical Perspective.Michael E. Cuffaro - 2018 - British Journal for the Philosophy of Science 69 (3):633-655.
    I argue that our judgements regarding the locally causal models that are compatible with a given constraint implicitly depend, in part, on the context of inquiry. It follows from this that certain quantum no-go theorems, which are particularly striking in the traditional foundational context, have no force when the context switches to a discussion of the physical systems we are capable of building with the aim of classically reproducing quantum statistics. I close with a general discussion of the possible implications (...)
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  32. Simon Friederich: Interpreting Quantum Theory: A Therapeutic Approach: Palgrave Macmillan, New York, 2015, xiii + 202 pp. [REVIEW]Florian Boge - 2017 - Erkenntnis 82 (2):443-449.
    Simon Friederich’s Therapeutic Approach to quantum theory (QT) sheds new light on the status of the quantum state. In particular, Friederich presents revisionary ideas on how to exactly differentiate objective from subjective elements of the theory and thereby improves upon previous stabs at an epistemic interpretation of quantum states. The book not only provides interesting perspectives for the cognoscenti but is also written with sufficient care and free of unnecessary technicalities so as to be accessible and worth reading for the (...)
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  33. 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 calculus. The previous attempts (...)
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  34. 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 calculus. The previous attempts (...)
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  35. Reconditioning in Discrete Quantum Field Theory.Stan Gudder - 2017 - International Journal of Theoretical Physics, Springer-Verlag, USA, 122:1-14.
    AUTHOR: STAN GUDDER (John Evans Professor of Mathematical Physics, University of Denver, USA) -- -/- We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator S(x0,r) where x0 and r are positive integers representing time and maximal total energy, respectively. The operator S(x0,r) is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy (x0,r). In order to maintain total (...)
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  36. On the tension between ontology and epistemology in quantum probabilities.Amit Hagar - 2017 - In Lombardi (ed.), What is Quantum Information. Cambridge: CUP. pp. 147-178.
    For many among the scientifically informed public, and even among physicists, Heisenberg's uncertainty principle epitomizes quantum mechanics. Nevertheless, more than 86 years after its inception, there is no consensus over the interpretation, scope, and validity of this principle. The aim of this chapter is to offer one such interpretation, the traces of which may be found already in Heisenberg's letters to Pauli from 1926, and in Dirac's anticipation of Heisenberg's uncertainty relations from 1927, that stems form the hypothesis of finite (...)
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  37. Could Inelastic Interactions Induce Quantum Probabilistic Transitions?Nicholas Maxwell - 2017 - In Shan Gao (ed.), Collapse of the Wave Function. Cambridge: Cambridge University Press. pp. 257-273.
    What are quantum entities? Is the quantum domain deterministic or probabilistic? Orthodox quantum theory (OQT) fails to answer these two fundamental questions. As a result of failing to answer the first question, OQT is very seriously defective: it is imprecise, ambiguous, ad hoc, non-explanatory, inapplicable to the early universe, inapplicable to the cosmos as a whole, and such that it is inherently incapable of being unified with general relativity. It is argued that probabilism provides a very natural solution to the (...)
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  38. Is QBism the Future of Quantum Physics? [REVIEW]Kelvin McQueen - 2017 - Quantum Times 2017.
    The purpose of this book is to explain Quantum Bayesianism (‘QBism’) to “people without easy access to mathematical formulas and equations” (4-5). Qbism is an interpretation of quantum mechanics that “doesn’t meddle with the technical aspects of the theory [but instead] reinterprets the fundamental terms of the theory and gives them new meaning” (3). The most important motivation for QBism, enthusiastically stated on the book’s cover, is that QBism provides “a way past quantum theory’s paradoxes and puzzles” such that much (...)
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  39. Quantum Mechanics in a New Light.Ulrich J. Mohrhoff - 2017 - Foundations of Science 22 (3):517-537.
    Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence of their correlata, and having justified the distinction between a domain in which outcome-indicating events occur and a domain whose properties only exist if their existence is indicated by such events, it explains the difference between the two domains as essentially the difference between the manifested world (...)
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  40. The Quantum Doomsday Argument.Alastair Wilson - 2017 - British Journal for the Philosophy of Science 68 (2).
    If the most familiar overlapping interpretation of Everettian quantum mechanics is correct, then each of us is constantly splitting into multiple people. This consequence gives rise to the quantum doomsday argument, which threatens to draw crippling epistemic consequences from EQM. However, a diverging interpretation of EQM undermines the quantum doomsday argument completely. This appears to tell in favour of the diverging interpretation. But it is surprising that a metaphysical question that is apparently underdetermined by the physics should be settled by (...)
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  41. Quantum cognition and bounded rationality.Reinhard Blutner & Peter Beim Graben - 2016 - Synthese 193 (10).
    We consider several puzzles of bounded rationality. These include the Allais- and Ellsberg paradox, the disjunction effect, and related puzzles. We argue that the present account of quantum cognition—taking quantum probabilities rather than classical probabilities—can give a more systematic description of these puzzles than the alternate treatments in the traditional frameworks of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always provide a deeper understanding and a true explanation of these puzzles. One reason is that quantum approaches introduce additional (...)
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  42. The Quantum Mechanics of Being and Its Manifestation.Ulrich Mohrhoff - 2016 - Cosmology 24.
    How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is answered without invoking knowledge or observers, by interpreting the necessary distinction between two kinds of physical quantities - unconditionally definite quantities and quantities that have values only if they are measured - as a distinction between the manifested world and its manifestation.(The arXived version contains (...)
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  43. Quantum mechanics as a deterministic theory of a continuum of worlds.Kim Joris Boström - 2015 - Quantum Studies: Mathematics and Foundations 2 (3):315-347.
    A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of Everett’s (...)
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  44. Counting Steps: a Finitist Interpretation of Objective Probability in Physics.Amit Hagar & Giuseppe Sergioli - 2015 - Epistemologia 37 (2):262-275.
    We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the 'distance' (in terms of physical resources) from a physical state to another, and (3) the size of the set of time--complexity functions that are compatible with the physical (...)
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  45. Imprecise Probabilities in Quantum Mechanics.Stephan Hartmann - 2015 - In Colleen E. Crangle, Adolfo García de la Sienra & Helen E. Longino (eds.), Foundations and Methods from Mathematics to Neuroscience. Stanford: CSLI Publications. pp. 77-82.
    In his entry on "Quantum Logic and Probability Theory" in the Stanford Encyclopedia of Philosophy, Alexander Wilce (2012) writes that "it is uncontroversial (though remarkable) the formal apparatus quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over the 'quantum logic' of projection operators on a Hilbert space." For a long time, Patrick Suppes has opposed this view (see, for example, the paper collected (...)
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  46. Relating Bell’s Local Causality to the Causal Markov Condition.Gábor Hofer-Szabó - 2015 - Foundations of Physics 45 (9):1110-1136.
    The aim of the paper is to relate Bell’s notion of local causality to the Causal Markov Condition. To this end, first a framework, called local physical theory, will be introduced integrating spatiotemporal and probabilistic entities and the notions of local causality and Markovity will be defined. Then, illustrated in a simple stochastic model, it will be shown how a discrete local physical theory transforms into a Bayesian network and how the Causal Markov Condition arises as a special case of (...)
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  47. CHSH Inequality: Quantum Probabilities as Classical Conditional Probabilities.Andrei Khrennikov - 2015 - Foundations of Physics 45 (7):711-725.
    In this note we demonstrate that the results of observations in the EPR–Bohm–Bell experiment can be described within the classical probabilistic framework. However, the “quantum probabilities” have to be interpreted as conditional probabilities, where conditioning is with respect to fixed experimental settings. Our approach is based on the complete account of randomness involved in the experiment. The crucial point is that randomness of selections of experimental settings has to be taken into account within one consistent framework covering all events related (...)
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  48. Review of: Christopher G. Timpson, Quantum Information Theory and the Foundations of Quantum Mechanics. [REVIEW]Michael E. Cuffaro - 2014 - Philosophy of Science 81 (4):681-684,.
  49. Preface Special Issue Foundations of Physics.Dennis Dieks, Décio Krause & Christian de Ronde - 2014 - Foundations of Physics 44 (12):1245-1245.
    The foundations of quantum mechanics are attracting new and significant interest in the scientific community due to the recent striking experimental and technical progress in the fields of quantum computation, quantum teleportation and quantum information processing. However, at a more fundamental level the understanding and manipulation of these novel phenomena require not only new laboratory techniques but also new understanding, development and interpretation of the formalism of quantum mechanics itself, a mathematical structure whose connection to what happens in physical reality (...)
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  50. No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics.Ehtibar N. Dzhafarov & Janne V. Kujala - 2014 - Foundations of Physics 44 (3):248-265.
    Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov’s probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice–Bob EPR paradigm, non-contextuality means that the identity of Alice’s spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis $\alpha _{i}$ chosen by Alice, irrespective of Bob’s axis $\beta _{j}$ (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice’s (...)
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