1,720,985 research outputs found
Does the Curvature Structure of Spacetime Determine Its Topology?
Full text linkWe explore the title question. After some topological preliminaries, we define a "curvature isomorphism" between spacetimes. We introduce a hierarchy of curvature conditions and show that at a certain level, a curvature isomorphism must be a homeomorphism. The highest level of the hierarchy is satisfied by a spacetime if every smooth scalar function on its manifold is an invariant scalar curvature function. We show that such "maximally structured" spacetimes exist and that a curvature isomorphism between them must be a diffeomorphism. We highlight a number of connections between our project and the one in which the topology of spacetime is determined from a causal relation between spacetime points (Malament 1977). We emphasize that analogous results are obtained here by considering only invariant properties of spacetime points -- no relations needed
Space and Time
Full text linkHere, formal tools are used to pose and answer several philosophical questions concerning space and time. The questions involve the properties of possible worlds allowed by the general theory of relativity. In particular, attention is given to various causal properties such as "determinism" and "time travel"
On the (In?)Stability of Spacetime Inextendibility
Full text linkLeibnizian metaphysics underpins the near universally held view that spacetime must be inextendible – that it must be “as large as it can be” in a sense. But here we demonstrate a surprising fact within the context of general relativity: the property of inextendibility turns out to be unstable when attention is restricted to certain collections of “physically reasonable” spacetimes
Some 'No Hole' Spacetime Properties Are Unstable
Full text linkWe show a sense in which the spacetime property of effective completeness -- a type of ``local hole-freeness'' or ``local inextendibility'' -- is not stable
Is the Universe As Large As It Can Be? A Study of Spacetime Possibility
Full text linkThis book concerns the modal structure of spacetime within the context of Einstein’s general relativity. The aim is to expose a rich set of philosophical issues somewhat informally and from a bird’s eye view. No familiarity with general relativity is presupposed. A large number of examples (worked out in coordinates) and corresponding diagrams (over 130) will play a central role in illustrating the ideas involved. One of the intended readers is a non-expert. She is perhaps a philosophy graduate student just getting started with an interest in better understanding cosmic possibility delimited by Einstein’s theory. Under her belt, she has little more than some basic set theory and a passing acquaintance with calculus and vector spaces. The other intended reader is the expert. She will find several interconnecting lines of current research mapped out and a clear thesis defended.
The investigation will focus on the maximality property of spacetime -- the requirement that (a model of) the universe must be “as large as it can be.” The maximality of spacetime is something of a dogma within the context of generality relativity. In the background, it is often presupposed by practitioners without comment in order to go on to investigate a number of other foundational topics (e.g. determinism). Here, I do not defend or oppose the case for spacetime maximality. Instead, I simply put forward a thesis that nonetheless runs counter to the prevailing orthodoxy: it is not at all clear that the universe is as large as it can be. To shed light on the situation, 120 precise questions are identified and most are settled (see the final page). My hope is that, by drawing attention to these issues, even more progress can be made by others
Heraclitus + Einstein = ?
Full text linkThis is a non-technical piece concerning a radical type of spacetime asymmetry. The ancient Greek philosopher Heraclitus is known for his theory of constant flux: "It is not possible to step twice into the same river.” It turns out that one can explore this idea within the context of Einstein's general relativity. A four-dimensional "Heraclitus spacetime" is a model of the universe in which no two events have the same structure. Such models exhibit a radical type of spacetime asymmetry. I first introduce the notion of Heraclitus spacetime. Next, I highlight a curious result: if a model universe has the Heraclitus property, then its local structure completely fixes its global structure as well (i.e. its shape). Finally, I sketch a way in which the radical asymmetry present in a Heraclitus spacetime can be used to clarify a number of topics in the philosophy of spacetime physics
On Feyerabend, General Relativity, and 'Unreasonable' Universes
Full text linkI investigate the principle *anything goes* within the context of general relativity. After a few preliminaries, I show a sense in which the universe is unknowable from within this context; I suggest that we 'keep our options open' with respect to competing models of it. Given the state of affairs, proceeding counter-inductively seems to be especially appropriate; I use this method to blur some of the usual lines between 'reasonable' and 'unreasonable' models of the universe. Along the way, one is led to a useful collection of variant theories of general relativity -- each theory incompatible with the standard formulation. One may contrast one variant theory with another in order to understand foundational questions within 'general relativity' in a more nuanced way. I close by sketching some of the work ahead if we are to embrace such a pluralistic methodology
The Universe Is Unknowable from Within It
Full text linkThis is a non-technical piece concerning the unknowability of the universe within the context of general relativity. It is well known that the region beyond the 'observable universe' is unknowable. What is not well known is this: even if one were somehow able to observe this unobservable region, the universe would remain unknowable. Indeed, the puzzling state of affairs would persist even if one were given an all-access pass to every possible observation at every possible place and time -- here, there, past, present, and future. Here, I argue that there is a sense in which the universe is fundamentally unknowable via observations made from within it
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