Philosophy of Physical Science

Edited by Hans Halvorson (Princeton University)
Assistant editors: Joshua Luczak, Thomas De De Saegher
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  1. No Purification Ontology, No Quantum Paradoxes.Giacomo Mauro D’Ariano - 2020 - Foundations of Physics 50 (12):1921-1933.
    It is almost universally believed that in quantum theory the two following statements hold: all transformations are achieved by a unitary interaction followed by a von-Neumann measurement; all mixed states are marginals of pure entangled states. I name this doctrine the dogma of purification ontology. The source of the dogma is the original von Neumann axiomatisation of the theory, which largely relies on the Schrődinger equation as a postulate, which holds in a nonrelativistic context, and whose operator version holds only (...)
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  2. Preface to Special Issue: Quantum Information Revolution: Impact to Foundations.Christopher A. Fuchs & Andrei Khrennikov - 2020 - Foundations of Physics 50 (12):1757-1761.
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  3. Extending the Agent in QBism.Jacques Pienaar - 2020 - Foundations of Physics 50 (12):1894-1920.
    According to the subjective Bayesian interpretation of quantum mechanics, the instruments used to measure quantum systems are to be regarded as an extension of the senses of the agent who is using them, and quantum states describe the agent’s expectations for what they will experience through these extended senses. How can QBism then account for the fact that instruments must be calibrated before they can be used to ‘sense’ anything; some instruments are more precise than others; more precise instruments can (...)
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  4. Are Quantum Spins but Small Perturbations of Ontological Ising Spins?Hans-Thomas Elze - 2020 - Foundations of Physics 50 (12):1875-1893.
    The dynamics-from-permutations of classical Ising spins is generalized here for an arbitrarily long chain. This serves as an ontological model with discrete dynamics generated by pairwise exchange interactions defining the unitary update operator. The model incorporates a finite signal velocity and resembles in many aspects a discrete free field theory. We deduce the corresponding Hamiltonian operator and show that it generates an exact terminating Baker–Campbell–Hausdorff formula. Motivation for this study is provided by the Cellular Automaton Interpretation of Quantum Mechanics. We (...)
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  5. ”The Unavoidable Interaction Between the Object and the Measuring Instruments”: Reality, Probability, and Nonlocality in Quantum Physics.Arkady Plotnitsky - 2020 - Foundations of Physics 50 (12):1824-1858.
    This article aims to contribute to the ongoing task of clarifying the relationships between reality, probability, and nonlocality in quantum physics. It is in part stimulated by Khrennikov’s argument, in several communications, for “eliminating the issue of quantum nonlocality” from the analysis of quantum entanglement. I argue, however, that the question may not be that of eliminating but instead that of further illuminating this issue, a task that can be pursued by relating quantum nonlocality to other key features of quantum (...)
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  6. SICs: Some Explanations.Ingemar Bengtsson - 2020 - Foundations of Physics 50 (12):1794-1808.
    The problem of constructing maximal equiangular tight frames or SICs was raised by Zauner in 1998. Four years ago it was realized that the problem is closely connected to a major open problem in number theory. We discuss why such a connection was perhaps to be expected, and give a simplified sketch of some developments that have taken place in the past 4 years. The aim, so far unfulfilled, is to prove existence of SICs in an infinite sequence of dimensions.
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  7. Quantum Versus Classical Entanglement: Eliminating the Issue of Quantum Nonlocality.Andrei Khrennikov - 2020 - Foundations of Physics 50 (12):1762-1780.
    We analyze the interrelation of quantum and classical entanglement. The latter notion is widely used in classical optic simulation of some quantum-like features of light. We criticize the common interpretation that “quantum nonlocality” is the basic factor differing quantum and classical realizations of entanglement. Instead, we point to the breakthrough Grangier et al. experiment on coincidence detection which was done in 1986 and played the crucial role in rejection of classical field models in favor of quantum mechanics. Classical entanglement sources (...)
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  8. Deriving Born’s Rule from an Inference to the Best Explanation.Alexia Auffèves & Philippe Grangier - 2020 - Foundations of Physics 50 (12):1781-1793.
    In previous articles we presented a simple set of axioms named “Contexts, Systems and Modalities”, where the structure of quantum mechanics appears as a result of the interplay between the quantized number of modalities accessible to a quantum system, and the continuum of contexts that are required to define these modalities. In the present article we discuss further how to obtain Born’s rule within this framework. Our approach is compared with other former and recent derivations, and its strong links with (...)
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  9. Respecting One’s Fellow: QBism’s Analysis of Wigner’s Friend.John B. DeBrota, Christopher A. Fuchs & Rüdiger Schack - 2020 - Foundations of Physics 50 (12):1859-1874.
    According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences of the same agent. Wigner’s conundrum of the friend, in which two agents ostensibly have different accounts of whether or not there is a measurement outcome, thus poses no paradox for QBism. Indeed the resolution of Wigner’s original thought experiment was central to the development of QBist thinking. The (...)
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  10. Quantum Causality Relations and the Emergence of Reality From Coherent Superpositions.Holger F. Hofmann - 2020 - Foundations of Physics 50 (12):1809-1823.
    The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional probabilities for (...)
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  11. The Zeroth Law of Thermodynamics in Special Relativity.L. Gavassino - 2020 - Foundations of Physics 50 (11):1554-1586.
    We critically revisit the definition of thermal equilibrium, in its operational formulation, provided by standard thermodynamics. We show that it refers to experimental conditions which break the covariance of the theory at a fundamental level and that, therefore, it cannot be applied to the case of moving bodies. We propose an extension of this definition which is manifestly covariant and can be applied to the study of isolated systems in special relativity. The zeroth law of thermodynamics is, then, proven to (...)
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  12. Local Model of Entangled Photon Experiments Compatible with Quantum Predictions Based on the Reality of the Vacuum Fields.Emilio Santos - 2020 - Foundations of Physics 50 (11):1587-1607.
    Arguments are provided for the reality of the quantum vacuum fields. A polarization correlation experiment with two maximally entangled photons created by spontaneous parametric down-conversion is studied in the Weyl–Wigner formalism, that reproduces the quantum predictions. An interpretation is proposed in terms of stochastic processes assuming that the quantum vacuum fields are real. This proves that local realism is compatible with a violation of Bell inequalities, thus rebutting the claim that it has been refuted by experiments. Entanglement appears as a (...)
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  13. A Puzzle for the Field Ontologists.Shan Gao - 2020 - Foundations of Physics 50 (11):1541-1553.
    It has been widely thought that the wave function describes a real, physical field in a realist interpretation of quantum mechanics. In this paper, I present a new analysis of the field ontology for the wave function. First, I argue that the non-existence of self-interactions for a quantum system such as an electron poses a puzzle for the field ontologists. If the wave function represents a physical field, then it seems odd that there are interactions between the fields of two (...)
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  14. Quantumness of States and Unitary Operations.Joanna Luc - 2020 - Foundations of Physics 50 (11):1645-1685.
    This paper investigates various properties that may by possessed by quantum states, which are believed to be specifically “quantum” and their opposites. It also considers their “absolute” counterparts in the following sense: a given state has a given property absolutely if after an arbitrary unitary transformation it still possesses it. The known relations between the listed properties and between their absolute counterparts are summarized. It is proven that the only two-qubit state that has zero quantum discord absolutely is the maximally (...)
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  15. Newtonian Fractional-Dimension Gravity and MOND.Gabriele U. Varieschi - 2020 - Foundations of Physics 50 (11):1608-1644.
    This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss’s law for gravity as well as other fundamental classical laws are extended to a D-dimensional metric space, where D can be a non-integer dimension. We show a possible connection between this Newtonian Fractional-Dimension Gravity and Modified Newtonian Dynamics, a leading alternative gravity model which accounts for the observed properties of galaxies and other astrophysical structures without (...)
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  16. Hardy Relations and Common Cause.Katsuaki Higashi - 2020 - Foundations of Physics 50 (11):1382-1397.
    Some researchers argued that in the non-existence proof of hidden variables, the existence of a common common-cause of multiple correlations is tacitly assumed and that the assumption is unreasonably strong. According to their idea, it is sufficient if the separate common-cause of each correlation exists. However, for such an idea, various no-go results are already known. Recently, Higashi showed that there exists no local separate common-cause model for the correlations that appear in Hardy’s famous argument. In this paper, I give (...)
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  17. Propagation Properties of Bound Electromagnetic Field: Classical and Quantum Viewpoints.A. L. Kholmetskii, O. V. Missevitch, T. Yarman & R. Smirnov-Rueda - 2020 - Foundations of Physics 50 (11):1686-1722.
    The present work is motivated by recent experiments aimed to measure the propagation velocity of bound electromagnetic field that reveal no retardation in the absence of EM radiation. We show how these findings can be incorporated into the mathematical structure of special relativity theory that allows us to reconsider some selected problems of classical and quantum electrodynamics. In particular, we come to the conclusion that the total four-momentum for a classical system “particles plus fields” ought to be a present state (...)
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  18. On the Equivalence Principle and Relativistic Quantum Mechanics.Maciej Trzetrzelewski - 2020 - Foundations of Physics 50 (11):1253-1269.
    Einstein’s Equivalence Principle implies that the Lorentz force equation can be derived from a geodesic equation by imposing a certain condition on the electromagnetic potential. We analyze the quantization of that constraint and find the corresponding differential equations for the phase of the wave function. We investigate these equations in the case of Coulomb potential and show that physically acceptable solutions do not exist. This result signals an inconsistency between Einstein’s Equivalence Principle and Relativistic Quantum Mechanics at an atomic level.
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  19. There is No New Problem for Quantum Mechanics.Lev Vaidman - 2020 - Foundations of Physics 50 (11):1728-1734.
    A recent claim by Meehan that quantum mechanics has a new “control problem” that puts limits on our ability to prepare quantum states and revises our understanding of the no-cloning theorem is examined. We identify flaws in Meehan’s analysis and argue that such a problem does not exist.
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  20. Conformal Invariance of the Newtonian Weyl Tensor.Neil Dewar & James Read - 2020 - Foundations of Physics 50 (11):1418-1425.
    It is well-known that the conformal structure of a relativistic spacetime is of profound physical and conceptual interest. In this note, we consider the analogous structure for Newtonian theories. We show that the Newtonian Weyl tensor is an invariant of this structure.
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  21. Derivation of Classical Mechanics in an Energetic Framework Via Conservation and Relativity.Philip Goyal - 2020 - Foundations of Physics 50 (11):1426-1479.
    The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and (...)
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  22. Elementary Charge and Neutrino’s Mass From Planck Length.Saulo Carneiro - 2020 - Foundations of Physics 50 (11):1376-1381.
    It is shown that the postulation of a minimum length for the horizons of a black hole leads to lower bounds for the electric charges and magnetic moments of elementary particles. If the minimum length has the order of the Planck scale, these bounds are given, respectively, by the electronic charge and by \. The latter implies that the masses of fundamental particles are bounded above by the Planck mass, and that the smallest non-zero neutrino mass is \eV. A precise (...)
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  23. Evolution of Superoscillations in the Dirac Field.Fabrizio Colombo & Giovanni Valente - 2020 - Foundations of Physics 50 (11):1356-1375.
    Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The study of the evolution of superoscillations as initial datum of field equations requires the notion of supershift, which generalizes the concept of superoscillations. The present paper has a dual purpose. The first one is to give an updated and self-contained explanation of the strategy to study the evolution of superoscillations by referring to the quantum-mechanical Schrödinger equation and its variations. The second purpose is to treat (...)
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  24. Conditional Action and Quantum Versions of Maxwell’s Demon.Heinz-Jürgen Schmidt - 2020 - Foundations of Physics 50 (11):1480-1508.
    We propose a new way of looking at the quantum Maxwell’s demon problem in terms of conditional action. A “conditional action” on a system is a unitary time evolution, selected according to the result of a previous measurement, which can reduce the entropy of the system. However, any conditional action can be realized by an unitary time evolution of a larger system and a subsequent Lüders measurement, whereby the entropy of the entire system is either increased or remains constant. We (...)
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  25. Fermi’s Golden Rule and the Second Law of Thermodynamics.D. Braak & J. Mannhart - 2020 - Foundations of Physics 50 (11):1509-1540.
    We present a Gedankenexperiment that leads to a violation of detailed balance if quantum mechanical transition probabilities are treated in the usual way by applying Fermi’s “golden rule”. This Gedankenexperiment introduces a collection of two-level systems that absorb and emit radiation randomly through non-reciprocal coupling to a waveguide, as realized in specific chiral quantum optical systems. The non-reciprocal coupling is modeled by a hermitean Hamiltonian and is compatible with the time-reversal invariance of unitary quantum dynamics. Surprisingly, the combination of non-reciprocity (...)
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  26. An Interaction-Free Quantum Measurement-Driven Engine.Cyril Elouard, Mordecai Waegell, Benjamin Huard & Andrew N. Jordan - 2020 - Foundations of Physics 50 (11):1294-1314.
    Recently highly-efficient quantum engines were devised by exploiting the stochastic energy changes induced by quantum measurement. Here we show that such an engine can be based on an interaction-free measurement, in which the meter seemingly does not interact with the measured object. We use a modified version of the Elitzur–Vaidman bomb tester, an interferometric setup able to detect the presence of a bomb triggered by a single photon without exploding it. In our case, a quantum bomb subject to a gravitational (...)
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  27. Triple Path to the Exponential Metric.Maxim Makukov & Eduard Mychelkin - 2020 - Foundations of Physics 50 (11):1346-1355.
    The exponential Papapetrou metric induced by scalar field conforms to observational data not worse than the vacuum Schwarzschild solution. Here, we analyze the origin of this metric as a peculiar space-time within a wide class of scalar and antiscalar solutions of the Einstein equations parameterized by scalar charge. Generalizing the three families of static solutions obtained by Fisher, Janis et al. :878. https://doi.org/10.1103/PhysRevLett.20.878, 1968), and Xanthopoulos and Zannias :2564, 1989), we prove that all three reduce to the same exponential metric (...)
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  28. On the Classification Between $$psi$$ ψ -Ontic and $$psi$$ ψ -Epistemic Ontological Models.Andrea Oldofredi & Cristian López - 2020 - Foundations of Physics 50 (11):1315-1345.
    Harrigan and Spekkens provided a categorization of quantum ontological models classifying them as \-ontic or \-epistemic if the quantum state \ describes respectively either a physical reality or mere observers’ knowledge. Moreover, they claimed that Einstein—who was a supporter of the statistical interpretation of quantum mechanics—endorsed an epistemic view of \ In this essay we critically assess such a classification and some of its consequences by proposing a twofold argumentation. Firstly, we show that Harrigan and Spekkens’ categorization implicitly assumes that (...)
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  29. Constructivism and Realism in Boltzmann’s Thermodynamics’ Atomism.Luiz Pinguelli Rosa, Elaine Andrade, Paulo Picciani & Jean Faber - 2020 - Foundations of Physics 50 (11):1270-1293.
    Ludwig Boltzmann is one of the foremost responsible for the development of modern atomism in thermodynamics. His proposition was revolutionary not only because it brought a new vision for Thermodynamics, merging a statistical approach with Newtonian physics, but also because he produced an entirely new perspective on the way of thinking about and describing physical phenomena. Boltzmann dared to flirt with constructivism and realism simultaneously, by hypothesizing the reality of atoms and claiming an inherent probabilistic nature related to many particles (...)
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  30. Intuitionist Physics.P.-M. Binder - 2020 - Foundations of Physics 50 (11):1411-1417.
    A recent proposal to formulate physics in terms of finite-information variables is examined, concentrating on its consequences for classical mechanics. Both shortcomings and promising avenues are discussed.
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  31. Preface of the Special Issue Probing the Limits of Quantum Mechanics: Theory and Experiment, Volume 2.Andrei Khrennikov, Hans de Raedt, Arkady Plotnitsky & Sergey Polyakov - 2020 - Foundations of Physics 50 (11):1735-1738.
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  32. Interventionist Explanation and the Problem of Single Variable Boundary Constraints.Isaac Wilhelm - 2020 - Noûs 54 (4):945-955.
    According to Interventionism, explanations cite invariant relations which hold among multiple variables. Interventionism incorrectly implies, however, that many common scientific explanations—which cite single‐variable boundary constraints—are not actually explanatory. So I propose a different account of explanation, similar in spirit to Interventionism, which gets those cases of scientific explanation right.
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  33. Misconceptions on Effective Field Theories and Spontaneous Symmetry Breaking: Response to Ellis’ Article.Thomas Luu & Ulf-G. Meißner - 2020 - Foundations of Physics 50 (10):1140-1151.
    In an earlier paper Luu and Meißner we discussed emergence from the context of effective field theories, particularly as related to the fields of particle and nuclear physics. We argued on the side of reductionism and weak emergence. George Ellis has critiqued our exposition in Ellis, and here we provide our response to his critiques. Many of his critiques are based on incorrect assumptions related to the formalism of effective field theories and we attempt to correct these issues here. We (...)
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  34. The Kac Ring or the Art of Making Idealisations.Julie Jebeile - 2020 - Foundations of Physics 50 (10):1152-1170.
    In 1959, mathematician Mark Kac introduced a model, called the Kac ring, in order to elucidate the classical solution of Boltzmann to the problem of macroscopic irreversibility. However, the model is far from being a realistic representation of something. How can it be of any help here? In philosophy of science, it is often argued that models can provide explanations of the phenomenon they are said to approximate, in virtue of the truth they contain, and in spite of the idealisations (...)
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  35. The Causal Closure of Physics in Real World Contexts.George F. R. Ellis - 2020 - Foundations of Physics 50 (10):1057-1097.
    The causal closure of physics is usually discussed in a context free way. Here I discuss it in the context of engineering systems and biology, where strong emergence takes place due to a combination of upwards emergence and downwards causation. Firstly, I show that causal closure is strictly limited in terms of spatial interactions because these are cases that are of necessity strongly interacting with the environment. Effective Spatial Closure holds ceteris parabus, and can be violated by Black Swan Events. (...)
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  36. The Science of $${\Theta \Delta }^{\Text{Cs}}$$.Wayne C. Myrvold - 2020 - Foundations of Physics 50 (10):1219-1251.
    There is a long tradition of thinking of thermodynamics, not as a theory of fundamental physics, but as a theory of how manipulations of a physical system may be used to obtain desired effects, such as mechanical work. On this view, the basic concepts of thermodynamics, heat and work, and with them, the concept of entropy, are relative to a class of envisaged manipulations. This article is a sketch and defense of a science of manipulations and their effects on physical (...)
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  37. Emergence in Solid State Physics and Biology.George F. R. Ellis - 2020 - Foundations of Physics 50 (10):1098-1139.
    There has been much controversy over weak and strong emergence in physics and biology. As pointed out by Phil Anderson in many papers, the existence of broken symmetries is the key to emergence of properties in much of solid state physics. By carefully distinguishing between different types of symmetry breaking and tracing the relation between broken symmetries at micro and macro scales, I demonstrate that the emergence of the properties of semiconductors is a case of strong emergence. This is due (...)
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  38. Truth Through Nonviolence.Venkata Rayudu Posina - 2016 - GITAM Journal of Gandhian Studies 5 (1):143-150.
    What is reality? How do we know? Answers to these fundamental questions of ontology and epistemology, based on Mahatma Gandhi's "experiments with truth", are: reality is nonviolent (in the sense of not-inconsistent), and nonviolence (in the sense of respecting-meaning) is the only means of knowing (Gandhi, 1940). Be that as it may, science is what we think of when we think of reality and knowing. How does Gandhi's nonviolence, discovered in his spiritual quest for Truth, relate to the scientific pursuit (...)
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  39. Cartography of the Space of Theories: An Interpretational Chart for Fields That Are Both (Dark) Matter and Spacetime.Niels C. M. Martens & Dennis Lehmkuhl - forthcoming - Studies in History and Philosophy of Modern Physics.
    This paper pushes back against the Democritean-Newtonian tradition of assuming a strict conceptual dichotomy between spacetime and matter. Our approach proceeds via the more narrow distinction between modified gravity/spacetime and dark matter. A prequel paper argued that the novel field Φ postulated by Berezhiani and Khoury's 'superfluid dark matter theory' is as much matter as anything could possibly be, but also below the critical temperature for superfluidity as much spacetime as anything could possibly be. Here we introduce and critically evaluate (...)
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  40. Das Paradoxe in Goodmans Paradox. Die Vernachlässigung des Funktionscharakters von Naturgesetzen als Grund der Paradoxie.Dieter Wandschneider - 2000 - In Wahrheit – Sein – Struktur. Auseinandersetzungen mit Metaphysik. Hildesheim, Zürich, New York: pp. 231–245.
    Essential for the concept of the law of nature is not only spatio-temporal universality, but also functionality in the sense of the dependency on physical conditions of natural entities. In the following it is explained in detail that just the neglect of this functional property is to be understood as the real reason for the occurrence of the Goodman paradox. As a consequence, the behavior of things seems to be completely at the mercy of the temporal change of unique absolute (...)
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  41. The Inconsistency of Empiricist Argumentation Concerning the Problem of the Lawfulness of Nature.Dieter Wandschneider - 1986 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 17:131–142.
    The well-known empiricist apories of the lawfulness of nature prevent an adequate philosophical interpretation of empirical science until this day. Clarification can only be expected through an immanent refutation of the empiricist point of view. My argument is that Hume’s claim, paradigmatic for modern empiricism, is not just inconsequent, but simply contradictory: Empiricism denies that a lawlike character of nature can be substantiated. But, as is shown, anyone who claimes experience to be the basis of knowledge (as the empiricist naturally (...)
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  42. Group Theoretical Derivation of Consistent Free Particle Theories.Giuseppe Nisticò - 2020 - Foundations of Physics 50 (9):977-1007.
    The difficulties of relativistic particle theories formulated by means of canonical quantization, such as those of Klein–Gordon and Dirac, ultimately led theoretical physicists to turn to quantum field theory to model elementary particle physics. In order to overcome these difficulties, the theories of the present approach are developed deductively from the physical principles that specify the system, without making use of canonical quantization. For a free particle these starting assumptions are invariance of the theory and covariance of position with respect (...)
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  43. Kepler Problem in Space with Deformed Lorentz-Covariant Poisson Brackets.M. I. Samar & V. M. Tkachuk - 2020 - Foundations of Physics 50 (9):942-959.
    We propose a Lorentz-covariant deformed algebra describing a -dimensional quantized spacetime, which in the nonrelativistic limit leads to undeformed one. The deformed Poincaré transformations leaving the algebra invariant are identified. In the classical limit the Lorentz-covariant deformed algebra yields the deformed Lorentz-covariant Poisson brackets. Kepler problem with the deformed Lorentz-covariant Poisson brackets is studied. We obtain that the precession angle of an orbit of the relativistic particle in the gravitational field depends on the mass of the particle, i.e. equivalence principle (...)
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  44. Trajectory Interpretation of Correspondence Principle: Solution of Nodal Issue.Ciann-Dong Yang & Shiang-Yi Han - 2020 - Foundations of Physics 50 (9):960-976.
    The correspondence principle states that the quantum system will approach the classical system in high quantum numbers. Indeed, the average of the quantum probability density distribution reflects a classical-like distribution. However, the probability of finding a particle at the node of the wave function is zero. This condition is recognized as the nodal issue. In this paper, we propose a solution for this issue by means of complex quantum random trajectories, which are obtained by solving the stochastic differential equation derived (...)
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  45. Markovian and Non-Markovian Quantum Measurements.Jennifer R. Glick & Christoph Adami - 2020 - Foundations of Physics 50 (9):1008-1055.
    Consecutive measurements performed on the same quantum system can reveal fundamental insights into quantum theory’s causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen interpretation, measurements affect the quantum system in such a way that the quantum superposition collapses after each measurement, erasing any memory of the prior state. We show here that counter to this view, un-amplified measurements have coherent ancilla density matrices that encode the memory of the entire set of quantum measurements (...)
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