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- Étienne Klein (2007). About the Confusion Between the Course of Time and the Arrow of Time. Foundations of Science 12 (3).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 formulation of Special Relativity, we are still not sure what we mean when we talk of “time” or “arrow of time”. We shall try to show that one source of this difficulty is our tendency to confuse, at least verbally, time and becoming, i.e. the course of time and the arrow of time, two concepts that the formalisms of modern physics are careful to distinguish.
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The theory of general relativity has produced some great insights into the nature of space and time. Unfortunately, its relevance to the problem of the direction of time has been overestimated. This paper points out that the problem of the direction of time can be formulated in purely local ways, and that in this kind of formulation considerations of general relativity are of little or no importance. On the basis of this, positions which assume that relativistic considerations are always relevant are criticised.
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 entailments between propositions about the past and the future. In the case of the causal arrow I argue that the conflict can be avoided by the adoption of a suitable closure principle.
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 entailments between propositions about the past and the future. In the case of the causal arrow I argue that the conflict can be avoided by the adoption of a suitable closure principle.
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 global non-entropic arrow can be transferred to the local level, where it takes the form of a non-spacelike local energy flow that provides the criterion for breaking the symmetry resulting from time-reversal invariant local laws.
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 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 entropy is a thermodynamic magnitude that is typically associated with subsystems of the universe: the entropy of the universe as a whole 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 the universe as a whole. We will call the arrow defined only on the basis of the geometrical properties of space-time, independently of any entropic considerations, the "cosmological arrow of time". In this paper we will argue that: (i) it is possible to define a cosmological arrow of time for the universe as a whole, if certain conditions are satisfied, and (ii) the standard models of contemporary cosmology satisfy these conditions.
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The aim of this paper is to analyze time-asymmetric quantum mechanics with respect to the problems of irreversibility and of time's arrow. We begin with arguing that both problems are conceptually different. Then, we show that, contrary to a common opinion, the theory's ability to describe irreversible quantum processes is not a consequence of the semigroup evolution laws expressing the non-time-reversal invariance of the theory. Finally, we argue that time-asymmetric quantum mechanics, either in Prigogine's version or in Bohm's version, does not solve the problem of the arrow of time because it does not supply a substantial and theoretically founded criterion for distinguishing between the two directions of time.
Discussion of Étienne Klein, About the confusion between the course of time and the arrow of time
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