Related papers: Physical Hilbert Spaces in Quantum Gravity
We analyze the size and evolution of quantum fluctuations of cosmologically relevant geometric observables, in the context of the effective relational cosmological dynamics of GFT models of quantum gravity. We consider the fluctuations of…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
A novel quantum time dilation effect is shown to arise when a clock moves in a quantum superposition of two relativistic velocities. This effect is argued to be measurable using existing atomic interferometry techniques, potentially…
This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity…
Every clock is a physical system and thereby ultimately quantum. A naturally arising question is how to describe time evolution relative to quantum clocks and, specifically, how the dynamics relative to different quantum clocks are related.…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
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. - This is motivated by the ``timeless''…
We know that space and time are treated almost equally in classical physics, but we also know that this is not the case for quantum mechanics. A quantum description of both space and time is important to really understand the quantum nature…
One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of…
Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and…
Given a bipartite quantum system in an energy eigenstate, the dynamical description for one component can be derived via entanglement using the other component as a clock. This is the essence of the Page and Wootters mechanism. Moreover, if…
't Hooft has recently developed a discretisation of (2+1) gravity which has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe several models in the continuum…
Recently, it was shown that the quantum effects of the matter, could be used to determine the conformal degree of freedom of the space-time metric. So both gravity and quantum are geometrical features. Gravity determines the causal…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
The "problem of time" in canonical quantum gravity refers to the difficulties involved in defining a Hilbert space structure on states -- and local observables on this Hilbert space -- for a theory in which the spacetime metric is treated…
Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…