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 are (...) two sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

This volume contains a selection of Professor Uzawa's important contributions to mathematical economics. Subjects covered by these nineteen essays include consumption, production, equilibrium, capital, growth, planning, international trade, and the theory of social overhead capital. Written in the 1960s and early 1970s, the papers form a basis upon which economic theory has developed over the last twenty years. The collection includes some of Uzawa's classic contributions, such as 'Preference and Rational Choice in the Theory of Consumption', 'Time Preference, the Consumption (...) Function, and Optimum Asset Holdings', 'Neutral Inventions and the Stability of Growth Equilibrium', 'On a Two-Sector Model of Economic Growth', 'Time Preference and the Penrose Effect in a Two-Class Model of Economic Growth', and 'On the Economics of Social Overhead Capital'. The collection will be useful not only in understanding the nature of the development in economic theory today, but also in reflecting upon the direction toward which economic theory will be advancing in the future. (shrink)

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 new light (...) on some of the great mysteries of the universe. (shrink)

One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or (...) the distant ''future''), the Past Hypothesis is not enough; we also need to postulate self-locating (de se) probabilities. However, I show that we can similarly use self-locating probabilities to strengthen its rival---the Fluctuation Hypothesis, leading to in-principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to 'empirical coherence' or 'simplicity.' That is a serious problem for the vision of providing a completely scientific explanation of time's arrow. (shrink)

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. (shrink)

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. (shrink)

While experience tells us that time flows from the past to the present and into the future, a number of philosophical and physical objections exist to this commonsense view of dynamic time. In an attempt to make sense of this conundrum, philosophers and physicists are forced to confront fascinating questions, such as: Can effects precede causes? Can one travel in time? Can the expansion of the Universe or the process of measurement in quantum mechanics define a direction in time? In (...) this book, researchers from both physics and philosophy attempt to answer these issues in an interesting, yet rigorous way. This fascinating book will be of interest to physicists and philosophers of science and educated general readers interested in the direction of time. (shrink)

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 time-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)

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. (shrink)

We observe entropy decrease towards the past. Does this imply that in the past the world was in a non-generic microstate? I point out an alternative. The subsystem to which we belong interacts with the universe via a relatively small number of quantities, which define a coarse graining. Entropy happens to depends on coarse-graining. Therefore the entropy we ascribe to the universe depends on the peculiar coupling between us and the rest of the universe. Low past entropy may be due (...) to the fact that this coupling is non-generic. I argue that for any generic microstate of a sufficiently rich system there are always special subsystems defining a coarse graining for which the entropy of the rest is low in one time direction. These are the subsystems allowing creatures that “live in time” —such as those in the biosphere— to exist. I reply to some objections raised to an earlier presentation of this idea, in particular by Bob Wald, David Albert and Jim Hartle. (shrink)

In this chapter, I argue that the loss of loved ones requires a revised vision of our relationship to past persons. In particular, I argue that relating to deceased loved ones as points on an ordered, forward-moving timeline—on which they grow more distant from us by the moment—has a distorting and damaging effect on our own identity. If we detach ourselves completely from those who sustain important aspects of our identity, this will cause a jagged break in our narrative where (...) a new self must be constructed (whether by us or our circumstances) ex nihilo. On the other hand, if we allow ourselves to drift into the past with the dead—resigning ourselves to existence as an historical object—we will find that we begin to fade away ourselves. Either way, both the self and the beloved are ultimately lost, since both depend on the lost union. To reject both options is a tremendously difficult task that will require rethinking time and our relationship to the past. I argue that we can look to Kierkegaard’s work on maintaining contemporaneity with the historical past, particularly his warnings about how we must not respond to the loss of a beloved. In the last section of the paper, I offer some suggestions for how we might, in a Kierkegaardian spirit, strive to maintain real union with deceased loved ones, thereby rising above the destructive current of time. (shrink)

A review of Huw Price's Time's Arrow and Archimedes' Point.

Reductive accounts of the direction of time are often paired with Humean accounts of laws, while non-reductive accounts of time are often paired with anti-Humean accounts of laws. The traditional pairing of views has recently come under question. This paper aims to clarify what sorts of anti-Humean views motivate anti-reductionism about the direction of time. It is argued that those who think (i) that the laws are metaphysically fundamental, and (ii) that the laws contain time-asymmetric contents, should treat the (...) class='Hi'>arrow of time as metaphysically fundamental. (shrink)

In view of the time-symmetric nature of the laws of physics, time asymmetry in the universe must arise from “initial” conditions. A fully time-symmetric oscillating model is presented which exists in a highly compressed, highly ordered state att=0 and evolves forward, in the thermodynamic sense, as ∣t ∣ increases. This model offers the possibility of accounting for several fundamental and puzzling aspects of our universe, including matter-antimatter asymmetry, the large entropy per baryon, primordial density enhancements sufficient to form galaxies, and (...) large-scale homogeneity. (shrink)

This concluding section applies the results of the previous part to some important thermodynamical systems. Even if time reversibility is allowed, it is shown that the flow vectors used to derive Onsager reciprocity from time translational invariance is of questionable validity. The fundamental fluctuation dissipation theorem of Callen, Welton, Green and Kubo which underpin descriptions of irreversibility, insofar as they are derived from time translational invariance, is also questioned; from Part I, they cannot be derived properly from time reversal symmetry. (...) The common view of entropy as some type of caloric fluid flow is critiqued as not conforming to the Kelvin Clausius Planck definition. An example of developing reciprocal relations to any order in the coupling indices based on the peculiar physical and defining characteristics of conductive heat is given for the steady state whenever a temperature gradient is present, free from time reversible and translation assumptions. A major challenge in the theory is to extend it to isothermal states. It is concluded that other more deterministic views mediated by authentic work anamnesis may be needed for long term coherence. (shrink)

Responding to Hasok Chang’s vision of the history and philosophy of science as the continuation of science by other means, I illustrate the methods of HPS and their utility through a historico-critical examination of the problem of “time’s arrow‘, that is to say, the problem posed by the claim by Boltzmann and others that the temporal asymmetry of many physical processes and indeed the very possibility of identifying each of the two directions we distinguish in time must have a (...) ground in the laws of nature. I claim that this problem has proved intractable chiefly because the standard mathematical representation of time employed in the formulation of the laws of nature “forgets‘ one of the connotations of the word ”time’ as it is used in ordinary language and in experimental physics. (shrink)

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 time-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)

«The chapter on «Times's Arrows» is a confusing blend of speculation and possibly wrong ideas.»From a review of M Gell‐Mann's «The Quark and the Jaguar» by P W Anderson in Physics World, August 1994.

The distribution of matter in our universe is strikingly time asymmetric. Most famously, the Second Law of Thermodynamics says that entropy tends to increase toward the future but not toward the past. But what explains this time-asymmetric distribution of matter? In this paper, I explore the idea that time itself has a direction by drawing from recent work on grounding and metaphysical fundamentality. I will argue that positing such a direction of time, in addition to time-asymmetric boundary conditions, enables a (...) better explanation of the thermodynamic asymmetry than is available otherwise. (shrink)

This paper explores the scientific viability of the concept of causality—by questioning a central element of the distinction between “fundamental” and non-fundamental physics. It will be argued that the prevalent emphasis on fundamental physics involves formalistic and idealized partial models of physical regularities abstracting from and idealizing the causal evolution of physical systems. The accepted roles of partial models and of the special sciences in the growth of knowledge help demonstrate proper limitations of the concept of fundamental physics. We expect (...) that a cause precedes its effect. But in some tension with this point, fundamental physical law is often held to be symmetrical and all-encompassing. Physical time, however, has not only measurable extension, as with spatial dimensions, it also has a direction—from the past through the present into the future. This preferred direction is time’s arrow. In spite of this standard contrast of time with space, if all the fundamental laws of physics are symmetrical, they are indifferent to time’s arrow. In consequence, excessive emphasis on the ideal of symmetrical, fundamental laws of physics generates skepticism regarding the common-sense and scientific uses of the concept of causality. The expectation has been that all physical phenomena are capable of explanation and prediction by reference to fundamental physicals laws—so that the laws and phenomena of statistical thermodynam- ics —and of the special sciences—must be derivative and/or secondary. The most important and oft repeated explanation of time’s arrow, however, is provided by the second law of thermodynamics. This paper explores the prospects for time’s arrow based on the second law. The concept of causality employed here is empirically based, though acknowledging practical scientific interests, and is linked to time’s arrow and to the thesis that there can be no causal change, in any domain of inquiry, without physical interaction. (shrink)