Related papers: Physical Hilbert Spaces in Quantum Gravity
Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the…
At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through…
We propose a generic mechanism for the emergence of a gravitational potential that acts on all classical objects in a quantum system. Our conjecture is based on the analysis of mutual information in many-body quantum systems. Since…
General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…
We study the dynamical evolution of two quantum clocks interacting with a relativistic gravitational potential. We find a time dilation effect for the clocks in agreement with the gravitational time dilation as obtained from the…
According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its classical trajectory through spacetime. In contrast, quantum theory allows the association of many simultaneous trajectories with a…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
The literature on quantum-gravity-inspired scenarios for the quantization of spacetime has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum-gravity…
We study gravitational back-reaction within the Page-Wootters formulation of quantum mechanics by treating time as a quantum degree of freedom. Our model introduces a distinction between global coordinate time, represented as a relational…
Phenomenological studies of quantum gravity have proposed a modification of the commutator between position and momentum in quantum mechanics so to introduce a minimal uncertainty in position in quantum mechanics. Such a minimal uncertainty…
We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation…
The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend…
We introduce a framework to study the emergence of time and causal structure in quantum many-body systems. In doing so, we consider quantum states which encode spacetime dynamics, and develop information theoretic tools to extract the…
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories.…
Several conceptual aspects of quantum gravity are studied on the example of the homogeneous isotropic LQC model. In particular: $(i)$ The proper time of the co-moving observers is showed to be a quantum operator {and} a quantum spacetime…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
In this work we derive general quantum phenomenological equations of gravitational dynamics and analyse its features. The derivation uses the formalism developed in thermodynamics of spacetime and introduces low energy quantum gravity…
Time plays different roles in quantum mechanics and gravity. These roles are examined and the problems that the conflict in the roles presents for quantum gravity are briefly summarised.