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  1. The Mathematical Universe.Max Tegmark - 2007 - Foundations of Physics 38 (2):101-150.
    I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and (...)
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  • Equilibrium in Gibbsian Statistical Mechanics.Roman Frigg & Charlotte Werndl - 2022 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. London, UK: Routledge.
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  • Physics and the Real World.George F. R. Ellis - 2006 - Foundations of Physics 36 (2):227-262.
    Physics and chemistry underlie the nature of all the world around us, including human brains. Consequently some suggest that in causal terms, physics is all there is. However, we live in an environment dominated by objects embodying the outcomes of intentional design (buildings, computers, teaspoons). The present day subject of physics has nothing to say about the intentionality resulting in existence of such objects, even though this intentionality is clearly causally effective. This paper examines the claim that the underlying physics (...)
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  • Upływ czasu i ontologia.Jerzy Gołosz - 2011 - Kraków, Polska: Jagiellonian University Press.
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  • Quantum Discreteness is an Illusion.H. Dieter Zeh - 2010 - Foundations of Physics 40 (9-10):1476-1493.
    I review arguments demonstrating how the concept of “particle” numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave functions) can be interpreted as occupation numbers for objects with a formal mass (defined by the field equation) and spatial wave number (“momentum”) characterizing classical field modes. A superposition of different oscillator eigenstates, all consisting of n modes having one node, while all others have none, defines (...)
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  • The Arrow of Time in Physics.David Wallace - 2013 - In Heather Dyke & Adrian Bardon (eds.), A Companion to the Philosophy of Time. Chichester, UK: Wiley. pp. 262–281.
    Every process studied in any science other than physics defines an arrow of time – to say nothing for the directedness of the processes of causation, inference, memory, control, and counterfactual dependence that occur in everyday life. The discussion in this chapter is confined to the arrow of time as it occurs in physics. The chapter briefly discusses those features of microscopic physics, which seem to conflict with time asymmetry. It explains just how this conflict plays out in the important (...)
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  • The arrow of time and meaning.Pierre Uzan - 2006 - Foundations of Science 12 (2):109-137.
    All the attempts to find the justification of the privileged evolution of phenomena exclusively in the external world need to refer to the inescapable fact that we are living in such an asymmetric universe. This leads us to look for the origin of the “arrow of time” in the relationship between the subject and the world. The anthropic argument shows that the arrow of time is the condition of the possibility of emergence and maintenance of life in the universe. Moreover, (...)
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  • Informational branching universe.Pierre Uzan - 2010 - Foundations of Science 15 (1):1-28.
    This paper suggests an epistemic interpretation of Belnap’s branching space-times theory based on Everett’s relative state formulation of the measurement operation in quantum mechanics. The informational branching models of the universe are evolving structures defined from a partial ordering relation on the set of memory states of the impersonal observer. The totally ordered set of their information contents defines a linear “time” scale to which the decoherent alternative histories of the informational universe can be referred—which is quite necessary for assigning (...)
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  • Quantum paradoxes, time, and derivation of thermodynamic law: Opportunities from change of energy paradigm.Helmut Tributsch - 2006 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 37 (2):287 - 306.
    Well known quantum and time paradoxes, and the difficulty to derive the second law of thermodynamics, are proposed to be the result of our historically grown paradigm for energy: it is just there, the capacity to do work, not directly related to change. When the asymmetric nature of energy is considered, as well as the involvement of energy turnover in any change, so that energy can be understood as fundamentally "dynamic", and time-oriented (new paradigm), these paradoxes and problems dissolve. The (...)
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  • Quantum Paradoxes, Time, and Derivation of Thermodynamic Law: Opportunities from Change of Energy Paradigm.Helmut Tributsch - 2006 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 37 (2):287-306.
    Well known quantum and time paradoxes, and the difficulty to derive the second law of thermodynamics, are proposed to be the result of our historically grown paradigm for energy: it is just there, the capacity to do work, not directly related to change. When the asymmetric nature of energy is considered, as well as the involvement of energy turnover in any change, so that energy can be understood as fundamentally "dynamic", and time-oriented, these paradoxes and problems dissolve. The most basic (...)
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  • Complexity, information and time.Rudolf Treumann - 1992 - World Futures 33 (4):213-237.
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  • Understanding probability and irreversibility in the Mori-Zwanzig projection operator formalism.Michael te Vrugt - 2022 - European Journal for Philosophy of Science 12 (3):1-36.
    Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig projection operator formalism, which is one of the most important methods of modern nonequilibrium statistical mechanics, allows for a systematic derivation of irreversible transport equations from reversible microdynamics and thus provides a useful framework for understanding this issue. However, discussions of the MZ formalism in philosophy of physics tend to focus on simple variants rather than (...)
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  • The Passage of Time as Causal Succession of Events.Avril Styrman - 2023 - Journal of Philosophy 120 (12):681-697.
    This work introduces a causal explanation of the passage of time, and contrasts it with rival explanations. In the causal explanation, laws of physics are shown to entail that events are in causal succession, and the passage of time is defined as their causal succession. The causal explanation is coupled with phenomenology of the passage of time, and contrasted with the project of making sense of the idea that time does not pass.
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  • The decoherence puzzle.P. C. E. Stamp - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (3):467-497.
  • Free will in the clustered-minds multiverse, and some comments on S. Sarasvathy’s ‘choice matters’.Christian D. Schade - 2020 - Mind and Society 19 (2):323-330.
    This paper sketches a new version of the multiverse interpretation of quantum mechanics, the clustered-minds multiverse, that has been presented in detail elsewhere. It briefly shows why it grants us with free will and reflects upon the possibilty of singular-universe explanations of free will. It also critically comments upon S. Sarasvathy's 'choice matters,' one of the other contributions to this mini symposium.
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  • Is classical mechanics time reversal invariant?Steven F. Savitt - 1994 - British Journal for the Philosophy of Science 45 (3):907-913.
  • Time, quantum mechanics, and decoherence.Simon Saunders - 1995 - Synthese 102 (2):235 - 266.
    State-reduction and the notion of actuality are compared to passage through time and the notion of the present; already in classical relativity the latter give rise to difficulties. The solution proposed here is to treat both tense and value-definiteness as relational properties or facts as relations; likewise the notions of change and probability. In both cases essential characteristics are absent: temporal relations are tenselessly true; probabilistic relations are deterministically true. The basic ideas go back to Everett, although the technical development (...)
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  • Enantiomorphy and time.Jan-Willem Romeijn - 2005 - International Studies in the Philosophy of Science 19 (2):167 – 190.
    This article argues that time-asymmetric processes in spacetime are enantiomorphs. Subsequently, the Kantian puzzle concerning enantiomorphs in space is reviewed to introduce a number of positions concerning enantiomorphy, and to arrive at a dilemma: one must either reject that orientations of enantiomorphs are determinate, or furnish space or objects with orientation. The discussion on space is then used to derive two problems in the debate on the direction of time. First, it is shown that certain kinds of reductionism about the (...)
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  • Enantiomorphy and Time.Jan-Willem Romeyn - 2005 - International Studies in the Philosophy of Science 19 (2):167-190.
    This article argues that time‐asymmetric processes in spacetime are enantiomorphs. Subsequently, the Kantian puzzle concerning enantiomorphs in space is reviewed to introduce a number of positions concerning enantiomorphy, and to arrive at a dilemma: one must either reject that orientations of enantiomorphs are determinate, or furnish space or objects with orientation. The discussion on space is then used to derive two problems in the debate on the direction of time. First, it is shown that certain kinds of reductionism about the (...)
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  • Causality and the Arrow of Classical Time.Fritz Rohrlich - 2000 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 31 (1):1-13.
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  • Causality and the arrow of classical time.Fritz Rohrlich - 2000 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 31 (1):1-13.
    It is claimed that the `problem of the arrow of time in classical dynamics' has been solved. Since all classical particles have a self-field (gravitational and in some cases also electromagnetic), their dynamics must include self-interaction. This fact and the observation that the domain of validity of classical physics is restricted to distances not less than of the order of a Compton wavelength (thus excluding point particles), leads to the conclusion that the fundamental classical equations of motion are not invariant (...)
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  • Comentaris sobre retrocausació de Phil Dowe.Víctor Rodríguez - 2005 - Enrahonar: Quaderns de Filosofía 37:113-121.
    https://revistes.uab.cat/enrahonar/article/view/v37-rodriguez.
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  • Asymmetry, Abstraction, and Autonomy: Justifying Coarse-Graining in Statistical Mechanics.Katie Robertson - 2020 - British Journal for the Philosophy of Science 71 (2):547-579.
    While the fundamental laws of physics are time-reversal invariant, most macroscopic processes are irreversible. Given that the fundamental laws are taken to underpin all other processes, how can the fundamental time-symmetry be reconciled with the asymmetry manifest elsewhere? In statistical mechanics, progress can be made with this question. What I dub the ‘Zwanzig–Zeh–Wallace framework’ can be used to construct the irreversible equations of SM from the underlying microdynamics. Yet this framework uses coarse-graining, a procedure that has faced much criticism. I (...)
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  • Quantum Interference and Many Worlds: A New Family of Classical Analogies. [REVIEW]M. J. Rave - 2011 - Foundations of Physics 41 (8):1318-1330.
    We present a new way of constructing classical analogies of quantum interference. These analogies share one common factor: they treat closed loops as fundamental entities. Such analogies can be used to understand the difference between quantum and classical probability; they can also be used to illuminate the many worlds interpretation of quantum mechanics. An examination of these analogies suggests that closed loops (particularly closed loops in time) may have special significance in interpretations of quantum interference, because they allow probabilities to (...)
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  • The asymmetry of radiation: Reinterpreting the Wheeler-Feynman argument.Huw Price - 1991 - Foundations of Physics 21 (8):959-975.
    This paper suggests a novel reinterpretation of the mathematical core of Wheeler-Feynman absorber theory, and hence a new route to the conclusion that the temporal asymmetry of classical electromagnetic radiation has the same origin as that of thermodynamics. The argument begins (Sec. 2) with a careful analysis of what the apparent asymmetry of radiation actually involves. Two major flaws in the standard version of the Wheeler-Feynman treatment of radiative asymmetry are then identified (Secs. 4–5), and the proposed reinterpretation is described (...)
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  • Hidden Underdetermination: A Case Study in Classical Electrodynamics.Wolfgang Pietsch - 2012 - International Studies in the Philosophy of Science 26 (2):125-151.
    In this article, I present a case study of underdetermination in nineteenth-century electrodynamics between a pure field theory and a formulation in terms of action at a distance. A particular focus is on the question if and how this underdetermination is eventually resolved. It turns out that after a period of overt underdetermination, during which the approaches are developed separately, the two programmes are merged. On the basis of this development, I argue that the original underdetermination survives in hidden form (...)
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  • Can the decoherence approach help to solve the measurement problem?Osvaldo Pessoa - 1997 - Synthese 113 (3):323-346.
    This work examines whether the environmentally-induced decoherence approach in quantum mechanics brings us any closer to solving the measurement problem, and whether it contributes to the elimination of subjectivism in quantum theory. A distinction is made between ,collapse, and ,decoherence,, so that an explanation for decoherence does not imply an explanation for collapse. After an overview of the measurement problem and of the open-systems paradigm, we argue that taking a partial trace is equivalent to applying the projection postulate. A criticism (...)
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  • The need for the historical understanding of nature in physics and chemistry.Leo Näpinen - 2006 - Foundations of Chemistry 9 (1):65-84.
    During the last decades the physico-chemical conception of self-organization of chemical systems has been created. The chemical systems in natural-historical processes do not have any creator: they rise up from irreversible processes by self-organization. The issue of self-organization in physics has led to a new interpretation of the laws of nature. As Ilya Prigogine has shown, they do not express certainties but possibilities and describe a world that must be understood in a historical way. In the new philosophical understanding of (...)
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  • Should philosophers take lessons from quantum theory?Christopher Norris - 1999 - Inquiry: An Interdisciplinary Journal of Philosophy 42 (3 & 4):311 – 342.
    This essay examines some of the arguments in David Deutsch's book The Fabric of Reality , chief among them its case for the so-called many-universe interpretation of quantum mechanics (QM), presented as the only physically and logically consistent solution to the QM paradoxes of wave/particle dualism, remote simultaneous interaction, the observer-induced 'collapse of the wave-packet', etc. The hypothesis assumes that all possible outcomes are realized in every such momentary 'collapse', since the observer splits off into so many parallel, coexisting, but (...)
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  • Contours of time: Topographic construals of past, present, and future in the Yupno valley of Papua New Guinea.Rafael Núñez, Kensy Cooperrider, D. Doan & Jürg Wassmann - 2012 - Cognition 124 (1):25-35.
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  • 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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  • Auto-affection and the Curvature of Spacetime: Derrida Reading Heidegger Reading Kant.Cathrine Bjørnholt Michaelsen - 2020 - International Journal of Philosophical Studies 28 (3):411-432.
    This paper has a twofold objective. First, it engages with the interrelation of time, space, and matter in Kant, Heidegger, and Derrida and questions whether and how this interrelation effects the possibility of self-relation. In Kant and the Problem of Metaphysics Heidegger suggests that the very structure of subjectivity is constituted by what he calls the ‘pure self-affection’ of time and thus the possibility of self-relation is intimately bound up with the temporalizing of time. In his 1964–65 seminar, Heidegger: the (...)
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  • On the notion of free will in the Free Will Theorem.Klaas Landsman - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 57:98-103.
    The Free Will Theorem of Conway \& Kochen on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will. Although Conway and Kochen informally claim that their theorem supports indeterminism and, in its wake, a libertarian agenda for free will, inferring the former from the Free Will Theorem is a \emph{petitio principii}. Of course, this also considerably weakens the case for (...)
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  • In Search of Time Lost: Asymmetry of Time and Irreversibility in Natural Processes. [REVIEW]A. L. Kuzemsky - 2020 - Foundations of Science 25 (3):597-645.
    In this survey, we discuss and analyze foundational issues of the problem of time and its asymmetry from a unified standpoint. Our aim is to discuss concisely the current theories and underlying notions, including interdisciplinary aspects, such as the role of time and temporality in quantum and statistical physics, biology, and cosmology. We compare some sophisticated ideas and approaches for the treatment of the problem of time and its asymmetry by thoroughly considering various aspects of the second law of thermodynamics, (...)
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  • The Universal Arrow of Time.Oleg Kupervasser, Hrvoje Nikolić & Vinko Zlatić - 2012 - Foundations of Physics 42 (9):1165-1185.
    Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of (...)
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  • About the confusion between the course of time and the arrow of time.Étienne Klein - 2007 - Foundations of Science 12 (3):203-221.
    A conclusion drawn after a conference devoted (in 1995) to the “arrow of time” was the following: “Indeed, it seems not a very great exaggeration to say that the main problem with “the problem of the direction of time” is to figure out exactly what the problem is supposed to be !” What does that mean? That more than 130 years after the work of Ludwig Boltzmann on the interpretation of irreversibility of physical phenomena, and that one century after Einstein’s (...)
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  • Can Quantum Theory be Applied to the Universe as a Whole?Claus Kiefer - 2010 - Foundations of Physics 40 (9-10):1410-1418.
    I argue that quantum theory can, and in fact must, be applied to the Universe as a whole. After a general introduction, I discuss two concepts that are essential for my chain of arguments: the universality of quantum theory and the emergence of classical behaviors by decoherence. A further motivation is given by the open problem of quantum gravity. I then present the main ingredients of quantum cosmology and discuss their relevance for the interpretation of quantum theory. I end with (...)
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  • Composite Time Concept for Quantum Mechanics and Bio-Psychology.Franz Klaus Jansen - 2018 - Philosophy Study 8 (2):49-66.
    Time has multiple aspects and is difficult to define as one unique entity, which therefore led to multiple interpretations in physics and philosophy. However, if the perception of time is considered as a composite time concept, it can be decomposed into basic invariable components for the perception of progressive and support-fixed time and into secondary components with possible association to unit-defined time or tense. Progressive time corresponds to Bergson’s definition of duration without boundaries, which cannot be divided for measurements. Time (...)
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  • Physics versus Semantics: A Puzzling Case of the Missing Quantum Theory. [REVIEW]Milan M. Ćirković - 2005 - Foundations of Physics 35 (5):817-838.
    A case for the project of excising of confusion and obfuscation in the contemporary quantum theory initiated and promoted by David Deutsch has been made. It has been argued that at least some theoretical entities which are conventionally labelled as “interpretations” of quantum mechanics are in fact full-blooded physical theories in their own right, and as such are falsifiable, at least in principle. The most pertinent case is the one of the so-called “Many-Worlds Interpretation” (MWI) of Everett and others. This (...)
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  • Three's a crowd: On causes, entropy and physical eschatology. [REVIEW]Milan M. Ćirković & Vesna Milošević-Zdjelar - 2004 - Foundations of Science 9 (1):1-24.
    Recent discussions of theorigins of the thermodynamical temporal asymmetry (thearrow of time) by Huw Price and others arecritically assessed. This serves as amotivation for consideration of relationshipbetween thermodynamical and cosmologicalcauses. Although the project of clarificationof the thermodynamical explanandum is certainlywelcome, Price excludes another interestingoption, at least as viable as the sort ofAcausal-Particular approach he favors, andarguably more in the spirit of Boltzmannhimself. Thus, the competition of explanatoryprojects includes three horses, not two. Inaddition, it is the Acausal-Particular approachthat could benefit enormously (...)
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  • Philosophical issues in electromagnetism.Mathias Frisch - 2008 - Philosophy Compass 4 (1):255-270.
    This paper provides a survey of several philosophical issues arising in classical electrodynamics arguing that there is a philosophically rich set of problems in theories of classical physics that have not yet received the attention by philosophers that they deserve. One issue, which is connected to the philosophy of causation, concerns the temporal asymmetry exhibited by radiation fields in the presence of wave sources. Physicists and philosophers disagree on whether this asymmetry reflects a fundamental causal asymmetry or is due to (...)
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  • (Dis-)solving the puzzle of the arrow of radiation.Mathias Frisch - 2000 - British Journal for the Philosophy of Science 51 (3):381-410.
    I criticize two accounts of the temporal asymmetry of electromagnetic radiation - that of Huw Price, whose account centrally involves a reinterpretation of Wheeler and Feynman's infinite absorber theory, and that of Dieter Zeh. I then offer some reasons for thinking that the purported puzzle of the arrow of radiation does not present a genuine puzzle in need of a solution.
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  • The Milky Way’s Supermassive Black Hole: How Good a Case Is It?: A Challenge for Astrophysics & Philosophy of Science.Andreas Eckart, Andreas Hüttemann, Claus Kiefer, Silke Britzen, Michal Zajaček, Claus Lämmerzahl, Manfred Stöckler, Monica Valencia-S., Vladimir Karas & Macarena García-Marín - 2017 - Foundations of Physics 47 (5):553-624.
    The compact and, with \ M\, very massive object located at the center of the Milky Way is currently the very best candidate for a supermassive black hole in our immediate vicinity. The strongest evidence for this is provided by measurements of stellar orbits, variable X-ray emission, and strongly variable polarized near-infrared emission from the location of the radio source Sagittarius A* in the middle of the central stellar cluster. Simultaneous near-infrared and X-ray observations of SgrA* have revealed insights into (...)
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  • Information Loss as a Foundational Principle for the Second Law of Thermodynamics.T. L. Duncan & J. S. Semura - 2007 - Foundations of Physics 37 (12):1767-1773.
    In a previous paper (Duncan, T.L., Semura, J.S. in Entropy 6:21, 2004) we considered the question, “What underlying property of nature is responsible for the second law?” A simple answer can be stated in terms of information: The fundamental loss of information gives rise to the second law. This line of thinking highlights the existence of two independent but coupled sets of laws: Information dynamics and energy dynamics. The distinction helps shed light on certain foundational questions in statistical mechanics. For (...)
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  • Compact Time and Determinism for Bosons: Foundations. [REVIEW]Donatello Dolce - 2011 - Foundations of Physics 41 (2):178-203.
    Free bosonic fields are investigated at a classical level by imposing their characteristic de Broglie periodicities as constraints. In analogy with finite temperature field theory and with extra-dimensional field theories, this compactification naturally leads to a quantized energy spectrum. As a consequence of the relation between periodicity and energy arising from the de Broglie relation, the compactification must be regarded as dynamical and local. The theory, whose foundamental set-up is presented in this paper, turns out to be consistent with special (...)
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  • Memory as a Property of Nature.Ted Dace - 2018 - Axiomathes 28 (5):507-519.
    Prerequisite to memory is a past distinct from present. Because wave evolution is both continuous and time-reversible, the undisturbed quantum system lacks a distinct past and therefore the possibility of memory. With the quantum transition, a reversibly evolving superposition of values yields to an irreversible emergence of definite values in a distinct and transient moment of time. The succession of such moments generates an irretrievable past and thus the possibility of memory. Bohm’s notion of implicate and explicate order provides a (...)
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  • The Thermodynamical Arrow of Time: Reinterpreting the Boltzmann–Schuetz Argument. [REVIEW]Milan M. Ćirković - 2002 - Foundations of Physics 33 (3):467-490.
    The recent surge of interest in the origin of the temporal asymmetry of thermodynamical systems (including the accessible part of the universe itself) has put forward two possible explanatory approaches to this age-old problem. Hereby we show that there is a third possible alternative, based on the generalization of the classical (“Boltzmann–Schuetz”) anthropic fluctuation picture of the origin of the perceived entropy gradient. This alternative (which we dub the Acausal-Anthropic approach) is based on accepting Boltzmann's statistical measure at its face (...)
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  • The view from no-when. [REVIEW]Craig Callender - 1998 - British Journal for the Philosophy of Science 49 (1):135 - 159.
    In Philip K. Dick’s Counter-Clock World the direction of time flips in 1986, putting the Earth into what its inhabitants call the ‘Hogarth Phase’. Named after the scientist who predicted that ‘time’s arrow' would change direction, the Hogarth Phase is a period in which entropy decreases instead of increases. During this time the dead call from their graves to be excavated, people clean their lungs by ‘smoking’ stubs that grow into mature cigarettes, coffee separates from cream, and so on. Although (...)
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  • Review article. The view from no-when.Craig Callender - 1998 - British Journal for the Philosophy of Science 49 (1):135-159.
  • Vacuum Radiation, Entropy, and Molecular Chaos.Jean E. Burns - 2007 - Foundations of Physics 37 (12):1727-1737.
    Vacuum radiation causes a particle to make a random walk about its dynamical trajectory. In this random walk the root mean square change in spatial coordinate is proportional to t 1/2, and the fractional changes in momentum and energy are proportional to t −1/2, where t is time. Thus the exchange of energy and momentum between a particle and the vacuum tends to zero over time. At the end of a mean free path the fractional change in momentum of a (...)
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