Aspects of Time

We introduce a complete and cut-free proof system for a sufficiently expressive fragment of Metric Temporal Logic over dense time domains in which a schema of induction is provable. So doing we extend results previously obtained by Montagna et al. to unbounded temporal operators.

We investigate the consequences of removing the infinitary axiom and rules from a previously defined proof system for a fragment of propositional metric temporal logic over dense time.

If you utter sentence ‘Obama was born in 1961’ now, you say something true about the past. Since the past will always be such that the year 1961 has the property of being a time in which Obama was born, it seems impossible that could ever be false in a future context of utterance. We shall consider the case of a sentence about the past exactly like , but which was true when uttered a few years ago and is no (...) longer true now. On this basis, we shall conclude that the past has changed. (shrink)

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

A common line of argument for the impossibility of closed causal loops is that they would involve causal paradoxes. The usual reply is that such loops impose heavy consistency constraints on the nature of causal connections in them; constraints that are overlooked by the impossibility arguments. Hugh Mellor has maintained that arguments for the possibility of causal loops also overlook some constraints, which are related to the chances (single-case, objective probabilities) that causes give to their effects. And he argues that (...) a consideration of these constraints demonstrates that causal loops are impossible. I consider Mellor's argument and more generally the nature of chance in causal loops. I argue that Mellor's line of reasoning is unwarranted since it is based on untenable premisses about the relation between chances and long-run frequencies in causal loops. Yet, this line of reasoning may still be of interest to those who maintain that causes determine the chances of their effects; for it raises some unresolved questions about the nature of chance in causal loops. (shrink)

The author discusses both dobbs' article and philpott's work as they apply to "linking quantum considerations to time intervals of an order of magnitude such that they can be consciously appreciated." (staff).

Time arises in the theory of gravity through the semiclassical approximation of the gravitational part of the solution of the Wheeler-De Witt equation in the manner shown by Banks (SCAG). We generalize Banks' procedure by grafting a Born-Oppenheimer type approximation onto SCAG. This allows for the feedback of matter onto gravity, wherein the latter is driven by the (quantum) mean energy-momentum tensor of matter. The wave function is nonvanishing in classically forbidden configurations of gravity. In SCAG this is described by (...) the evolution of matter in imaginary time. This is interpreted as an inverse temperature, and the norm of the matter wave function, no longer conserved for these gravitational configurations, is a partition function. A simple cosmological model is worked out to illustrate these ideas. In this model it is shown that the temperature of the matter which emerges into the classically permitted region is the inverse bounce time of the bounce executed by the system in the forbidden region (behind the horizon).Time present and time past are both perhaps present in time future. And time future contained in time past. If all time is eternally present All time is unredeemable.—T. S. Eliot, “Burnt Norton,”Four Quartets, 1943. (shrink)

This paper investigates what the source of time-asymmetry is in thermodynamics, and comments on the question whether a time-symmetric formulation of the Second Law is possible.

These nine essays address fundamental questions about time in philosophy, physics, linguistics, and psychology. Are there facts about the future? Could we affect the past? In physics, general relativity and quantum theory give contradictory treatments of time. So in the current search for a theory of quantum gravity, which should give way: general relativity or quantum theory? In linguistics and psychology, how does our language represent time, and how do our minds keep track of it?

As the study of time has flourished in the physical and human sciences, the philosophy of time has come into its own as a lively and diverse area of academic research. Philosophers investigate not just the metaphysics of time, and our experience and representation of time, but the role of time in ethics and action, and philosophical issues in the sciences of time, especially with regard to quantum mechanics and relativity theory. This Handbook presents twenty-three specially written essays by leading (...) figures in their fields: it is the first comprehensive collaborative study of the philosophy of time, and will set the agenda for future work. (shrink)

Why does time seem to flow in one direction? Can we influence the past? Is only the present real? Does relativity conflict with our common understanding of time? How does time relate to free will? Could science do away with time? These questions and others about time are among the most puzzling problems in philosophy and science. In this exciting collection of original articles, eminent philosophers propose novel answers to these and other questions. Based on the latest research in philosophy (...) and physics, these essays will be enjoyable to anyone with a speculative turn of mind. (shrink)

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 (...) such reversals may be familiar from works of fiction, we are utterly unfamiliar with them in experience. The processes of nature behave in a temporally asymmetric manner. Once the cream mixes with the coffee, it stays that way, never to return to its original separated state. Neither cigarettes nor people ever fully reconstitute themselves. This kind of asymmetric behaviour is ubiquitous in thermodynamic, radiative, and quantum mechanical phenomena. But we also find our common-sense impression ofthe world painted with temporally asymmetric concepts. Time feels like it is ‘f|owing’ forward and causation appears to be an asymmetric relation. These phenomena and impressions stand in sharp contrast with the world as perceived through eyes tutored by modem science. Spacetime, rather than.. (shrink)

This thesis is an attempt to accurately formulate and solve one of the problems associated with the direction of time. Processes in nature appear to be 'irreversible', for instance, heat flows from hot to cold but never from cold to hot. The problem of the direction of time, roughly put, is the difficulty of squaring this irreversible behavior with the apparent fact that the fundamental laws of physics are completely reversible. ;In the first three chapters I critically review the foundations (...) of statistical mechanics. After arguing that entropy is an objective property of the thermodynamic world, I contrast the 'Boltzmannian' single-system approach to statistical mechanics with the 'Gibbsian' many-system approach. Based in part on its ability to handle irreversibility, I judge the Boltzmann approach to be superior from a philosophical perspective. I argue, however, that the statistical mechanical probabilities cannot be interpreted in such a way as to allow the theory to give the sort of explanation originally desired. ;The next four chapters are devoted to the direction of time. Chapters four and five attempt to provide the problem with the philosophically mature geography that has so far eluded it. Chapter six discusses the problem in the context of quantum mechanics, and chapter seven criticizes the problem's standard formulation. I show that the problem is really a much more general one than has previously been appreciated; indeed, I try to show that it is a problem afflicting all the special sciences. ;Finally, the remaining three chapters investigate three separate issues. Chapter eight discusses the tensed theory of time. I claim the best argument for the tensed theory relies on various temporal asymmetries, e.g., the asymmetry of causation. I provide reasons for not being persuaded by this argument. The tensed theory, I conclude, is not incoherent, as many have claimed, instead it is simply an implausible explanation of our experience. Chapter nine examines the possibility that quantum mechanics implies our world is temporally anisotropic, and chapter ten looks at some conceptual difficulties associated with our conception of time reversal invariance. (shrink)

The recent development of the theory of fluctuation relations has led to new insights into the ever-lasting question of how irreversible behavior emerges from time-reversal symmetric microscopic dynamics. We provide an introduction to fluctuation relations, examine their relation to dissipation and discuss their impact on the arrow of time question.