Results for 'Arrow of time'

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  1.  57
    Does a Computer Have an Arrow of Time?Owen J. E. Maroney - 2010 - Foundations of Physics 40 (2):205-238.
    Schulman (Entropy 7(4):221–233, 2005) has argued that Boltzmann’s intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support (...)
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  2.  29
    Arrow of Time in Rigged Hilbert Space Quantum Mechanics.Robert C. Bishop - 2004 - International Journal of Theoretical Physics 43 (7):1675–1687.
    Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels-Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is discussed focusing on (...)
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  3. The Thermodynamical Arrow of Time: Reinterpreting the Boltzmann–Schuetz Argument. [REVIEW]Milan M. Cirkovic - 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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  4.  31
    Time-Reversal, Irreversibility and Arrow of Time in Quantum Mechanics.M. Castagnino, M. Gadella & O. Lombardi - 2006 - Foundations of Physics 36 (3):407-426.
    The aim of this paper is to analyze time-asymmetric quantum mechanics with respect of its validity as a non time-reversal invariant, time-asymmetric theory as well as of its ability to determine an arrow of time.
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  5.  42
    The Arrow of Time and Meaning.Pierre Uzan - 2007 - 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 (...)
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  6.  83
    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 (...)
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  7. Gnoseology, Ontology, and the Arrow of Time.J. J. Sanguineti & M. Castagnino - 1998 - Acta Philosophica 7 (2):235-265.
    This paper studies the problem of the arrow of time from the scientific and philosophical perspective. The scientific section (Castagnino) poses the topic according to the instruments of measuring employed in physical theories, specially when they are applied to dynamic chaotic systems in which a temporal asymmetry is shown. From the analysis of “two schools” (epistemological and ontological), the conclusion is favorable to the reality (both ontological and epistemological) of the difference between past and future, with the recourse (...)
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  8.  51
    Comment On: “Causality and the Arrow of Classical Time”, by Fritz Rohrlich.Carlo Rovelli - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (3):397-405.
    Rohrlich claims that “the problem of the arrow of time in classical dynamics has been solved”. The solution he proposes is based on the equations governing the motion of extended particles. Rohrlich claims that these equations, which must take self-interaction into account, are not invariant under time reversal. I dispute this claim, on several grounds.
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  9. Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical Probabilities.Eddy Keming Chen - forthcoming - In Valia Allori (ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature. World Scientific.
    In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there (...)
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  10. 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 (...)
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  11.  78
    The Arrow of Time and the Action of the Mind at the Molecular Level.Jean E. Burns - 2006 - In Daniel P. Sheehan (ed.), Frontiers of Time. American Inst. Of Physics.
    A new event is defined as an intervention in the time reversible dynamical trajectories of particles in a system. New events are then assumed to be quantum fluctuations in the spatial and momentum coordinates, and mental action is assumed to work by ordering such fluctuations. It is shown that when the cumulative values of such fluctuations in a mean free path of a molecule are magnified by molecular interaction at the end of that path, the momentum of a molecule (...)
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  12.  78
    The Global Non-Entropic Arrow of Time: From Global Geometrical Asymmetry to Local Energy Flow.Mario Castagnino & Olimpia Lombardi - 2009 - Synthese 169 (1):1-25.
    Since the nineteenth century, the problem of the arrow of time has been traditionally analyzed in terms of entropy by relating the direction past-to-future to the gradient of the entropy function of the universe. In this paper, we reject this traditional perspective and argue for a global and non-entropic approach to the problem, according to which the arrow of time can be defined in terms of the geometrical properties of spacetime. In particular, we show how the (...)
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  13.  19
    The Second Law of Thermodynamics and the Psychological Arrow of Time.Meir Hemmo & Orly Shenker - forthcoming - British Journal for the Philosophy of Science.
    Can the second law of thermodynamics explain our mental experience of the direction of time? According to an influential approach, the past hypothesis of universal low entropy also explains how the psychological arrow comes about. We argue that although this approach has many attractive features, it cannot explain the psychological arrow after all. In particular, we show that the past hypothesis is neither necessary nor sufficient to explain the psychological arrow on the basis of current physics. (...)
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  14. The Global Arrow of Time as a Geometrical Property of the Universe.Mario Castagnino, Olimpia Lombardi & Luis Lara - 2003 - Foundations of Physics 33 (6):877-912.
    Traditional discussions about the arrow of time in general involve the concept of entropy. In the cosmological context, the direction past-to-future is usually related to the direction of the gradient of the entropy function of the universe. But the definition of the entropy of the universe is a very controversial matter. Moreover, thermodynamics is a phenomenological theory. Geometrical properties of space-time provide a more fundamental and less controversial way of defining an arrow of time for (...)
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  15. The Arrow of Time: From Universe Time-Asymmetry to Local Irreversible Processes. [REVIEW]Matías Aiello, Mario Castagnino & Olimpia Lombardi - 2008 - Foundations of Physics 38 (3):257-292.
    In several previous papers we have argued for a global and non-entropic approach to the problem of the arrow of time, according to which the “arrow” is only a metaphorical way of expressing the geometrical time-asymmetry of the universe. We have also shown that, under definite conditions, this global time-asymmetry can be transferred to local contexts as an energy flow that points to the same temporal direction all over the spacetime. The aim of this paper (...)
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  16.  89
    On the Brussels School's Arrow of Time in Quantum Theory.Vassilios Karakostas - 1996 - Philosophy of Science 63 (3):374-400.
    This paper examines the problem of founding irreversibility on reversible equations of motion from the point of view of the Brussels school's recent developments in the foundations of quantum statistical mechanics. A detailed critique of both their 'subdynamics' and 'transformation' theory is given. It is argued that the subdynamics approach involves a generalized form of 'coarse-graining' description, whereas, transformation theory cannot lead to truly irreversible processes pointing to a preferred direction of time. It is concluded that the Brussels school's (...)
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  17.  86
    Does Quantum Electrodynamics Have an Arrow of Time?☆.David Atkinson - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (3):528-541.
    Quantum electrodynamics is a time-symmetric theory that is part of the electroweak interaction, which is invariant under a generalized form of this symmetry, the PCT transformation. The thesis is defended that the arrow of time in electrodynamics is a consequence of the assumption of an initial state of high order, together with the quantum version of the equiprobability postulate.
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  18.  48
    The Arrow of Time in the Equations of Motion.Fritz Rohrlich - 1998 - Foundations of Physics 28 (7):1045-1056.
    It is argued that time's arrow is present in all equations of motion. But it is absent in the point particle approximations commonly made. In particular, the Lorentz-Abraham-Dirac equation is time-reversal invariant only because it approximates the charged particle by a point. But since classical electrodynamics is valid only for finite size particles, the equations of motion for particles of finite size must be considered. Those equations are indeed found to lack time-reversal invariance, thus ensuring an (...)
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  19.  62
    The Arrow of Time in Quantum Gravity.Chuang Liu - 1993 - Philosophy of Science 60 (4):619-637.
    This essay is a philosophical evaluation of some of the findings of Wald and Penrose in which they claim to have supported an arrow (or the irreversibility) of time in quantum gravity. First, the notion of lawlike irreversibility (or anisotropy) of time is spelled out, then the general situation in quantum mechanics is briefly discussed. Finally, the findings in quantum gravity are evaluated against such a background. My conclusion is that the arrow of time found (...)
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  20.  4
    Does Quantum Electrodynamics Have an Arrow of Time?David Atkinson - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (3):528-541.
    Quantum electrodynamics is a time-symmetric theory that is part of the electroweak interaction, which is invariant under a generalized form of this symmetry, the PCT transformation. The thesis is defended that the arrow of time in electrodynamics is a consequence of the assumption of an initial state of high order, together with the quantum version of the equiprobability postulate.
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  21.  4
    Does Quantum Electrodynamics Have an Arrow of Time?David Atkinson - 2005 - Studies in History and Philosophy of Modern Physics 37 (3):528-541.
    Quantum electrodynamics is a time-symmetric theory that is part of the electroweak interaction, which is invariant under a generalized form of this symmetry, the PCT transformation. The thesis is defended that the arrow of time in electrodynamics is a consequence of the assumption of an initial state of high order, together with the quantum version of the equiprobability postulate.
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  22.  62
    Time's Arrow and Archimedes' Point: New Directions for the Physics of Time.Huw Price - 1997 - Oup Usa.
    Why is the future so different from the past? Why does the past affect the future and not the other way round? The universe began with the Big Bang - will it end with a `Big Crunch'? Now in paperback, this book presents an innovative and controversial view of time and contemporary physics. Price urges physicists, philosophers, and anyone who has ever pondered the paradoxes of time to look at the world from a fresh perspective, and throws fascinating (...)
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  23.  25
    The Arrow of Time in Physics.David Wallace - unknown
    I provide a self-contained introduction to the problem of the arrow of time in physics, concentrating on the irreversibility of dynamical processes as described in statistical mechanics.
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  24. Absolute Becoming, Relational Becoming, and the Arrow of Time.Mauro Dorato - unknown
    My first and main claim is that physics cannot provide empirical evidence for the objectivity of absolute becoming, for the simple reason that it must presuppose it, at least to the extent that classical spacetime theories presuppose an ontology of events. However, the fact that a theory of absolute becoming must be situated in the a priori realm of metaphysics does not make becoming completely irrelevant for physics, since my second claim will consist in showing that relational becoming, once appropriately (...)
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  25.  3
    Looking at the Arrow of Time and Loschmidt’s Paradox Through the Magnifying Glass of Mathematical-Billiard.Mario Stefanon - forthcoming - Foundations of Physics:1-21.
    The contrast between the past-future symmetry of mechanical theories and the time-arrow observed in the behaviour of real complex systems doesn’t have nowadays a fully satisfactory explanation. If one confides in the Laplace-dream that everything be exactly and completely describable by the known mechanical differential equations, the whole experimental evidence of the irreversibility of real complex processes can only be interpreted as an illusion due to the limits of human brain and shortness of human history. In this work (...)
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  26.  28
    The Mathematical Representation of the Arrow of Time.Meir Hemmo & Orly Shenker - 2012 - Iyyun 61:167-192.
    This paper distinguishes between 3 meanings of reversal, all of which are mathematically equivalent in classical mechanics: velocity reversal, retrodiction, and time reversal. It then concludes that in order to have well defined velocities a primitive arrow of time must be included in every time slice. The paper briefly mentions that this arrow cannot come from the Second Law of thermodynamics, but this point is developed in more details elsewhere.
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  27.  9
    Arrow of Time Without a Past Hypothesis.Dustin Lazarovici & Paula Reichert - unknown
    The paper discusses recent proposals by Carroll and Chen, as well as Barbour, Koslowski, and Mercati to explain the arrow of time without a Past Hypothesis, i.e. the assumption of a special initial state of the universe. After discussing the role of the Past Hypothesis and the controversy about its status, we explain why Carroll's model - which establishes an arrow of time as typical - can ground sensible predictions and retrodictions without assuming something akin to (...)
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  28.  16
    Introduction to the Philosophy of Statistical Mechanics: Can Probability Explain the Arrow of Time in the Second Law of Thermodynamics?Meir Hemmo Orly Shenker - 2011 - Philosophy Compass 6 (9):640-651.
    The arrow of time is a familiar phenomenon we all know from our experience: we remember the past but not the future and control the future but not the past. However, it takes an effort to keep records of the past, and to affect the future. For example, it would take an immense effort to unmix coffee and milk, although we easily mix them. Such time directed phenomena are subsumed under the Second Law of Thermodynamics. This law (...)
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  29.  87
    Introduction to the Philosophy of Statistical Mechanics: Can Probability Explain the Arrow of Time in the Second Law of Thermodynamics?Orly Shenker & Meir Hemmo - 2011 - Philosophy Compass 6 (9):640-651.
    The arrow of time is a familiar phenomenon we all know from our experience: we remember the past but not the future and control the future but not the past. However, it takes an effort to keep records of the past, and to affect the future. For example, it would take an immense effort to unmix coffee and milk, although we easily mix them. Such time directed phenomena are sub- sumed under the Second Law of Thermodynamics. This (...)
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  30.  64
    The Arrow of Time in Cosmology.Mario Castagnino, Olimpia Lombardi & Luis Lara - unknown
    Scientific cosmology is an empirical discipline whose objects of study are the large-scale properties of the universe. In this context, it is usual to call the direction of the expansion of the universe the "cosmological arrow of time". However, there is no reason for privileging the ‘radius’ of the universe for defining the arrow of time over other geometrical properties of the space-time. Traditional discussions about the arrow of time in general involve the (...)
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  31.  25
    Zagzebski on the Arrow of Time.Hugh Rice - 2005 - Faith and Philosophy 22 (3):363-369.
    Linda Zagzebski has recently argued that there is a conflict between a common view of the asymmetry of time and various other metaphysical hypotheses. She identifies conflicts in the case of the modal arrow of time and in the case of the causal arrow of time. In the case of the modal arrow I argue that on one view there is no conflict and that on another the principle should be abandoned that there are (...)
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  32.  24
    Dimensional Symmetry Breaking, Information and the Arrow of Time in Cantorian Space.M. S. El Naschie - 1997 - World Futures 49 (3):391-400.
    (1997). Dimensional symmetry breaking, information and the arrow of time in cantorian space. World Futures: Vol. 49, The Quest for a Unified Theory of Information, pp. 391-400.
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  33.  26
    The Arrow of Time in Classical Electrodynamics.Fritz Rohrlich - unknown
    The reason for the arrow of time in electromagnetic radiation is explicated.
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  34.  46
    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 (...)
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  35.  25
    Quantum Gravity, the Origin of Time and Time's Arrow.J. W. Moffat - 1993 - Foundations of Physics 23 (3):411-437.
    The local Lorentz and diffeomorphism symmetries of Einstein's gravitational theory are spontaneously broken by a Higgs mechanism by invoking a phase transition in the early universe, at a critical temperature Tc below which the symmetry is restored. The spontaneous breakdown of the vacuum state generates an external time, and the wave function of the universe satisfies a time-dependent Schrödinger equation, which reduces to the Wheeler-deWitt equation in the classical regime for T (...)
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  36. The Arrow of Time and the Moving Image of Eternity.Raymond Aaron Younis - 2008 - Journal of Religious History 32 (1):109-116..
  37.  5
    Time’s Arrow Today: Recent Physical and Philosophical Work on the Direction of Time.Katinka Ridderbos & Steven F. Savitt - 1997 - Philosophical Review 106 (4):627.
    One of the questions that is addressed, from various perspectives, is the origin of time-asymmetry. Given the time-symmetry of the dynamical laws, all inferences about the future that are derivable from a dynamical theory are matched by inferences about the past. For Huw Price, who discusses the origins of cosmological time asymmetry, this is reason to treat all time-asymmetric cosmological theories with caution. He dismisses both the inflationary model and Stephen Hawking’s proposal to account for (...)-asymmetry with his famous “no boundary condition.” Instead, on the basis of the fact that we have no a priori reasons to distinguish between initial and final conditions, he advocates Gold’s time-symmetric model for the universe, in which the thermodynamical arrow of time is tied to the expansion of the universe, so that in the contracting phase towards the big crunch, entropy decreases. (shrink)
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  38.  22
    Time’s Arrow Today: Recent Physical and Philosophical Work on the Direction of Time.Katinka Ridderbos - 1997 - Philosophical Review 106 (4):627-628.
    One of the questions that is addressed, from various perspectives, is the origin of time-asymmetry. Given the time-symmetry of the dynamical laws, all inferences about the future that are derivable from a dynamical theory are matched by inferences about the past. For Huw Price, who discusses the origins of cosmological time asymmetry, this is reason to treat all time-asymmetric cosmological theories with caution. He dismisses both the inflationary model and Stephen Hawking’s proposal to account for (...)-asymmetry with his famous “no boundary condition.” Instead, on the basis of the fact that we have no a priori reasons to distinguish between initial and final conditions, he advocates Gold’s time-symmetric model for the universe, in which the thermodynamical arrow of time is tied to the expansion of the universe, so that in the contracting phase towards the big crunch, entropy decreases. (shrink)
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  39. Relativity Theory May Not Have the Last Word on the Nature of Time: Quantum Theory and Probabilism.Nicholas Maxwell - 2017 - In G. Ghirardi & S. Wuppulur (eds.), Space, Time and the Limits of Human Understanding. Springer. pp. 109-124.
    Two radically different views about time are possible. According to the first, the universe is three dimensional. It has a past and a future, but that does not mean it is spread out in time as it is spread out in the three dimensions of space. This view requires that there is an unambiguous, absolute, cosmic-wide "now" at each instant. According to the second view about time, the universe is four dimensional. It is spread out in both (...)
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  40.  61
    Time's Arrow and Archimedes' Point: New Directions for the Physics of Time[REVIEW]Gordon Belot - 1998 - Philosophical Review 107 (3):477.
    A review of Huw Price's Time's Arrow and Archimedes' Point.
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  41.  17
    From Eternity to Here: The Quest for the Ultimate Theory of Time.Sean M. Carroll - 2010 - Dutton.
    This book provides an account of the nature of time, especially time's arrow and the role of entropy, at a semi-popular level. Special attention is given to statistical mechanics, the past hypothesis, and possible cosmological explanations thereof.
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  42. In Search of the Arrow of Time. Temporal Asymmetries in Leibniz.Jean-Pascal Anfray - 2012 - Studia Leibnitiana 44 (1):81-106.
    This paper examines the problem of the basis of time’s asymmetry. I hold the view that there is an objective temporal asymmetry in Leibniz’s philosophy of time. I closely examine various asymmetrical phenomena, which can be candidates as an explanation of time’s asymmetry: (1) causation; (2) the flow of time; (3) the modal difference between past and present; (4) counterfactual dependence; and, finally (5) the asymmetry of the world’s progress and its direction and (6) of the (...)
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  43. Probability, Arrow of Time and Decoherence.Guido Bacciagaluppi - 2006 - Studies in History and Philosophy of Modern Physics 38 (2):439-456.
    This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard approach to time symmetry in the decoherent histories literature is criticised, and an alternative approach is proposed, based on two decoherence conditions within the one-vector formalism. In turn, (...)
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  44.  6
    Probability, Arrow of Time and Decoherence.Guido Bacciagaluppi - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):439-456.
    This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard approach to time symmetry in the decoherent histories literature is criticised, and an alternative approach is proposed, based on two decoherence conditions within the one-vector formalism. In turn, (...)
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  45.  32
    When We Do Have a Classical Arrow of Time.Bryan W. Roberts - unknown
    I point out that some common folk wisdom about time reversal invariance in classical mechanics is strictly incorrect, by showing some explicit examples in which classical time reversal invariance fails, even among conservative systems. I then show that there is nevertheless a broad class of familiar classical systems that are time reversal invariant.
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  46. Causation and the Arrow of Time.Alexander R. Pruss - unknown
    “We are always already thrown into concrete factual circumstances, facing possibilities that we need to come to grips with. By choosing some we exclude others, thus making them no longer possible. What we are thrown into is the past and present, and the possibilities loom ahead of us, though we may try to turn our back on them. The future is the home of the possibilities while the present and past define the circumstances in which we make our choices, circumstances (...)
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  47. The Significance of Causally Coupled, Stable Neuronal Assemblies for the Psychological Time Arrow.Harald Atmanspacher - manuscript
    Stable neuronal assemblies are generally regarded as neural correlates of mental representations. Their temporal sequence corresponds to the experience of a direction of time, sometimes called the psychological time arrow. We show that the stability of particular, biophysically motivated models of neuronal assemblies, called coupled map lattices, is supported by causal interactions among neurons and obstructed by non-causal or anti-causal interactions among neurons. This surprising relation between causality and stability suggests that those neuronal assemblies that are stable (...)
     
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  48.  10
    Weak Interactions and the Curious Little Arrow of Time.Bryan W. Roberts - unknown
    In this talk from ETH Zurich’s Workshop on Time in Physics, Bryan Roberts introduces weak interactions and argues that the laws of nature are directed in time.
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  49.  2
    Are the Laws of Nature Time Reversal Symmetric?: The Arrow of Time, or Better: The Arrow of Directional Processes.Paul Weingartner - 2006 - In Michael Stöltzner & Friedrich Stadler (eds.), Time and History: Proceedings of the 28. International Ludwig Wittgenstein Symposium, Kirchberg Am Wechsel, Austria 2005. De Gruyter. pp. 289-300.
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  50.  7
    Sharpening the Electromagnetic Arrow(s) of Time.John Earman - 2011 - In Craig Callender (ed.), The Oxford Handbook of Philosophy of Time. Oxford University Press.
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