An elementary notion of gauge equivalence is introduced that does not require any Lagrangian or Hamiltonian apparatus. It is shown that in the special case of theories, such as general relativity, whose symmetries can be identified with spacetime diffeomorphisms this elementary notion has many of the same features as the usual notion. In particular, it performs well in the presence of asymptotic boundary conditions.

This essay revisits some classic problems in the philosophy of space and time concerning the counting of possibilities. I argue that we should think that two Newtonian worlds can differ only as to when or where things happen and that general relativistic worlds can differ in something like the same way—the first of these theses being quaintly heterodox, the second baldly heretical, according to the mores of contemporary philosophy of physics.

I will discuss only one of the several entwined strands of the philosophy of space and time, the question of the relation between the nature of motion and the geometrical structure of the world.1 This topic has many of the virtues of the best philosophy of science. It is of long-standing philosophical interest and has a rich history of connections to problems of physics. It has loomed large in discussions of space and time among contemporary philosophers of science. Furthermore, there (...) is, I think, widespread agreement that recent insights here have lead to a genuine deepening of our understanding. (shrink)

Accelerating Expansion explores some of the philosophical implications of modern cosmology, focused on the significance that the discovery of the accelerating expansion of the Universe has for our understanding of time, geometry, and physics. The appearance of the cosmological constant in the equations of general relativity allows one to model universes in which space has an inherent tendency towards expansion. This constant, introduced by Einstein but subsequently abandoned by him, returned to centre stage with the discovery of the accelerating expansion. (...) This pedagogically-oriented essay begins with a study of the most basic and elegant relativistic world that involves a positive cosmological constant, de Sitter spacetime. It then turns to the relatives of de Sitter spacetime that dominate modern relativistic cosmology. Some of the topics considered include: the nature of time and simultaneity in de Sitter worlds; the sense in which de Sitter spacetime is a powerful dynamical attractor; the limited extent to which observation can give us information about the topology of space in a world undergoing accelerated expansion; and cosmologists' favourite sceptical worry about the reliability of evidence and the possibility of knowledge, the problem of Boltzmann brains. (shrink)

It is often said that the Aharonov-Bohm effect shows that the vector potential enjoys more ontological significance than we previously realized. But how can a quantum-mechanical effect teach us something about the interpretation of Maxwell's theory—let alone about the ontological structure of the world—when both theories are false? I present a rational reconstruction of the interpretative repercussions of the Aharonov-Bohm effect, and suggest some morals for our conception of the interpretative enterprise.

Stephen Hawking has argued that universes containing evaporating black holes can evolve from pure initial states to mixed final ones. Such evolution is non-unitary and so contravenes fundamental quantum principles on which Hawking's analysis was based. It disables the retrodiction of the universe's initial state from its final one, and portends the time-asymmetry of quantum gravity. Small wonder that Hawking's paradox has met with considerable resistance. Here we use a simple result for C*-algebras to offer an argument for pure-to-mixed state (...) evolution in black hole evaporation, and review responses to the Hawking paradox with respect to how effectively they rebut this argument. (shrink)

Dünyada müxtəlif dillər mövcuddur. Hal-hazırda əlavə xarici dil öyrənməyə maraq artmaqdadır. Təbii ki bu hər bir şəxsin öz istəyinə və seçiminə bağlıdır. Yəni hər kəs, hər hansı bir dili öyrəndiyi zaman, qarşısında iki məqsəd dayanır; ya o dili sevir, ya da o dili öyrənmək onun üçün lazımdır. Hər bir vətəndaşın borcudur ki, əvvəlcə öz ana dilini mükəmməl şəkildə öyrənsin. Lakin elm və texnologiyanın yüksək inkişaf etdiyi bir zamanda yalnız ana dilini bilmək kifayət etmir. İnsanın hər bir sahədə inkişafı üçün bacardığı (...) qədər başqa dillərə də yiyələnməsi artıq zəruridir. Yeni dil öyrənmənin faydaları çoxdur, yaddaşın güclənməsinə, söz ehtiyatının artmasına, nitqin gözəlləşməsinə səbəb olur. Həmçinin yeni dil öyrənməklə, insanın özünə güvəni artır, ünsiyyət dairəsi genişlənir. Bununla insan yalnız yeni sözlər deyil, yeni mədəniyyətlərlə də tanış olur və nəticədə dünyagörüşü artır. (shrink)

This chapter is concerned with the representation of time and change in classical (i.e., non-quantum) physical theories. One of the main goals of the chapter is to attempt to clarify the nature and scope of the so-called problem of time: a knot of technical and interpretative problems that appear to stand in the way of attempts to quantize general relativity, and which have their roots in the general covariance of that theory. The most natural approach to these questions is via (...) a consideration of more clear cases. So much of the chapter is given over to a discussion of the representation of time and change in other, better understood theories, starting with the most straightforward cases and proceeding through a consideration of cases that lead up to the features of general relativity that are responsible for the problem of time. (shrink)

The paper is about the physical theories which result when one identifies points in phase space related by symmetries; with applications to problems concerning gauge freedom and the structure of spacetime in classical mechanics.

ZusammenfassungPrinzipien und Dialektik. Zwei Arten Dialektik: Die Rückkehr zum «Anhypoteton» und das dialektisierende Denken. Beide Tendenzen sind gleichsam charakterisiert durch die Hervorhebung der Aktivität des Denkens. Das formale Denken aber sucht den Ursprung dieser Aktivität, während das dialektisierende Denken deren Anwendung feststellen will. Auf dem Suchen nach einem ersten Ursprung ist das formale Denken in Gefahr bloss formale Bedingungen zu erreichen. Das dialektisierende Denken will aber nur die Orientierung in dem gegebenen gegenwärtigen Suchen feststellen; dabei scheint es die Idee einer (...) ewigen Ordnung der Dinge preiszugcben, bleibt jedoch der menschlichen Situation treu. Beide Richtungen haben Sinn für entgegengesetzte Ziele. Möglichkeit einer anthropologischen Problematik. (shrink)

There is a widespread impression that General Relativity, unlike Quantum Mechanics, is in no need of an interpretation. I present two reasons for thinking that this is a mistake. The first is the familiar hole argument. I argue that certain skeptical responses to this argument are too hasty in dismissing it as being irrelevant to the interpretative enterprise. My second reason is that interpretative questions about General Relativity are central to the search for a quantum theory of gravity. I illustrate (...) this claim by examining the interpretative consequences of a particular technical move in canonical quantum gravity. (shrink)

Gordon Belot investigates the distinctive notion of geometric possibility that relationalists rely upon. He examines the prospects for adapting to the geometric case the standard philosophical accounts of the related notion of physical possibility, with particular emphasis on Humean, primitivist, and necessitarian accounts of physical and geometric possibility. This contribution to the debate concerning the nature of space will be of interest not only to philosophers and metaphysicians concerned with space and time, but also to those interested in laws (...) of nature, modal notions, or more general issues in ontology. (shrink)