The problem of time in quantum gravity is often presented as a consequence of applying quantum theory to general relativity. These notes adopt a broader perspective. We first examine how time enters classical mechanics, relativity, quantum theory, and quantum field theory, distinguishing three principal aspects: causal order, temporal duration, and the present. This analysis shows that the conceptual difficulties associated with time do not arise only when gravity is quantised. Tensions between causal structure, clocks, observables, and measurement are already present in the theories from which quantum gravity is constructed. We then survey responses to the problem of time across the principal approaches to quantum gravity. These include canonical and Wheeler-DeWitt quantisation, path-integral and histories formulations, perturbative and background-dependent approaches, causal sets, and twistor theory. The programmes are compared according to whether they retain an external time, render time problematic through quantisation, or incorporate causal or temporal structure into their foundations. Particular emphasis is placed on questions arising from quantum foundations and relativistic quantum information. We conclude by examining linearised gravity and weak-gravity quantum systems. This regime shows that the problem of time is not confined to Planck-scale physics, but arises already in attempts to provide a predictive and operationally meaningful quantum description of spacetime near flat geometry.
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146 pages. Notes for lectures delivered at the School "Time, Causality and Memory in Quantum Physics", Stockholm, 2026; organized by the COST Action "Relativistic Quantum Information"
The problem of time in quantum gravity is often presented as a consequence of applying quantum theory to general relativity. These notes adopt a broader perspective. We first examine how time enters classical mechanics, relativity, quantum theory, and quantum field theory, distinguishing three principal aspects: causal order, temporal duration, and the present. This analysis shows that the conceptual difficulties associated with time do not arise only when gravity is quantised. Tensions between causal structure, clocks, observables, and measurement are already present in the theories from which quantum gravity is constructed. We then survey responses to the problem of time across the principal approaches to quantum gravity. These include canonical and Wheeler-DeWitt quantisation, path-integral and histories formulations, perturbative and background-dependent approaches, causal sets, and twistor theory. The programmes are compared according to whether they retain an external time, render time problematic through quantisation, or incorporate causal or temporal structure into their foundations. Particular emphasis is placed on questions arising from quantum foundations and relativistic quantum information. We conclude by examining linearised gravity and weak-gravity quantum systems. This regime shows that the problem of time is not confined to Planck-scale physics, but arises already in attempts to provide a predictive and operationally meaningful quantum description of spacetime near flat geometry.
Abstract Quantum mechanics and relativity are two of the most successful theoretical frameworks in modern physics, yet their conceptual foundations remain difficult to reconcile at the deepest level. Quantum theory describes physical systems through states, observables, probabilities, measurement contexts, superposition, entanglement, and nonclassical correlations. Relativity describes physical processes through space-time structure, causal order, invariant physical law, observer-dependent decomposition of time and space, and constraints on signal propagation. This article examines the conceptual relationship between quantum measurement, relativistic causality, and space-time description. The purpose is not to present a mathematical unification but to analyze how the two frameworks organize physical explanation differently and where their interpretive tensions arise. Special attention is given to the measurement problem, the status of quantum states, the role of observers and reference frames, the meaning of locality, the distinction between correlation and causal influence, and the challenge of describing quantum processes without privileging a single global time. The article argues that many apparent conflicts between quantum theory and relativity result from importing classical intuitions into domains where they no longer apply. Quantum entanglement does not permit controllable faster-than-light communication, yet it challenges classical separability. Relativity forbids superluminal signaling, yet it does not require that all physically meaningful correlations be reducible to local classical properties. Measurement introduces another difficulty because standard quantum theory often describes state update in a way that appears instantaneous, while relativistic space-time does not provide a universal present. The discussion develops a conceptual framework in which quantum measurement is treated as a physical interaction, relativistic causality as a constraint on operational influence, and space-time description as an organizing structure for events rather than a simple background stage. This analysis is relevant for quantum field theory, quantum information, relativistic quantum foundations, and future approaches to quantum gravity.
Canonical quantization applied to closed systems leads to static equations, the Wheeler-deWitt equation in Quantum Gravity and the time independent Schrödinger equation in Quantum Mechanics. How to restore time is the Problem of Time(s). Integrating developments are: a) entanglement of a microscopic system with its classical environment accords it a time evolution description, the time dependent Schrödinger equation, where t is the laboratory time measured by clocks; b) canonical quantization of Special Relativity yields both the Dirac Hamiltonian and a self adjoint "time" operator, restoring to position and time the equivalent footing accorded to energy and momentum in Relativistic Quantum Mechanics. It introduces an intrinsic time property τ associated with the mass of the system, and a basis additional to the usual configuration, momentum and energy basis. As a generator of momentum displacements and consequently of energy, it invalidates Pauli's objection to the existence of a time operator. It furthermore complies with the requirements to condition the other observables in the conditional interpretation of QG. As Pauli's objection figures explicit or implicitly in most current developments of QM and QG, its invalidation opens to research the effect of this new two times perspective on such developments.
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. This theory is in fully four-dimensional form and free from the need for a fixed causal structure. Usual quantum mechanics is recovered as an approximation to this more general framework that is appropriate in those situations where spacetime geometry behaves classically. (Talk given at the Workshop on Physics at the Planck Scale, Puri, India, December12-21, 1994. This talk is a precis of the author's 1992 Les Houches Lectures: Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime, gr-qc/9304006).
Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its role in the dynamics of systems and hinders any formulation to merge quantum mechanics with general relativity, specifically when considering quantum gravity. To overcome those limitations, several authors tried to construct an operator which is conjugate to the Hamiltonian of quantum systems implementing some essential features of the relativistic time. These formulations use the concept of internal or intrinsic time instead of the universal coordinate time used in textbooks. Furthermore, recently it is remarked that the consideration of time with relativistic features could enhance the analysis techniques in quantum information processing and have an impact on its status in causal orders and causal structures of quantum information. The role of clocks, their accuracy and stability has become an important issue in quantum information processing. This article present a substantiative review of recent works which reflect the possibility of utilizing quantum time, measured by quantum clock devised according to Page-Wootters scheme, to stand as a resource for quantum information processing.
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.
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.