Results for 'Retrocausality'

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  1. Retrocausality at no extra cost.Peter William Evans - 2015 - Synthese 192 (4):1139-1155.
    One obstacle faced by proposals of retrocausal influences in quantum mechanics is the perceived high conceptual cost of making such a proposal. I assemble here a metaphysical picture consistent with the possibility of retrocausality and not precluded by the known physical structure of our reality. This picture employs two relatively well-established positions—the block universe model of time and the interventionist account of causation—and requires the dismantling of our ordinary asymmetric causal intuition and our ordinary intuition about epistemic access to (...)
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  2.  86
    Retrocausal Models for EPR.Richard Corry - 2015 - Studies in the History and Philosophy of Modern Physics 49:1-9.
    This paper takes up Huw Price׳s challenge to develop a retrocausal toy model of the Bell-EPR experiment. I develop three such models which show that a consistent, local, hidden-variables interpretation of the EPR experiment is indeed possible, and which give a feel for the kind of retrocausation involved. The first of the models also makes clear a problematic feature of retrocausation: it seems that we cannot interpret the hidden elements of reality in a retrocausal model as possessing determinate dispositions to (...)
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  3. Retrocausality and Quantum Measurement.David T. Pegg - 2008 - Foundations of Physics 38 (7):648-658.
    A retrocausal interpretation of quantum mechanics is examined and is applied to the problem of measuring an optical qubit before the qubit is actually created. Although the predictions of the retrocausal interpretation are the same as for the conventional causal picture, it provides a new perspective which should give a useful way of understanding some quantum mechanical processes.
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  4.  32
    On retrocausality.Paul Fitzgerald - 1974 - Philosophia 4 (4):513-551.
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  5. Retrocausal quantum mechanics: Maudlin's challenge revisited.Peter J. Lewis - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):442-449.
    In 1994, Maudlin proposed an objection to retrocausal approaches to quantum mechanics in general, and to the transactional interpretation in particular, involving an absorber that changes location depending on the trajectory of the particle. Maudlin considered this objection fatal. However, the TI did not die; rather, a number of responses were developed, some attempting to accommodate Maudlin's example within the existing TI, and others modifying the TI. I argue that none of these responses is fully adequate. The reason, I submit, (...)
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  6.  30
    Is Retrocausal Quantum Mechanics Consistent with Special Relativity?Shan Gao - 2022 - Foundations of Physics 52 (1):1-4.
    Retrocausal quantum mechanics (RQM) provides a local causal explanation of Bell correlations. It is widely thought that RQM is consistent with special relativity. In this paper, I point out that this view is not wholly right. It is argued that RQM violates the Lorentz invariance of the temporal relation between cause and effect for certain spacelike separated events in Bell-type experiments.
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  7. Toy Models for Retrocausality.Huw Price - 2008 - Studies in Studies in History and Philosophy of Modern Physics 39 (4):752-761.
    A number of writers have been attracted to the idea that some of the peculiarities of quantum theory might be manifestations of 'backward' or 'retro' causality, underlying the quantum description. This idea has been explored in the literature in two main ways: firstly in a variety of explicit models of quantum systems, and secondly at a conceptual level. This note introduces a third approach, intended to complement the other two. It describes a simple toy model, which, under a natural interpretation, (...)
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  8.  26
    Retrocausal models for EPR.Richard Corry - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 49:1-9.
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  9.  16
    A Retrocausal Interpretation of Classical Collision Between Rigid Bodies.Chunghyoung Lee - 2020 - Foundations of Science 25 (3):559-571.
    When two bodies collide with each other, they change their motion. Many physics textbooks explain that the change in motion is caused by the force or impulse exerted on the body during the collision. This is not the whole story, I argue, in case the bodies are rigid. In this case, the change in motion cannot be causally explained solely by how the bodies are configured before and during the collision but instead should be explained partly by what happens after (...)
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  10.  20
    Lorentz-Invariant, Retrocausal, and Deterministic Hidden Variables.Aurélien Drezet - 2019 - Foundations of Physics 49 (10):1166-1199.
    We review several no-go theorems attributed to Gisin and Hardy, Conway and Kochen purporting the impossibility of Lorentz-invariant deterministic hidden-variable model for explaining quantum nonlocality. Those theorems claim that the only known solution to escape the conclusions is either to accept a preferred reference frame or to abandon the hidden-variable program altogether. Here we present a different alternative based on a foliation dependent framework adapted to deterministic hidden variables. We analyse the impact of such an approach on Bohmian mechanics and (...)
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  11.  59
    Changing the past: Retrocausality and narrative construction.Cornelis van Putten - 2006 - Metaphilosophy 37 (2):254–258.
    This article is a reply to Jeanne Peijnenburg's argument for retrocausality in "Shaping Your Own Life." Although it is perfectly possible to make sense of the way Peijnenburg deals with the subject of changing the past, there is no need to think this implies retrocausality.
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  12.  43
    Retrocausation and the formal assimilation of classical electrodynamics to Newtonian mechanics: A reply to Nissim-Sabat's "on Grunbaum and retrocausation".Adolf Grünbaum & Allen I. Janis - 1979 - Philosophy of Science 46 (1):136-160.
    Dirac's classical electrodynamics countenances "preaccelerations" of charged particles at a time t as mathematical functions of external forces applied after the time t. These preaccelerations have been interpreted as evidence for physical retrocausation upon assuming that, in electrodynamics no less than in Newton's second law, external forces sustain an asymmetric causal relation to accelerations. And this retrocausal interpretation has just been defended against the critiques in (Grunbaum 1976), (Grunbaum and Janis, 1977 and 1978) by appeal to the formal assimilation of (...)
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  13. Quantum retrocausation: theory and experiment: San Diego, California, USA, 13-14 June 2011.Daniel P. Sheehan (ed.) - 2011 - Melville, N.Y.: American Institute of Physics.
    This conference proceedings would be of interest to theoretical and experimental physicists in the areas of foundations of physics, nature of time, foundations of quantum mechanics, quantum measurement, quantum computation. Philosophers of science and physics. Retrocausation, the process whereby the future affects its past, is central to the modern movement to understand the fundamental physical nature of time. This conference volume presents the most recent theoretical and experimental results at the forefront of the nascent field of physical chronology.
     
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  14. Does time-symmetry imply retrocausality? How the quantum world says “Maybe”?Huw Price - 2012 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (2):75-83.
    It has often been suggested that retrocausality offers a solution to some of the puzzles of quantum mechanics: e.g., that it allows a Lorentz-invariant explanation of Bell correlations, and other manifestations of quantum nonlocality, without action-at-a-distance. Some writers have argued that time-symmetry counts in favour of such a view, in the sense that retrocausality would be a natural consequence of a truly time-symmetric theory of the quantum world. Critics object that there is complete time-symmetry in classical physics, and (...)
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  15.  22
    Retrocausality and quantum mechanics.David Thomas Pegg - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):830-840.
  16.  46
    Is There Really "Retrocausation" in Time-Symmetric Approaches to Quantum Mechanics?Ruth Kastner - unknown
    Time-symmetric interpretations of quantum theory are often presented as featuring "retrocausal" effects in addition to the usual forward notion of causation. This paper examines the ontological implications of certain time- symmetric theories, and finds that no dynamical notion of causation applies to them, either forward or backward. It is concluded that such theories actually describe a static picture, in which the notion of causation is relegated to a descriptor of static relationships among events. In addition, these theories lead to an (...)
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  17. Two roads to retrocausality.Emily Adlam - 2022 - Synthese 200 (5):1-36.
    In recent years the quantum foundations community has seen increasing interest in the possibility of using retrocausality as a route to rejecting the conclusions of Bell’s theorem and restoring locality to quantum physics. On the other hand, it has also been argued that accepting nonlocality leads to a form of retrocausality. In this article we seek to elucidate the relationship between retrocausality and locality. We begin by providing a brief schema of the various ways in which violations (...)
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  18. Quantum mechanics and retrocausality.David Atkinson - manuscript
    The classical electrodynamics of point charges can be made finite by the introduction of effects that temporally precede their causes. The idea of retrocausality is also inherent in the Feynman propagators of quantum electrodynamics. The notion allows a new understanding of the violation of the Bell inequalities, and of the world view revealed by quantum mechanics. Published in The Universe, Visions and Perspectives, edited by N. Dadhich and A. Kembhavi, Kluwer Academic Publishers, 2000, pages 35-50.
     
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  19.  66
    Retrocausation acting in the single-electron double-slit interference experiment.Noboru Hokkyo - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):762-766.
  20.  21
    Retrocausation acting in the single-electron double-slit interference experiment.Noboru Hokkyo - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):762-766.
  21. Retrocausal Effects as a Consequence of Orthodox Quantum Mechanics Refined to Accommodate The Principle of Sufficient Reason.Henry P. Stapp - 2011 - AIP Conference Proceedings 1408.
    The principle of sufficient reason asserts that anything that happens does so for a reason: no definite state of affairs can come into being unless there is a sufficient reason why that particular thing should happen. This principle is usually attributed to Leibniz, although the first recorded Western philosopher to use it was Anaximander of Miletus. The demand that nature be rational, in the sense that it be compatible with the principle of sufficient reason, conflicts with a basic feature of (...)
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  22.  6
    Quantum Retrocausation III: San Diego, CA, USA, 15-16 June 2016.Daniel Peter Sheehan (ed.) - 2017 - Melville, New York: AIP Publishing.
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  23.  19
    A Local $$psi $$-Epistemic Retrocausal Hidden-Variable Model of Bell Correlations with Wavefunctions in Physical Space.Indrajit Sen - 2019 - Foundations of Physics 49 (2):83-95.
    We construct a local \-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state \\rangle \) as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state \\rangle \) which is different from the prepared quantum state \\rangle \) and has an ontic status. The ontic state of a single particle consists (...)
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  24.  22
    Changing the past: Retrocausality and narrative construction.Cornelis Putten - 2006 - Metaphilosophy 37 (2):254-258.
    This article is a reply to Jeanne Peijnenburg's argument for retrocausality in “Shaping Your Own Life.” Although it is perfectly possible to make sense of the way Peijnenburg deals with the subject of changing the past, there is no need to think this implies retrocausality.
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  25. Time-symmetry without retrocausality: How the quantum can withhold the solace.Huw Price - unknown
    It has been suggested that some of the puzzles of QM are resolved if we allow that there is retrocausality in the quantum world. In particular, it has been claimed that this approach offers a path to a Lorentz-invariant explanation of Bell correlations, and other manifestations of quantum "nonlocality", without action-at-a-distance. Some writers have suggested that this proposal can be supported by an appeal to time-symmetry, claiming that if QM were made "more time-symmetric", retrocausality would be a natural (...)
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  26.  37
    On Grunbaum and retrocausation in classical electrodynamics.Charles Nissim-Sabat - 1979 - Philosophy of Science 46 (1):118-135.
    A detailed analysis is made of Grunbaum's claim that the Abraham-Lorentz (AL) and Dirac-Lorentz (DL) equations have no bearing on causality. It is pointed out that (a) both equations are derived from F = ma, and thus should obey the same causality conditions as Newton's law, (b) independently of what boundary conditions are imposed, non-causal behavior is always along the same straight line as the force, (c) the distinction in status between laws and boundary conditions which Grunbaum imposes is one (...)
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  27. Frontiers of time: Retrocausation--Experiment and Theory: San Diego, California, 20-22 June 2006.Daniel P. Sheehan (ed.) - 2006 - Melville, N.Y.: American Institute of Physics.
    Traditional causation posits that the past alone influences the present. In principle, however, the basic laws of physics permit the future an equal measure of influence: retrocausation. This symposium explores theoretical developments and experimental evidence for retrocausation. It is unique in stressing recent experiments in this exciting and potentially important new field.
     
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  28. Why Delayed Choice Experiments do NOT imply Retrocausality.David Ellerman - 2015 - Quantum Studies: Mathematics and Foundations 2 (2):183-199.
    There is a fallacy that is often involved in the interpretation of quantum experiments involving a certain type of separation such as the: double-slit experiments, which-way interferometer experiments, polarization analyzer experiments, Stern-Gerlach experiments, and quantum eraser experiments. The fallacy leads not only to flawed textbook accounts of these experiments but to flawed inferences about retrocausality in the context of delayed choice versions of separation experiments.
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  29.  12
    GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality.Daniel Rohrlich & Guy Hetzroni - 2018 - Entropy 20 (6):478.
    We review an argument that bipartite "PR-box" correlations, though designed to respect relativistic causality, in fact violate relativistic causality in the classical limit. As a test of this argument, we consider Greenberger-Horne-Zeilinger (GHZ) correlations as a tripartite version of PR-box correlations, and ask whether the argument extends to GHZ correlations. If it does-i.e., if it shows that GHZ correlations violate relativistic causality in the classical limit-then the argument must be incorrect (since GHZ correlations do respect relativistic causality in the classical (...)
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  30.  25
    How Does Time Flow in Living Systems? Retrocausal Scaffolding and E-series Time.Naoki Nomura, Koichiro Matsuno, Tomoaki Muranaka & Jun Tomita - 2019 - Biosemiotics 12 (2):267-287.
    Anticipatory acts or predictive behavior are prerequisites for living organisms to sustain their survival when escaping from a predator, catching prey, or schooling. For example, catching prey requires that the predator perform some procedures that are equivalent to estimating the directional movement of the prey, its speed and its distance relative to the predator. Underlying these procedures is time experience, which does not adhere to man-made mechanical clocks. Living organisms keep time based on the local activities of each participant and (...)
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  31. The myth of retrocausation in classical electrodynamics.Adolf Grünbaum - 1978 - Epistemologia 1 (2):353.
  32.  70
    Quantum Causal Models, Faithfulness, and Retrocausality.Peter W. Evans - 2018 - British Journal for the Philosophy of Science 69 (3):745-774.
    Wood and Spekkens argue that any causal model explaining the EPRB correlations and satisfying the no-signalling constraint must also violate the assumption that the model faithfully reproduces the statistical dependences and independences—a so-called ‘fine-tuning’ of the causal parameters. This includes, in particular, retrocausal explanations of the EPRB correlations. I consider this analysis with a view to enumerating the possible responses an advocate of retrocausal explanations might propose. I focus on the response of Näger, who argues that the central ideas of (...)
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  33. Is preacceleration of particles in dirac's electrodynamics a case of backward causation? The myth of retrocausation in classical electrodynamics.Adolf Grünbaum - 1976 - Philosophy of Science 43 (2):165-201.
    Is it a "conceptual truth" or only a logically contingent fact that, in any given kind of case, an event x which asymmetrically causes ("produces") an event y likewise temporally precedes y or at least does not temporally succeed y? A bona fide physical example in which the cause retroproduces the effect would show that backward causation is no less conceptually possible than forward causation. And it has been claimed ([9], p. 151; [4], p. 41) that in Dirac's classical electrodynamics (...)
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  34.  16
    Cambiando el pasado: ventajas de la retrocausación.Hernán Miguel & Rolando Núñez Pradenas - 2016 - Revista de Humanidades de Valparaíso 7:7-22.
    Since its inception, quantum mechanics has faced a series of “mysteries” that emerge from it if we consider this scientific theory from a realistic point of view. In the early development of the theory, scientists like Albert Einstein noticed the consequences of accepting a theory like this, which allow phenomena such as non-locality. This led a part of the scientific community to believe that quantum mechanics was an incomplete theory, since there should be variables that might explain those “disturbing” phenomena (...)
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  35.  28
    Two Replication Studies of a Time-Reversed (Psi) Priming Task and the Role of Expectancy in Reaction Times.Marilyn Schlitz, Daryl Bem, David Marcusson-Clavertz, Etzel Cardena, Jennifer Lyke, Raman Grover, Susan Blackmore, Patrizio Tressoldi, Serena Roney-Dougal, Dick Bierman, Jacob Jolij, Eva Lobach, Glenn Hartelius, Thomas Rabeyron, William Bengston, Sky Nelson, Garret Moddel & Arnaud Delorme - 2021 - Journal of Scientific Exploration 35 (1):65-90.
    Two experiments involving an international collaboration of experimenters sought to replicate and extend a previously published psi experiment on precognition by Daryl Bem that has been the focus of extensive research. The experiment reverses the usual cause–effect sequence of a standard psychology experiment using priming and reaction times. The preregistered confirmatory hypothesis is that response times to incongruent stimuli will be longer than response times to congruent stimuli even though the prime has not yet appeared when the participant records their (...)
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  36. Evidence of Macroscopic Quantum Phenomena and Conscious Reality Selection.Cynthia Sue Larson - 2014 - Cosmos and History 10 (1):34-47.
    The purpose of this paper is to present an overview of emergent examples of macroscopic quantum phenomena. While quantum theory asserts that such quantum behaviors as superposition, entanglement, and coherence are possible for all objects, assumptions that quantum processes operate exclusively within the quantum realm have contributed to on-going bias toward presumed primacy of classical physics in the macroscopic realm. Non-trivial quantum macroscopic effects are now recognized in the fields of biology, quantum physics, quantum computing, quantum astronomy, and neuroscience, with (...)
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  37.  74
    Recent Advances in Post-Quantum Physics.Jack Sarfatti - manuscript
  38. Governing Without A Fundamental Direction of Time: Minimal Primitivism about Laws of Nature.Eddy Keming Chen & Sheldon Goldstein - 2022 - In Yemima Ben-Menahem (ed.), Rethinking Laws of Nature. Springer. pp. 21-64.
    The Great Divide in metaphysical debates about laws of nature is between Humeans, who think that laws merely describe the distribution of matter, and non-Humeans, who think that laws govern it. The metaphysics can place demands on the proper formulations of physical theories. It is sometimes assumed that the governing view requires a fundamental / intrinsic direction of time: to govern, laws must be dynamical, producing later states of the world from earlier ones, in accord with the fundamental direction of (...)
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  39. Laws of Nature as Constraints.Emily Adlam - 2022 - Foundations of Physics 52 (1):1-41.
    The laws of nature have come a long way since the time of Newton: quantum mechanics and relativity have given us good reasons to take seriously the possibility of laws which may be non-local, atemporal, ‘all-at-once,’ retrocausal, or in some other way not well-suited to the standard dynamical time evolution paradigm. Laws of this kind can be accommodated within a Humean approach to lawhood, but many extant non-Humean approaches face significant challenges when we try to apply them to laws outside (...)
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  40.  19
    What Does ‘(Non)-absoluteness of Observed Events’ Mean?Emily Adlam - 2024 - Foundations of Physics 54 (1):1-43.
    Recently there have emerged an assortment of theorems relating to the ‘absoluteness of emerged events,’ and these results have sometimes been used to argue that quantum mechanics may involve some kind of metaphysically radical non-absoluteness, such as relationalism or perspectivalism. However, in our view a close examination of these theorems fails to convincingly support such possibilities. In this paper we argue that the Wigner’s friend paradox, the theorem of Bong et al and the theorem of Lawrence et al are all (...)
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  41.  35
    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 invited as part of the David Bohm Centennial symposium (...)
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  42.  19
    Seeming Backward-in-Time Actions in Forward-in-Time Realistically Interpreted Orthodox Relativistic Quantum Field Theory.Henry Stapp - 2017 - Cosmos and History 13 (2):53-64.
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  43.  27
    Entanglement Swapping and Action at a Distance.Huw Price & Ken Wharton - 2021 - Foundations of Physics 51 (6):1-24.
    A 2015 experiment by Hanson and Delft colleagues provided further confirmation that the quantum world violates the Bell inequalities, being the first Bell test to close two known experimental loopholes simultaneously. The experiment was also taken to provide new evidence of ‘spooky action at a distance’. Here we argue for caution about the latter claim. The Delft experiment relies on entanglement swapping, and our main claim is that this geometry introduces an additional loophole in the argument from violation of the (...)
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  44.  35
    Lagrangian Description for Particle Interpretations of Quantum Mechanics: Entangled Many-Particle Case.Roderick I. Sutherland - 2017 - Foundations of Physics 47 (2):174-207.
    A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion, field evolution and conservation laws can all be deduced from a single Lagrangian density expression. The formalism presented is Lorentz invariant. This paper follows on from a previous one which was limited to the single-particle case. The present paper treats the more general case of many (...)
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  45. The wave function as a true ensemble.Jonte Hance & Sabine Hossenfelder - 2022 - Proceedings of the Royal Society 478 (2262).
    In quantum mechanics, the wavefunction predicts probabilities of possible measurement outcomes, but not which individual outcome is realised in each run of an experiment. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local ψ-ensemble interpretations which reproduce (...)
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  46. EPR communication: Signals from the future?John Cramer - manuscript
    Last June I was an invited speaker at the symposium “Frontiers of Time: Reverse Causation—Experiment and Theory,” part of a meeting of the American Association for the Advancement of Science (AAAS) held on the beautiful campus of the University of San Diego. (Here, reverse causation means a violation of that most mysterious law of physics, the Principle of Causality, which requires that any cause must precede its effects in all reference frames.) I had originally intended to just talk about my (...)
     
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  47.  40
    Precognition: The Only Form of Psi?S. B. Marwaha & E. C. May - 2016 - Journal of Consciousness Studies 23 (3-4):76-100.
    Based on empirical evidence we discuss the nature of precognition, and address the questions whether retrocausation/ precognition violates causality, whether precognition implies determinism, the questions of actual or probable futures, from where does the information arise, and other observed properties of precognition. This is followed by a discussion on the primacy of precognition by examining the various categories of psi. In our analysis, precognition is most likely the only form of psi, subsuming within it clairvoyance, telepathy, micro-PK, and the survival (...)
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  48.  26
    Probabilities and Certainties Within a Causally Symmetric Model.Roderick I. Sutherland - 2022 - Foundations of Physics 52 (4):1-17.
    This paper is concerned with the causally symmetric version of the familiar de Broglie–Bohm interpretation, this version allowing the spacelike nonlocality and the configuration space ontology of the original model to be avoided via the addition of retrocausality. Two different features of this alternative formulation are considered here. With regard to probabilities, it is shown that the model provides a derivation of the Born rule identical to that in Bohm’s original formulation. This derivation holds just as well for a (...)
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  49. Hypercomputation and the Physical Church‐Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
    A version of the Church-Turing Thesis states that every effectively realizable physical system can be simulated by Turing Machines (‘Thesis P’). In this formulation the Thesis appears to be an empirical hypothesis, subject to physical falsification. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. The conclusions are that these models reduce to supertasks, i.e. infinite computation, and that even supertasks are no solution for recursive incomputability. This yields that the realization (...)
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  50.  13
    A Realistic Theory of Quantum Measurement.Alan K. Harrison - 2022 - Foundations of Physics 52 (1):1-32.
    We propose that the ontic understanding of quantum mechanics can be extended to a fully realistic theory that describes the evolution of the wavefunction at all times, including during a measurement. In such an approach the wave equation should reduce to the standard wave equation when there is no measurement, and describe state reduction when the system is measured. The general wave equation must be nonlinear and nonlocal, and we require it to be time-symmetric; consequently, this approach is not a (...)
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