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)

Two approaches toward the arrow of time for scattering processes have been proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm, involves preparations and registrations in laboratory operations and results in two semigroups oriented in the forward direction of time. The other, employed by the Brussels-Austin group, is more general, involving excitations and de-excitations of systems, and apparently results in two semigroups oriented in opposite directions of time. It turns out that these two (...) class='Hi'>time arrows can be related to each other via Wigner's extensions of the spacetime symmetry group. Furthermore, their are subtle differences in causality as well as the possibilities for the existence and creation of time-reversed states depending on which time arrow is chosen. (shrink)

I propose that, in addition to the commonly recognized increase of entropy, two more time arrows influence living beings. The increase of damage reactions, which produce aging and genetic variation, and the decrease of the rate of entropy production involved in natural selection are neglected arrows of time. Although based on the statistical theory of the arrow of time, they are distinguishable from the general arrow of the increase of entropy. Physiology under healthy conditions only (...) obeys the increase of entropy arrow. But aging, death, and evolution are determined by the other time arrows as well. Paradoxes emerge from conflicts among the specific determinisms associated with each arrow. These conflicts, along with uncertainties intrinsic to the low-number statistics of the arrows of damage reactions and decrease of the rate of production of entropy, highlight the limits of determinism at different levels of biology and its dependence on time span and number of organisms. The recognition of the three time arrows opens new perspectives for the problem of compatibility of the flow of time in physics and psychology. (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)

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 due (...) to causal neuronal interactions, and thus correlated with mental representations, generate a psychological time arrow. Yet this impact of causal interactions among neurons on the directed sequence of mental representations does not rule out the possibility of mentally less efficacious non-causal or anti-causal interactions among neurons. (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)

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, (...) and how to overcome pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

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)

Many philosophers and scientists have claimed that time has an arrow that points in a special direction. The Roman poet Ovid may have referred to this one-way property of time when he said, “Time itself glides on with constant motion, ever as a flowing river.” However, understanding this arrow is not … Continue reading The Arrow of Time →.

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 context of thermodynamics and statistical mechanics. The chapter then reviews the main strategies available for resolving the conflict between reversible microdynamics and irreversible macrodynamics, working within the context of the quantitative, time‐irreversible evolution laws that seem to apply to large‐scale phenomena. Finally, it offers a broad the discussion covering other arrows of time within physics. (shrink)

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 their semi-group operators and (...) time arrows. Finally a possible realist interpretation of the rigged Hilbert space formulation of quantum mechanics is considered. (shrink)

We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been proposed, this one involves no additional space-time structure as would be provided by a (possibly dynamical) foliation of space-time. This is achieved through the interplay of opposite microcausal and macrocausal (i.e., thermodynamic) arrows of time. PACS numbers 03.65.Ud; 03.65.Ta; 03.30.+p..

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 a Past (...) Hypothesis. We then propose a definition of a Boltzmann entropy for a classical N-particle system with gravity, suggesting that a Newtonian gravitating universe might provide a relevant example of Carroll's entropy model. This invites comparison with the work of Barbour, Koslowski, and Mercati that identifies typical arrows of time in a relational formulation of classical gravity on shape space. We clarify the difference between this gravitational arrow in terms of shape complexity and the entropic arrow in absolute spacetime, and work out the key advantages of the relationalist theory. We end by pointing out why the entropy concept relies on absolute scales and is thus not relational. (shrink)

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.

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, according to Bohr’s, Poincaré’s and Watanabe’s analysis, this agreement between the earlier-later direction of entropy increase and the past-future direction of life is the very condition of the possibility for meaningful action, representation and creation. Beyond this relationship of logical necessity between the meaning process and the arrow of time the question of their possible physical connection is explored. To answer affirmatively to this question, the meaning process is modelled as an evolving tree-like structure, called “Semantic Time”, where thermodynamic irreversibility can be shown. (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 (...) class='Hi'>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 problem of the direction of electromagnetic time, i.e., the complete dominance of retarded electromagnetic radiation over advanced radiation in the universe, is considered in the context of a generalized form of the Wheeler-Feynman absorber theory in an open expanding universe with a singularity atT=0. It is shown that the application of a four-vector reflection boundary condition at the singularity leads to the observed dominance of retarded radiation; it also clarifies the role of advanced and retarded waves in the (...) emission of very weakly absorbed radiation such as neutrinos. (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)

This essay offers a meta-level analysis in the sociology and history of physics in the context of the "Arrow of Time" or so-called "Two Times" problem. In effect, it argues that the two topics are intertwined, and it is only by coming to grips with the sociological aspects, involving adherence to certain metaphysical, epistemological and methodological beliefs and practices, that real progress can be made in the physics.

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 time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker’s map. (shrink)

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 arrow (...) of time. Similarly, more careful considerations of the equations of motion for gravitational interactions also show an arrow of time. The existence of arrows of time in quantum dynamics is also emphasized. (shrink)

Elvio Fachinelli was a leading Italian psychoanalyst of the 1960s-80s whose clinical, theoretical, and radical work resonated well beyond his discipline. In The Still Arrow, Fachinelli launched an interdisciplinary investigation ranging from anthropology to politics and the history of religions to the critique of ideology. From a psychoanalytic standpoint, individual obsessional neurosis is firmly connected to a process of repudiation of death. But Fachinelli argued that similar elaborations on time are also present at the group level, in disparate social (...) and historical contexts, for instance, in the archaic transformation of the dead into ancestors and in what he named "the fascist phenomenon." Originally written in Italian in 1979, this book displays Fachinelli's eclectic methodology, which came to serve as a precursor to Slavoj Zizek's work. Fachinelli differs from Freud's attempt in Totem and Taboo to equate individual psycho-libidinal predicaments with those of whole societies, and he points out an unbridgeable difference between the two. At the same time, for Fachinelli, that difference always remains one of degree, not of principle. He explores many questions about time, such as history's status not only as the sum of all possible histories but also of impossible ones. This first English translation of Fachinelli's work, The Still Arrow introduces a major critical European voice to the larger readership. (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)

The epistemic arrow of time is the fact that our knowledge of the past seems to be both of a different kind and more detailed than our knowledge of the future. Just like with the other arrows of time, it has often been speculated that the epistemic arrow arises due to the second law of thermodynamics. In this paper, we investigate the epistemic arrow of time using a fully formal framework. We begin by defining a memory (...) system as any physical system whose present state can provide information about the state of the external world at some time other than the present. We then identify two types of memory systems in our universe, along with an important special case of the first type, which we distinguish as a third type of memory system. We show that two of these types of memory systems are time-symmetric, able to provide knowledge about both the past and the future. However, the third type of memory systems exploits the second law of thermodynamics, at least in all of its instances in our universe that we are aware of. The result is that in our universe, this type of memory system only ever provides information about the past. We also argue that human memory is of this third type, completing the argument. We end by scrutinizing the basis of the second law itself. This uncovers a previously unappreciated formal problem for common arguments that try to derive the second law from the “Past Hypothesis”, i.e., from the claim that the very early universe was in a state of extremely low entropy. Our analysis is indebted to prior work by one of us but expands and improves upon this work in several respects. (shrink)

Based on the hypothesis that the (non-reversible) arrow of time is intrinsic in any system, no matter how small, the consequences are discussed. Within the framework of local quantum physics it is shown how such a semi-group action of time can consistently be extended to that of the group of spacetime translations in Minkowski space. In presence of massless excitations, however, there arise ambiguities in the theoretical extensions of the time translations to the past. The corresponding loss (...) of quantum information on states upon time is determined. Finally, it is explained how the description of operations in classical terms combined with constraints imposed by the arrow of time leads to a quantum theoretical framework. These results suggest that the arrow of time is fundamental in nature and not merely a consequence of statistical effects on which the Second Law is based. (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)

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 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 (...) can be changed from its original direction to any other direction. In this way mental action can produce effects through the ordering of thermal motions. Examples are given which show that the ordering of 10^4 10^5 molecules is sufficient to (a) produce detectible PK results and (b) open sufficient ion channels in the brain to initiate a physical action. The relationship of the above model to the arrow of time is discussed. (shrink)

The reason for the arrow of time in electromagnetic radiation is explicated.

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 in quantum (...) gravity is at best de facto (nonlawlike). (shrink)

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, (...) considerations of forwards and backwards decoherence and of decoherence and recoherence suggest that a time-directed interpretation of probabilities, if adopted, should be both contingent and perspectival. (shrink)

DIVA new look at Kenneth Arrow’s classic study of the economics of health care: is his formulation still relevant 40 years later?/div.

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, (...) considerations of forwards and backwards decoherence and of decoherence and recoherence suggest that a time-directed interpretation of probabilities, if adopted, should be both contingent and perspectival. (shrink)

Time in electromagnetism shares many features with time in other physical theories. But there is one aspect of electromagnetism's relationship with time that has always been controversial, yet has not always attracted the limelight it deserves: the electromagnetic arrow of time. Beginning with a re-analysis of a famous argument between Ritz and Einstein over the origins of the radiation arrow, this chapter frames the debate between modern Einsteinians and neo-Ritzians. It tries to find a clean statement (...) of what the arrow is and then explains how it relates to the cosmological and thermodynamic arrows, representing the most developed and sophisticated attack yet, in either the physics or philosophy literature, on the electromagnetic arrow of time. (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 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)

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. (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)

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)