This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www.beyondspacetime.net.) This chapter sketches how spacetime emerges in causal set theory and demonstrates how this question is deeply entangled with genuinely philosophical concerns.
This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www.beyondspacetime.net.) This chapter sketches how spacetime emerges in causal set theory and demonstrates how this question is deeply entangled with genuinely philosophical concerns.
Causal set theory starts out from a central result in general relativity according to which the causal structure determines, up to a so-called ‘conformal factor’, the geometry of a relativistic spacetime. 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. There are two areas in physics in which space or spacetime may emerge from something qualitatively rather different: wave function monism in quantum mechanics and quantum theories of gravity. The former case concerns a particular interpretative issue in non-relativistic quantum mechanics. The severity and the characteristics of the disappearance of spacetime differ from one approach to quantum gravity to another.
This paper explores the fundamental nature of spacetime from the perspective of emergent causal structures, rooted in quantum mechanical principles. We propose a theoretical framework that treats spacetime not as a pre-existing background, but as a collective phenomenon arising from the interaction of quantum causal relations. By analyzing the constraints of causality and quantum coherence, we derive key implications for the emergence of classical spacetime geometry and the limits of local realism. Our results suggest a new way to bridge quantum mechanics and gravitational theory, providing a foundation for future studies in quantum gravity and spacetime physics.
Introduction In this chapter we apply the concepts presented in Chapter 22 to a topic that has been of much theoretical interest in recent decades: causal set theory (CST). It is interesting and useful to review the status of CST relative to other foundational topics in mathematical physics that have been and remain of prime significance to empirical physics, namely, special relativity (SR), general relativity (GR), and quantum mechanics (QM). Those great frameworks are built on foundations that presuppose the continuity of space and time. Despite this, it is an empirical fact that we are surrounded by discreteness in the form of atoms, so it is natural to see how that discreteness fits in with the continuity of space and time. We have attempted in this book to show that the application of discrete principles to QM can go far beyond the basic Planck quantum of action. We have gone as far as discretizing empirical time, in the form of the stage concept. However, as far as relativity in either of its manifestations is concerned, the case for any form of discreteness has not yet been established empirically, although great efforts are being made in that direction in the program known as quantum gravity . We have particularly in mind the discretization approaches to GR of Regge (Regge, 1961) and Penrose (Penrose, 1971). Regge's approach is a classically based discretization of the Riemannian manifold concept, so has at best a generalized propositional classification (GPC) of two. Penrose's spin network paradigm started as a quantum description of spacetime and has led to much work in the area of spin networks in the hope of unifying GR and QM. However, workers in spin networks and related branches of quantum gravity have focued their attention on the mathematical complexities and hardly any on the role of observers and their apparatus, leading to a GPC classification of quantum gravity as one, that is, as mathematical physics and not physics. Claims made that such programs represent empirical physics have not been empirically substantiated to date; quantum gravity at this time remains empirically vacuous, despite the best efforts of many theorists over many decades.
I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.
I take non-locality to be the Michaelson Morley experiment of the early 21st Century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: i. If we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. ii. There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime.If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: Matter not only curves spacetime, but “creates” spacetime.We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity.This quantum creation of spacetime consists in: i. Fully non-local entangled coherent quantum variables.ii. The onset of locality via decoherence. iii. A metric in Hilbert Space among entangled quantum variables by the sub-additive von Neumann Entropy between pairs of variables. iv. Mapping from metric distances in Hilbert Space to metric distances in classical spacetime by episodic actualization events.v. Discrete spacetime is the relations among these discrete actualization events. vi. “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously.vii. The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. viii. The arrow of time history of these events is recorded in the very structure of the spacetime constructed. ix. Actual Time is a succession of two or more actual events.The theory inevitably yields a UV cut-off of a new type. The cut-off is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition.This quantum creation of spacetime modifies general relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity.Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed.Possible observational and experimental tests based on: i. the existence of Sub- Planckian photons, ii. knee and ankle discontinuities in the high energy gamma ray spectrum, and iii. possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use.The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.
Abstract We consider the observables describing spatiotemporal properties in the context of two of the most popular approaches to quantum gravity (QG), namely String Theory and Loop QG. In both approaches these observables are described by non-commuting operators. In analogy with recent arguments put forward in the context of non-relativistic quantum mechanics [see Calosi and Mariani (Philos. Compass 16(4):e12731, 2021) for a review], we suggest that the physical quantities corresponding to those observables may be interpreted as ontologically indeterminate—i.e., indeterminate in a way that is non-epistemic and semantic-independent. This working hypothesis has not received enough attention in the current debate on QG, and yet it may prove explanatory useful in several respects. First, it provides a clear background for understanding how some features of QG are ontologically continuous to features of quantum mechanics. Second, it sets the stage for asking new interesting questions about QG, for instance concerning the status of the so-called Eigenstate-Eigenvalue link. Third, it indirectly shows how the debate on ontological indeterminacy may extend well beyond the non-relativistic case, contrary to what seems to be assumed. Fourth, and perhaps more importantly, it provides a promising alternative to the received view on QG [Wüthrich et al. (Philosophy Beyond Spacetime: Implications from Quantum Gravity, Oxford University Press, Oxford, 2021)] according to which spacetime is not fundamental. On the view we shall suggest, spacetime may be indeterminate and yet fundamental.