Gödel's remarks concerning the ideality of time are examined. In the literature, some of these remarks have been somewhat neglected while others have been heavily criticized. In this note, we propose a clear and defensible sense in which Gödel's work bears on the question of whether there is an objective lapse of time in our world.

This book explores the idea of time travel from the first account in English literature to the latest theories of physicists such as Kip Thorne and Igor Novikov. This very readable work covers a variety of topics including: the history of time travel in fiction; the fundamental scientific concepts of time, spacetime, and the fourth dimension; the speculations of Einstein, Richard Feynman, Kurt Goedel, and others; time travel paradoxes, and much more.

Here, we clarify the relationship among three space-time conditions of interest: geodesic completeness, hole-freeness, and inextendibility. In addition, we introduce a related fourth condition: effective completeness.

Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the (...) subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time. (shrink)

We present a counterexample to Krasnikov's much discussed time machine no-go result. In addition, we prove a positive statement: a time machine existence theorem under a modest "no holes" assumption.

This paper is an enquiry into the logical, metaphysical, and physical possibility of time travel understood in the sense of the existence of closed worldlines that can be traced out by physical objects. We argue that none of the purported paradoxes rule out time travel either on grounds of logic or metaphysics. More relevantly, modern spacetime theories such as general relativity seem to permit models that feature closed worldlines. We discuss, in the context of Gödel's infamous argument for the ideality (...) of time based on his eponymous spacetime, what this apparent physical possibility of time travel means. Furthermore, we review the recent literature on so-called time machines, i.e., of devices that produce closed worldlines where none would have existed otherwise. Finally, we investigate what the implications of the quantum behaviour of matter for the possibility of time travel might be and explicate in what sense time travel might be possible according to leading contenders for full quantum theories of gravity such as string theory and loop quantum gravity. (shrink)

Cosmologists often use certain global properties to exclude "physically unreasonable" cosmological models from serious consideration. But, on what grounds should these properties be regarded as "physically unreasonable" if we cannot rule out, even with a robust type of inductive reasoning, the possibility of the properties obtaining in our own universe?

It is often thought that presentism is incompatible with time travel. I will argue that this common view is incorrect. Specifically, I will argue that presentism is compatible with some stories that involve closed timelike curves, and that some of these stories are time-travel stories.

Indeed, this is the first serious book-length study of the subject by a philosopher of science.

As we navigate through life, we model time as flowing, the present as special, and the past as “dead.” This model of time—manifest time—develops in childhood and later thoroughly infiltrates our language, thought, and behavior. It is part of what makes a human life recognizably human. Yet if physics is correct, this model of the world is deeply mistaken. This book is about this conflict between manifest and physical time. The first half dives into the physics and philosophy to establish (...) the conflict’s existence; but it also argues that the claim that physics “spatializes” time is overstated. Rather, even relativity theory makes time special in deep and significant ways. The second half turns to psychology, biology, and more, seeking to understand why creatures like us develop manifest time. The novel picture that results is that manifest time is a natural reaction to the many cognitive and evolutionary challenges that we face. For subjects embedded in our circumstances, it makes sense to develop—even if fundamentally wrong. (shrink)

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no-go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time machine. (...) We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently “potent” to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident “yes” has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer. (shrink)

Time travel has been a staple of science fiction. With the advent of general relativity it has been entertained by serious physicists. But, especially in the philosophy literature, there have been arguments that time travel is inherently paradoxical. The most famous paradox is the grandfather paradox: you travel back in time and kill your grandfather, thereby preventing your own existence. To avoid inconsistency some circumstance will have to occur which makes you fail in this attempt to kill your grandfather. Doesn't (...) this require some implausible constraint on otherwise unrelated circumstances? We examine such worries in the context of modern physics. (shrink)

Here, we examine hole-freeness - a condition sometimes imposed to rule out seemingly artificial spacetimes. We show that under existing definitions (and contrary to claims made in the literature) there exist inextendible, globally hyperbolic spacetimes which fail to be hole-free. We then propose an updated formulation of the condition which enables us to show the intended result. We conclude with a few general remarks on the strength of the definition and then formulate a precise question which may be interpreted as: (...) Are all physically reasonable spacetimes hole-free? (shrink)

For the past 20 years causality violations and superluminal motion have been the object of intensive study as physical and geometrical phenomena. This book compiles the results of its author and also reviews other work in the field. In particular, the following popular questions are addressed: Is causality protected by quantum divergence at the relevant Cauchy horizon? How much "exotic matter" would it take to create a time machine or a warp drive? What is the difference between a "discovered" time (...) machine and a created one? Why does a time traveler fail to kill their grandfather? How should we define the speed of gravity and what is its magnitude? (shrink)