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.
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.
In this paper we consider the observables describing fundamental spatiotemporal properties and relations in the context of Quantum Gravity (QG). As we will show, in both Loop Quantum Gravity and in String Theory, these observables are non-commuting ones. By analogy with some recent arguments put forward in the context of non-relativistic quantum mechanics (QM), we shall propose to interpret these physical quantities as ontologically indeterminate -- i.e., indeterminate in a non-epistemic, mind-independent way. This result has two important consequences for current debates in philosophy of physics. First, it shows that ontological indeterminacy may extend well beyond the non-relativistic case, thereby also suggesting a conceptual continuity between QM and QG. Second, when applied to QG, the notion of indeterminacy may provide a unified philosophical framework for understanding very distinct approaches that are usually considered incompatible.
Understand the intrinsic physical meaning of quantum formalism leads ontologically to admit that one fundamental side of reality is purely contradictory, irreducibly random, objectively indeterminate and intrinsically independent of relativistic space-time. It means also that physical reality has another fundamental side, i.e. space-time, and that both are irreducible to each other. Quantum reality, discretized by the Planck constant, assume coherent states and partially ordered variables (that are commutative or not), while on the other side, relativistic space-time, structured by the speed of light, assume coherent variables and partially ordered states (that are causally related or not). From this point of view, fields would be only a derived mixture of these two sides. But quantum reality and relativistic space-time seem to be mixed in two kinds of fields themselves irreducible to each other. If, on one hand, quantum field theory has already formalized the way that quantum reality locates, evolves and interacts on a relativistic background, on the other hand, quantum gravity tends to formalize the way that smooth and causally ordered space-time emerges on a quantum background. But no unification of the two fundamental sides of reality must be waited at this derived level. Unification could perhaps intervene only upstream, in a pure variation preceding and underlying its double distinction in variables and states of variation, i.e. its quantization or its localization and their derived mixtures.
The dissertation investigates some relevant metaphysical issues arising in the context of spacetime theories. In particular, the inquiry focuses on general relativity and canonical quantum gravity. A formal definition of spacetime theory is proposed and, against this framework, an analysis of the notions of general covariance, symmetry and background independence is performed. It is argued that many conceptual issues in general relativity and canonical quantum gravity derive from putting excessive emphasis on general covariance as an ontological prin-ciple. An original metaphysical position grounded in scientific essential- ism and causal realism (weak essentialism) is developed and defended. It is argued that, in the context of general relativity, weak essentialism supports spacetime substantivalism. It is also shown that weak essentialism escapes arguments from metaphysical underdetermination by positing a particular kind of causation, dubbed geometric. The proposed interpretive framework is then applied to Bohmian mechanics, pointing out that weak essentialism nicely fits into this theory. In the end, a possible Bohmian implementation of loop quantum gravity is considered, and such a Bohmian approach is interpreted in a geometric causal fashion. Under this interpretation, Bohmian loop quantum gravity straightforwardly commits us to an ontology of elementary extensions of space whose evolution is described by a non-local law. The causal mechanism underlying this evolution clarifies many conceptual issues related to the emergence of classical spacetime from the quantum regime. Although there is as yet no fully worked out physical theory of quantum gravity, it is argued that the proposed approach sets up a standard that proposals for a serious ontology in this field should meet.
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.
Quantum gravity suggests that spacetime may not be fundamental, and it has been argued that we can understand a theory without a fundamental spacetime if we are able to claim that spacetime 'emerges' from some non-spatiotemporal entities. In this sense, strategies like functionalism have been deployed to claim that this emergence is possible and plausible, both in principle and in practice for current approaches to quantum gravity. In this article I argue that this analysis is incomplete, as it tends to overlook the way the dynamics of these theories is 'quantum' in a way that differs from standard quantum theory. The challenge for the emergentist (and for the quantum gravity theorist) is to give an interpretation not only to the kinematical and classical aspects of these theories, but to the dynamical and quantum ones, and to show how the spacetime roles can be fulfilled, if possible at all. Therefore, I argue that some current approaches to quantum gravity seem to fail to provide meaningful theories, that spacetime functionalism is of no help, and that the position of the spacetime emergentists is weakened, as they lack any example of a successful reduction of spacetime to some truly quantum non-spatiotemporal stuff.
Measurements play a crucial role in quantum mechanics because they serve two fundamental purposes. First, they enable the extraction of information about a quantum system; second, they give rise to new physical effects that do not appear in classical physics, one important example being the measurement-induced state update, where the act of measurement alters the system’s state. For these reasons, the mathematical description of measurements plays a primary role in the foundational postulates of the theory. However, the essence of what happens during a measurement remains poorly understood, even within the relatively easy realm of non-relativistic quantum theory. The situation becomes even less transparent in the relativistic setting, where the requirement to preserve causality and prevent faster-than-light signalling introduces both formal and interpretational challenges, complicating the very mathematical formulation of a measurement theory. As for quantum gravity, the idea of applying quantum measurements within or onto a quantum spacetime remains virtually unexplored, presenting a vast and uncharted frontier for theoretical inquiry. Building on recent advances across several areas at the intersection of quantum foundations, quantum information theory, relativistic quantum theory, and quantum gravity, the last few years saw a surge of interest in formulating a consistent framework for describing local measurements in a relativistic context. The main results of this endeavour are two distinct proposals for a relativistic measurement postulate for quantum field theory in generic spacetimes. While these two proposals are still being understood, and a growing research community is working to clarify their implications and potential interconnections, the field of relativistic quantum measurements has now reached a level of maturity that allows us to ask both formal and interpretive questions on a solid footing. All this only applies to the regime in which quantum field theory in curved spacetime remains valid: nothing can yet be said about measurements at the Planck energy, where quantum gravitational effects are expected to become important. This thesis presents an introduction to the theory of measurements in non-relativistic and relativistic quantum mechanics, along with four original research articles that explore aspects of measurements in both fields, as well as the potential extension of measurement theory to the domain of quantum gravity. The first article examines the limitations of realistic measurement apparatuses in non-relativistic quantum theory, establishing reasonable bounds for the precision that can be achieved with a given apparatus composed of many quantum components. The second article explores how to extract information from a newly introduced class of quantum systems, defined as those that cannot be replicated and thus fall outside the usual scope of quantum mechanics. Then, it applies the methodology to quantum field theory, demonstrating that classical results, such as the Unruh effect, can still be observed in this setting. The third article discusses detector-based measurements in quantum field theory. This is a recently proposed method that extends the non-relativistic measurement postulate to the relativistic regime by means of Unruh-de Witt detectors. The article highlights some conceptual and mathematical issues with the framework and proposes a solution using algebraic quantum field theory. The outcome is a self-consistent scheme for introducing local measurements in quantum field theory via measuring detectors. Finally, the fourth article uses the measurement scheme above to study how what we learned in the past years about local measurements can be extended to quantum gravity. This is achieved through the holographic principle realised in terms of the AdS-CFT correspondence. In conclusion, this thesis contributes to the development of both non-relativistic and relativistic measurement theories and introduces ideas and questions related to the role of measurement in quantum gravity. Though preliminary, this work opens a pathway toward studying measuring observers in quantum gravity.