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 2004 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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309 found
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1 — 50 / 309
  1. added 2020-04-27
    The Mechanism Behind Probability.Sydney Ernest Grimm - manuscript
    Changes within observable reality at the lowest level of reality seem to occur in accordance with the probability theory in mathematics. It is quite remarkable that nature itself has chosen the probability theory to arrange all the changes within the structure of the basic quantum fields. This rises a question about the distribution of properties in space and time.
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  2. added 2020-03-16
    Quantum Theory Without Hilbert Spaces.C. Anastopoulos - 2001 - Foundations of Physics 31 (11):1545-1580.
    Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence functional, introduced by the consistent histories approach to quantum theory. The acceptance of relative phases as a primitive ingredient of any quantum theory, (...)
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  3. added 2020-03-11
    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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  4. added 2020-03-11
    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 66:14-23.
    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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  5. added 2020-02-11
    Studies in the Foundations of Quantum Mechanics.Allen Stairs - 1982 - Philosophy of Science 49 (3):481-484.
  6. added 2020-02-03
    The Ontic Probability Interpretation of Quantum Theory - Part II: Einstein's Incompleteness/Nonlocality Dilemma.Felix Alba-Juez - manuscript
    After pinpointing a conceptual confusion (TCC), a Reality preconception (TRP1), and a fallacious dichotomy (TFD), the famous EPR/EPRB argument for correlated ‘particles’ is studied in the light of the Ontic Probability Interpretation (TOPI) of Quantum Theory (QT). Another Reality preconception (TRP2) is identified, showing that EPR used and ignored QT predictions in a single paralogism. Employing TFD and TRP2, EPR unveiled a contradiction veiled in its premises. By removing nonlocality from QT’s Ontology by fiat, EPR preordained its incompleteness. The Petitio (...)
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  7. added 2020-02-03
    The Ontic Probability Interpretation of Quantum Theory - Part I: The Meaning of Einstein's Incompleteness Claim.Felix Alba-Juez - manuscript
    Ignited by Einstein and Bohr a century ago, the philosophical struggle about Reality is yet unfinished, with no signs of a swift resolution. Despite vast technological progress fueled by the iconic EPR paper (EPR), the intricate link between ontic and epistemic aspects of Quantum Theory (QT) has greatly hindered our grip on Reality and further progress in physical theory. Fallacies concealed by tortuous logical negations made EPR comprehension much harder than it could have been had Einstein written it himself in (...)
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  8. added 2019-12-26
    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. added 2019-11-05
    Is the Reality Criterion Analytic?David Glick & Florian J. Boge - forthcoming - Erkenntnis:1-7.
    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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  10. added 2019-11-05
    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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  11. added 2019-06-06
    Decision Theory and Information Propagation in Quantum Physics.Alan Forrester - 2007 - Studies in History and Philosophy of Modern Physics 38 (4):815-831.
    In recent papers, Zurek [(2005). Probabilities from entanglement, Born's rule pk=|ψk|2 from entanglement. Physical Review A, 71, 052105] has objected to the decision-theoretic approach of Deutsch [(1999) Quantum theory of probability and decisions. Proceedings of the Royal Society of London A, 455, 3129–3137] and Wallace [(2003). Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation. Studies in History and Philosophy of Modern Physics, 34, 415–438] to deriving the Born rule for quantum probabilities on the grounds that it courts (...)
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  12. added 2019-06-06
    Probability, Arrow of Time and Decoherence.Guido Bacciagaluppi - 2006 - Studies in History and Philosophy of Modern Physics 38 (2):439-456.
    This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard approach to time symmetry in the decoherent histories literature is criticised, and an alternative approach is proposed, based on two decoherence conditions within the one-vector formalism. In turn, considerations of forwards (...)
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  13. added 2019-06-06
    The Emergence of the Macroworld: A Study of Intertheory Relations in Classical and Quantum Mechanics.Malcolm R. Forster & Alexey Kryukov - 2003 - Philosophy of Science 70 (5):1039-1051.
    Classical mechanics is empirically successful because the probabilistic mean values of quantum mechanical observables follow the classical equations of motion to a good approximation (Messiah 1970, 215). We examine this claim for the one-dimensional motion of a particle in a box, and extend the idea by deriving a special case of the ideal gas law in terms of the mean value of a generalized force used to define "pressure." The examples illustrate the importance of probabilistic averaging as a method of (...)
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  14. added 2019-06-05
    Stephen L. Adler, Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory. Cambridge: Cambridge University Press , 283 Pp., $50.00. [REVIEW]GianCarlo Ghirardi - 2005 - Philosophy of Science 72 (4):642-645.
  15. added 2019-06-05
    The Shaky Game: Einstein, Realism, and the Quantum Theory. Arthur Fine.Paul Teller - 1988 - Philosophy of Science 55 (1):155-156.
  16. added 2019-05-17
    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, 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.
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  17. added 2019-02-14
    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 66:135-144.
    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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  18. added 2019-01-28
    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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  19. added 2019-01-28
    Category-Theoretic Analysis of the Notion of Complementarity for Quantum Systems.Elias Zafiris - 2006 - International Journal of General Systems 35 (1):69-89.
    In this paper we adopt a category-theoretic viewpoint in order to analyze the semantics of complementarity for quantum systems. Based on the existence of a pair of adjoint functors between the topos of presheaves of the Boolean kind of structure and the category of the quantum kind of structure, we establish a twofold complementarity scheme which constitutes an instance of the concept of adjunction. It is further argued that the established scheme is inextricably connected with a realistic philosophical attitude, although (...)
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  20. added 2019-01-28
    Sheaf-Theoretic Representation of Quantum Measure Algebras.Elias Zafiris - 2006 - Journal of Mathematical Physics 47 (9).
    We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization at the level of (...)
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  21. added 2019-01-22
    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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  22. added 2018-09-06
    Information Causality, the Tsirelson Bound, and the 'Being-Thus' of Things.Michael E. Cuffaro - forthcoming - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics.
    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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  23. added 2018-06-12
    Van Fraassen and Ruetsche on Preparation and Measurement.Bradley Monton - 1999 - Philosophy of Science 66 (3):91.
    Ruetsche (1996) has argued that van Fraassen's (1991) Copenhagen Variant of the Modal Interpretation (CVMI) gives unsatisfactory accounts of measurement and of state preparation. I defend the CVMI against Ruetsche's first argument by using decoherence to show that the CVMI does not need to account for the measurement scenario which Ruetsche poses. I then show, however, that there is a problem concerning preparation, and the problem is more serious than the one Ruetsche focuses on. The CVMI makes no substantive predictions (...)
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  24. added 2018-05-29
    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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  25. added 2018-02-18
    John von Neumann's Mathematical “Utopia” in Quantum Theory.Giovanni Valente - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):860-871.
    This paper surveys John von Neumann's work on the mathematical foundations of quantum theories in the light of Hilbert's Sixth Problem concerning the geometrical axiomatization of physics. We argue that in von Neumann's view geometry was so tied to logic that he ultimately developed a logical interpretation of quantum probabilities. That motivated his abandonment of Hilbert space in favor of von Neumann algebras, specifically the type II1II1 factors, as the proper limit of quantum mechanics in infinite dimensions. Finally, we present (...)
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  26. added 2018-02-17
    The Emergent Multiverse: Quantum Theory According to the Everett Interpretation.David Wallace - 2012 - Oxford University Press.
    David Wallace argues that we should take quantum theory seriously as an account of what the world is like--which means accepting the idea that the universe is constantly branching into new universes. He presents an accessible but rigorous account of the 'Everett interpretation', the best way to make coherent sense of quantum physics.
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  27. added 2018-02-17
    On Predictions in Retro-Causal Interpretations of Quantum Mechanics.Joseph Berkovitz - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):709-735.
  28. added 2018-02-17
    Quantum Probability From Subjective Likelihood: Improving on Deutsch's Proof of the Probability Rule.David Wallace - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):311-332.
    I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but the proof is simpler and proceeds from weaker decision-theoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.
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  29. added 2018-02-17
    Probability in GRW Theory.Roman Frigg & Carl Hoefer - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):371-389.
    GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single (...)
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  30. added 2018-02-17
    Measurement Outcomes and Probability in Everettian Quantum Mechanics.David J. Baker - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (1):153-169.
    The decision-theoretic account of probability in the Everett or many-worlds interpretation, advanced by David Deutsch and David Wallace, is shown to be circular. Talk of probability in Everett presumes the existence of a preferred basis to identify measurement outcomes for the probabilities to range over. But the existence of a preferred basis can only be established by the process of decoherence, which is itself probabilistic.
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  31. added 2018-02-17
    Does Probabilism Solve the Great Quantum Mystery?Nicholas Maxwell - 2004 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 19 (3):321-336.
    What sort of entities are electrons, photons and atoms given their wave-like and particle-like properties? Is nature fundamentally deterministic or probabilistic? Orthodox quantum theory evades answering these two basic questions by being a theory about the results of performing measurements on quantum systems. But this evasion results in OQT being a seriously defective theory. A rival, somewhat ignored strategy is to conjecture that the quantum domain is fundamentally probabilistic. This means quantum entities, interacting with one another probabilistically, must differ radically (...)
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  32. added 2018-02-17
    Everettian Rationality: Defending Deutsch's Approach to Probability in the Everett Interpretation.David Wallace - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):415-439.
    An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the Everett interpretation, and that in this context, it essentially succeeds. Some comments are made about the criticism of Deutsch's proof by Barnum, Caves, Finkelstein, Fuchs, and Schack; it is argued that the flaw which they point out in the proof does not apply if the Everett interpretation is assumed.
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  33. added 2018-02-17
    What Econometrics Cannot Teach Quantum Mechanics.Joseph Berkovitz - 1995 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 26 (2):163-200.
    Cartwright and Humphreys have suggested theories of probabilistic causation for singular events, which are based on modifications of traditional causal linear modelling. On the basis of her theory, Cartwright offered an allegedly local, and non-factorizable, common-cause model for the EPR experiment. In this paper I consider Cartwright's and Humphreys' theories. I argue that, provided plausible assumptions obtain, local models for EPR in the framework of these theories are committed to Bell inequalities, which are violated by experiment.
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  34. added 2018-02-16
    A Loose and Separate Certainty: Caves, Fuchs and Schack on Quantum Probability One.Allen Stairs - 2011 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (3):158-166.
  35. added 2017-09-21
    Probabilistic Inequalities And Upper Probabilities In Quantum Mechanical Entanglement.J. De Barros & Patrick Suppes - 2010 - Manuscrito 33 (1):55-71.
    In this paper we analyze the existence of joint probabilities for the Bell-type and GHZ entangled states. We then propose the usage of nonmonotonic upper probabilities as a tool to derive consistent joint upper probabilities for the contextual hidden variables. Finally, we show that for the extreme example of no error, the GHZ state allows for the definition of a joint upper probability that is consistent with the strong correlations.
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  36. added 2017-07-07
    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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  37. added 2017-05-06
    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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  38. added 2017-02-24
    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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  39. added 2017-02-15
    EPR, Bell and Quantum Probability.S. Gudder - forthcoming - Foundations of Physics.
  40. added 2017-02-14
    Does Chance Hide Necessity ? A Reevaluation of the Debate ‘Determinism - Indeterminism’ in the Light of Quantum Mechanics and Probability Theory.Louis Vervoort - 2013 - Dissertation, University of Montreal
    In this text the ancient philosophical question of determinism (“Does every event have a cause ?”) will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic: quantum events would have no causes but happen by irreducible chance. Arguably the clearest theorem that leads to this conclusion is Bell’s theorem. The commonly accepted ‘solution’ to the theorem is ‘indeterminism’, in agreement with the Copenhagen interpretation. Here it is recalled that indeterminism (...)
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  41. added 2017-02-14
    Interpretations of Probability in Quantum Mechanics: A Case of “Experimental Metaphysics”.Geoffrey Hellman - 2009 - In Wayne C. Myrvold & Joy Christian (eds.), Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle. Springer. pp. 211--227.
  42. added 2017-02-11
    Weak Objectification, Joint Probabilities, and Bell Inequalities in Quantum Mechanics.P. Busch, P. Lahti & P. Mittelstaedt - 1992 - Foundations of Physics 22 (7):949-962.
    The weak objectification of physical properties is shown to yield the same probabilistic implications as strong objectification and can therefore be refuted on the basis of suitable interference experiments. An alternative test of hypothetical objectification statements, as they occur in the EPR experiment, is based on joint probabilities and the ensuing Bell inequalities. Quantum mechanics turns out to be partially compatible with Bell's inequalities even in cases where weak objectification is excluded by interference.
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  43. added 2017-02-11
    Propensities, Correlations, and Metaphysics.Michael Redhead - 1992 - Foundations of Physics 22 (3):381-394.
    An attempt is made to defend realism and the absence of space-like causation in quantum mechanics, by invoking indeterminism and a new necessary condition for stochastic causality, we term robustness. This condition is defended against recent critical attacks by Cartwright and Jones, and by Healey, and the violation of the robustness condition in Bell-type correlation experiments is shown to follow if an appropriate interpretation of the state vector is employed.
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  44. added 2017-02-11
    Closed Currents, Vector Fields, and Phenomena.R. W. Tucker - 1988 - Foundations of Physics 18 (8):851-864.
    A pedagogical discussion is given of the role played by certain vector fields and closed currents in the formulation and interpretation of quantum mechanics and quantum field theory.
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  45. added 2017-02-11
    Reality, Locality, and Probability.Stanley P. Gudder - 1984 - Foundations of Physics 14 (10):997-1010.
    It is frequently argued that reality and locality are incompatible with the predictions of quantum mechanics. Various investigators have used this as evidence for the existence of hidden variables. However, Bell's inequalities seem to refute this possibility. Since the above arguments are made within the framework of conventional probability theory, we contend that an alternative solution can be found by an extension of this theory. Elaborating on some ideas of I. Pitowski, we show that within the framework of a generalized (...)
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  46. added 2017-02-11
    Classical Probability and the Quantum Mechanical Trace Formulation for Expectations.Peter D. Finch - 1982 - Foundations of Physics 12 (4):327-345.
    The trace formulation of quantum mechanical expectations is derived in a classical deterministic setting by averaging over an assembly of states. Interference of probabilities is discussed and its usual Hilbert space formulation is questioned. Nevertheless, it is shown that the observable predictions of quantum statics remain unchanged in the framework developed here.
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  47. added 2017-02-09
    Formal Problems of Probability Theory in the Light of Quantum Mechanics III.M. Strauss - 1939 - Synthese 4 (12):65 - 72.
    (1) The form of scientific probability sentences is given unambiguously for the first time by quantum mechanics (form (II); all scientific probability statements can be written in this form. (2) The rules of transformation are also determined by quantum mechanics they agree with the axioms given by Reichenbach (1), p. 118. (3) Frequency interpretation agreeing with the statistical tests used in scientific practice can be given in the frame of truth-semantics at least aa a first approximation.
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  48. added 2017-02-07
    Experiment-Dependent Priors in Psychology and Physics.Robert F. Bordley & Joseph B. Kadane - 1999 - Theory and Decision 47 (3):213-227.
    Sometimes conducting an experiment to ascertain the state of a system changes the state of the system being measured. Kahneman & Tversky modelled this effect with ‘support theory’. Quantum physics models this effect with probability amplitude mechanics. As this paper shows, probability amplitude mechanics is similar to support theory. Additionally, Viscusi's proposed generalized expected utility model has an analogy in quantum mechanics.
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  49. added 2017-02-03
    Do Our Observations Depend Upon the Quantum State of the Universe?Don N. Page - unknown
    Here I shall call elements (1)-(3) the quantum state (or the “state”), since they give the quantum state of the universe that obeys the dynamical laws and is written in terms of the kinematic variables, and I shall call elements (4)-(6) the probability rules (or the “rules”), since they specify what it is that has probabilities (here taken to be the results of observations, Oj, or “observations” for short), the rules for extracting these observational probabilities from the quantum state, and (...)
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  50. added 2017-02-02
    Insufficiency of the Quantum State for Deducing Observational Probabilities.Don Page - unknown
    It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an observer. Then the probability of an observation cannot be deduced simply from the quantum state (say as the expectation value of the projection operator for the observation, as in traditional quantum theory). One needs additional rules to (...)
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