Exact Philosophy of Spacetime

2006

The sixteen papers collected in this volume are expanded and revised versions of talks delivered at the Second International Conference on the Ontology of Spacetime, organized by the International Society for the Advanced Study of Spacetime (John Earman, President) at Concordia University (Montreal) from 9 to 11 June 2006. Most chapters are devoted to subjects directly relating to the ontology of spacetime. This book starts with four papers that discuss the ontological status of spacetime and the processes occurring in it from a point of view that is first of all conceptual and philosophical. The focus then slightly shifts in the five papers that follow, to considerations more directly involving technical considerations from relativity theory. After this, Time, Becoming and Change take centre stage in the next five papers. This book ends with two excursions into relatively uncharted territory: a consideration of the status of Kaluza-Klein theory, and an investigation of possible rel...

We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated without any reference to knowing subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing, but a complex of relations among things. In this way, the original program of Leibniz is consummated, in the sense that space is ultimately an order of coexistents, and time is an order of successives. In this context, we show that the metric and topological properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be extended to encompass a Riemannian space-time.

We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated without any reference to cognoscent subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing but a complex of relations among things. In this way, the original program of Leibniz is consummated, in the sense that space is ultimately an order of coexistents, and time is an order of succesives. In this context, we show that the metric and topological properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be extended to encompass a Riemmanian space-time.

I present a discussion of some issues in the ontology of spacetime. After a characterisation of the controversies among relationists, substantivalists, eternalists, and presentists, I offer a new argument for rejecting presentism, the doctrine that only present objects exist. Then, I outline and defend a form of spacetime realism that I call event substantivalism. I propose an ontological theory for the emergence of spacetime from more basic entities (timeless and spaceless ‘events’). Finally, I argue that a relational theory of pre-geometric entities can give rise to substantival spacetime in such a way that relationism and substantivalism are not necessarily opposed positions, but rather complementary. In an appendix I give axiomatic formulations of my ontological views.

2016

This paper is a brief (and hopelessly incomplete) non-standard introduction to the philosophy of space and time. It is an introduction because I plan to give an overview of what I consider some of the main questions about space and time: Is space a substance over and above matter? How many dimensions does it have? Is space-time fundamental or emergent? Does time have a direction? Does time even exist? Nonetheless, this introduction is not standard because I conclude the discussion by presenting the material with an original spin, guided by a particular understanding of fundamental physical theories, the so-called primitive ontology approach.

This paper is a brief (and hopelessly incomplete) non-standard introduction to the philosophy of space and time. It is an introduction because I plan to give an overview of what I consider some of the main questions about space and time: Is space a substance over and above matter? How many dimensions does it have? Is space-time fundamental or emergent? Does time have a direction? Does time even exist? Nonetheless, this introduction is not standard because I conclude the discussion by presenting the material with an original spin, guided by a particular understanding of fundamental physical theories, the so-called primitive ontology approach.

The intention of this paper is that of proposing a method of approaching the problem of spacetime ontology that is, at least at the beginning, independent from the previous ones concerning the "Hole Argument": to propose an approach based on the possibility of describing the gravitational field at three distinct levels. Observing the theory of General Relativity from this perspective, we can find a "triple modality" for describing the gravitational field that is essentially based on a geometric interpretation of the spacetime structure. The gravitational field is now no longer "visible" in terms of its autonomous degrees of freedom, but it is analyzable through three levels: a first one, called the potential level, a second one, known as the connections level and, finally, a third level, that of the Riemann tensor, which is peculiar to General Relativity only. Focusing from the beginning on what is called the "third level" seems to present immediately a first advantage: to lead directly to a description of spacetime properties in terms of gauge-invariant quantites, which allows to "short circuit" the long path that, in the treatises analyzed, leads to identify the "ontic part" of the metric field. It is then shown how to this last level it is possible to establish a "primitive level of objectivity" of spacetime in terms of the effects that matter exercises in extended domains of spacetime geometrical structure; these effects are described by invariants of the Riemann tensor, in particular of its irreducible part: the Weyl tensor.

The Routledge Handbook of Emergence, 2019

Research in quantum gravity strongly suggests that our world in not fundamentally spatiotemporal, but that spacetime may only emerge in some sense from a non-spatiotemporal structure, as this paper illustrates in the case of causal set theory and loop quantum gravity. This would raise philosophical concerns regarding the empirical coherence and general adequacy of theories in quantum gravity. If it can be established, however, that spacetime emerges in the appropriate circumstances and how all its relevant aspects are explained in fundamental non-spatiotemporal terms, then the challenge is fully met. It is argued that a form of spacetime functionalism offers the most promising template for this project. Space and time, it seems, must be part and parcel of the ontology of any physical theory; of any theory with a credible claim to being a physical theory, that is. After all, physics is the science of the fundamental constitution of the material bodies, their motion in space and time, and indeed of space and time themselves. Usually implicit, Larry has given expression to this common intuition: What could possibly constitute a more essential, a more ineliminable, component of our conceptual framework than that ordering of phenomena which places them in space and time? The spatiality and temporality of things is, we feel, the very condition of their existing at all and having other, less primordial, features... We could imagine a world without electric charge, without the atomic constitution of matter, perhaps without matter at all. But a world not in time? A world not spatial? Except to some Platonists, I suppose, such a world seems devoid of real being altogether. (45) The worry here, I take it, goes beyond a merely epistemic concern regarding the inconceivability of a non-spatiotemporal world; rather, it is that such a world would violate some basic necessary condition of physical existence. It is contended that space and time partially ground a material world. The alternative to a spatiotemporal world, it is suggested, is a realm of merely abstract entities. 1 Part of what it means to be 'physically salient' (Huggett and Wüthrich 2013) is to be in space and time. In other words, what it is to give a physical explanation of aspects of our manifest world is, among other things, to offer a theory of how objects are and move in space and time. * I thank Robin Hendry and Tom Lancaster for their insightful and challenging comments on an earlier draft of this paper. This work was partly performed under a collaborative agreement between the University of Illinois at Chicago and the University of Geneva and made possible by grant number 56314 from the John Templeton Foundation and its content are solely the responsibility of the author and do not represent the official views of the John Templeton Foundation. 1 The defenders of the claim that the world is purely abstract, formal, or mathematical-as opposed to partly abstract, formal, or mathematical-are usually referred to as 'Pythagoreans', rather than as 'Platonists'.

Third International Conference on the Nature and Ontology of Spacetime (Concordia University, Montreal, June 13-15, 2008), 2008

The spacetime ontology is considered in General Relativity (GR) in view of the choice of a frame of reference (FR). Various approaches to a description of the FR, such as coordinate systems, monads and tetrads are reviewed. It is shown that any of the existing FR definitions require a preexisting background spacetime, which, if defined independently of the FR, renders the spacetime absolute in violation of the principle of relativity, or, if defined within an inertial FR (IFR), as it is usually done, makes the argument circular. Consequently, defining a FR in a preexisting spacetime is unacceptable. We show that a FR defines a differentiable manifold with, generally, non-Euclidean geometry. In a noninertial FR (NIFR) the observer must chose a coordinative definition either admitting existence of a universal – inertial – force or settling for non'(uclidean spacetime. Following Reichenbach, it is preferable to eliminate all universal forces and opt for a non-Euclidean geometry. It is shown that a metric-affine space (L4,g) is best suited to describe the geometry of spacetime within a FR. Considering a gravitational field in an arbitrary FR, we show within the framework of Einstein’s GR that the gravity is described by nonmetricity of spacetime. This result may shed new light on the nature of the cosmological constant and dark energy.

Philosophies, 2018

The epistemological rupture of Copernicus, the laws of planetary motions of Kepler, the comprehensive physical observations of Galileo and Huygens, the conception of relativity, and the physical theory of Newton were components of an extremely fertile and influential cognitive environment that prompted the restless Leibniz to shape an innovative theory of space and time. This theory expressed some of the concerns and intuitions of the scientific community of the seventeenth century, in particular the scientific group of the Academy of Sciences of Paris, but remained relatively unknown until the twentieth century. After Einstein, however, the relational theory of Leibniz gained wider respect and fame. The aim of this article is to explain how Leibniz foresaw relativity, through his critique of contemporary mechanistic philosophy.