Related papers: Unitarity, clock dependence and quantum recollapse…
The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock.…
We offer a new proposal for cosmic singularity resolution based upon a quantum cosmology with a unitary bounce. This proposal is illustrated via a novel quantization of a mini-superspace model in which there can be superpositions of the…
The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we…
We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as…
We construct the Hamiltonian formulation of the isotropic Universe in a generic metric f(R)-theory in the Jordan frame. We canonically quantize the Universe volume via a polymer formulation, and we adopt the scalar field naturally arising…
We consider classical and quantum dynamics of a free particle in de Sitter's space-times with different topologies to see what happens to space-time singularities of removable type in quantum theory. We find analytic solution of the…
We describe quantization schemes for scalar field cosmology in the metric variables with fundamental discreteness imposed with a lattice. The variables chosen for quantization determine the lattice, and each lattice produces distinct…
Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular…
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 components of the Riemann tensor in the tetrad basis are quantized and, through the Einstein equation, we find the local expectation value in the ontological interpretation of quantum mechanics of the energy density and pressure of a…
The basic tenet of the present work is the assumption of the lack of external and fixed time in the Universe. This assumption is best embodied by general relativity, which replaces the fixed space-time structure with the gravitational…
We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a…
A fundamental issue for any quantum cosmological theory is to specify how probabilities can be assigned to various quantum events or sequences of events such as the occurrence of singularities or bounces. In previous work, we have…
A commonly adopted relational account of time evolution in generally-covariant systems, and more specifically in quantum cosmology, is argued to be unsatisfactory, insofar as it describes evolution relative to observed readings of a clock…
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.…
In a recent paper [Phys. Rev. D 92:084012, 2015], the author studied the classical $(1+1)$-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in Ho\v{r}ava-Lifshitz (HL) theory of gravity. This theory is…
It is expected that a quantum theory of gravity will radically alter our current notion of spacetime geometry. However, contrary to what was commonly assumed for many decades, quantum gravity effects could manifest in scales much larger…
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,…