Related papers: Quantum Singularities in Static Spacetimes
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
We perform the canonical quantization of a relativistic spinless particle moving in a curved and static spacetime. We show that the classical theory already describes at the same time both particle and antiparticle. The analyses involves…
We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of $k = \pm 1$ Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for…
We introduce the set of constraints the wave function of the Universe has to satisfy in order to describe an Universe undergoing through the process of spontaneous breaking of supersymmetry and discuss the way this may lead to the emergence…
Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge…
General relativity allows a variety of future singularities to occur in the evolution of the universe. At these future singularities, the universe will end in a singular state after a finite proper time and geometrical invariants of the…
Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine…
Simple classical mechanical systems and solution spaces of classical field theories involve singularities. In certain situations these singularities can be understood in terms of stratified Kaehler spaces. We give an overview of a research…
In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lema\^{\i}tre-Robertson-Walker, de…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
Classical models for dark energy can exhibit a variety of singularities, many of which occur for scale factors much bigger than the Planck length. We address here the issue whether some of these singularities, the big freeze and the big…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…
Exact solutions of several nonstationary problems of quantum mechanics are obtained. It is shown that if the initial conditions of the problem correspond to the localized-in-space particle, then it moves exactly along the 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…
The aim of these notes is to elucidate some aspects of quantum field theory in curved spacetime, especially those relating to the notion of particles. A selection of issues relevant to wave-particle duality is given. The case of a generic…
We argue that, in order to obtain decoherence of spacetime, we should consider quantum conformal metric fluctuations of spacetime. This could be the required environment in the problem of selfmeasurement of spacetime in quantum gravity.