Beyond Spacetime: The Foundations of Quantum Gravity

I discuss nature and origin of the problem of quantum gravity. I examine the knowledge that may guide us in addressing this problem, and the reliability of such knowledge. In particular, I discuss the subtle modification of the notions of space and time engendered by general relativity, and how these might merge into quantum theory. I also present some reflections on methodological questions, and on some general issues in philosophy of science which are are raised by, or a relevant for, the research on quantum gravity.

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2019

Important features of space and time are taken to be missing in quantum gravity, allegedly requiring an explanation of the emergence of spacetime from non-spatio-temporal theories. In this paper, we argue that the explanatory gap between general relativity and non-spatio-temporal quantum gravity theories might significantly be reduced with two moves. First, we point out that spacetime is already partially missing in the context of general relativity when understood from a dynamical perspective. Second, we argue that most approaches to quantum gravity already start with an in-built distinction between structures to which the asymmetry between space and time can be traced back.

The Creation of Ideas in Physics, 1995

I describe the history of my attempts to arrive at a discrete substratum underlying the spacetime manifold, culminating in the hypothesis that the basic structure has the form of a partial-order (i.e. that it is a causal set). Like the other speakers in this session, I too am here much more as a working scientist than as a philosopher. Of course it is good to remember Peter Bergmann's description of the physicist as "in many respects a philosopher in workingman's* clothes", but today I'm not going to change into a white shirt and attempt to draw philosophical lessons from the course of past work on quantum gravity. Instead I will merely try to recount a certain part of my own experience with this problem, explaining how I arrived at the idea of what I will call a causal set. This and similar structures have been proposed more than once as discrete replacements for spacetime. My excuse for not telling you also how others arrived at essentially the same idea [1] is naturally that my case is the only one I can hope to reconstruct with even minimal accuracy.

Quantum theory lives in abstract, complex, linear Hilbert space, is unitary and non-dissipative, and has been shown not to be embeddable in spacetime for N ≥ 2 quantum entities. It is per definition unobservable (in itself). Classical physics describes the causal, nonlinear dynamics of actual events, which lie in, and also define, four-dimensional spacetime. The "Born Rule" connects abstract quantum theory with real events in classical spacetime. It is postulated separately and cannot be deduced from quantum theory, as it is both non-unitary and irreversible, i.e. dissipative. Separating and treating it correctly in this manner resolves a number of fundamental problems of gravitation vs. quantum theory, such as the black hole information paradox, the cosmological constant problem and quantization of general relativity.

2021

The present volume collects essays on the philosophical foundations of quantum theories of gravity, such as loop quantum gravity and string theory. Central for philosophical concerns is quantum gravity's suggestion that space and time, or spacetime, may not exist fundamentally, but instead be a derivative entity emerging from non-spatiotemporal degrees of freedom. In the spirit of naturalised metaphysics, contributions to this volume consider the philosophical implications of this suggestion. In turn, philosophical methods and insights are brought to bear on the foundations of quantum gravity itself. For instance, the idea of functionalism, borrowed from the philosophy of mind and discussed by several essays, exemplifies this mutual interaction the collection seeks to foster.

arXiv (Cornell University), 2011

More precisely, it ought to turn into a quantum field theory on the Minkowski spacetime of special relativity.

2004

The secret network of the universe: How quantum geometry might complete Einstein's dream. - An informal introduction to quantum geometry (loop quantum gravity), spin networks, quantum black holes, and the work of Abhay Ashtekar, Carlo Rovelli, Lee Smolin and others.

We all have rather definite notions of what dimension means but these have to be ex- tended when we consider objects such as frac- tals. Gravity directly determines the structure of space time and quantum eects can make determination of its dimension a non-trivial is- sue.

Synthese, 2019

This paper argues against the proposal to draw from current research into a physical theory of quantum gravity the ontological conclusion that spacetime or spatiotemporal relations are not fundamental. As things stand, the status of this proposal is like the one of all the other claims about radical changes in ontology that were made during the development of quantum mechanics and quantum field theory. However, none of these claims held up to scrutiny as a consequence of the physics once the theory was established and a serious discussion about its ontology had begun. Furthermore, the paper argues that if spacetime is to be recovered through a functionalist procedure in a theory that admits no fundamental spacetime, standard functionalism cannot serve as a model: all the known functional definitions are definitions in terms of a causal role for the motion of physical objects and hence presuppose spatiotemporal relations.

In this paper we have two aims: first, to draw attention to the close connexion between interpretation and scientific understanding; second, to give a detailed account of how theories without a spacetime can be interpreted, and so of how they can be understood. In order to do so, we of course need an account of what is meant by a theory 'without a spacetime': which we also provide in this paper. We describe three tools, used by physicists, aimed at constructing interpretations which are adequate for the goal of understanding. We analyse examples from high-energy physics illustrating how physicists use these tools to construct interpretations and thereby attain understanding. The examples are: the 't Hooft approximation of gauge theories, random matrix models, causal sets, loop quantum gravity, and group field theory.