Related papers: A Summary: Quantum Singularities in Static and Con…
We review the investigations on the quantum structure of spactime, to be found at the Planck scale if one takes into account the operational limitations to localization of events which result from the concurrence of Quantum Mechanics and…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria…
In this note, we attempt to provide some insights into the structure of non-perturbative descriptions of quantum gravity using known examples of gauge-theory / gravity duality. We argue that in familiar examples, a quantum description of…
The Hawking-Penrose theorem is not covariant under field redefinitions. Should the invariance under such transformations be a true principle in Nature, spacetime singularities become dubious objects. We here review the concept of covariant…
This paper examines two cosmological models of quantum gravity (from string theory and loop quantum gravity) to investigate the foundational and conceptual issues arising from quantum treatments of the big bang. While the classical…
We consider particle dynamics in singular gravitational field. In 2d spacetime the system splits into two independent gravitational systems without singularity. Dynamical integrals of each system define $sl(2,R)$ algebra, but the…
In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both…
We conjecture that space-like singularities are simply regions in which all available degrees of freedom are excited, and the system cycles randomly through generic quantum states in its Hilbert space. There is no simple geometric…
In recent years, the picture of discrete space time has been studied in the context of stochastic theory. There are a number of ramifications, which are briefly examined. We argue that the causality of physiics has its roots in the…
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In…
In a predicative framework from basic logic, defined for a model of quantum parallelism by sequents, we characterize a class of first order domains, termed {\em virtual singletons}, which allows a generalization of the notion of duality,…
We study the phase space of periodically modulated gravitational cavity by means of quantum recurrence phenomena. We report that the quantum recurrences serve as a tool to connect phase space of the driven system with spectrum in quantum…
Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a…
In this paper, conformal motions are studied in plane symmetric static spacetimes. The general solution of conformal Killing equations and the general form of the conformal Killing vector for these spacetimes are presented. All…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
The formalism for histories-based generalized quantum mechanics developed in two earlier papers is applied to the treatment of histories (of particles or fields or more general objects) in curved spacetimes (which need not admit foliation…
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…
String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework…
We examine consequences of the density matrix approach to quantum theory in the context of a model spacetime containing closed timelike curves and find that in general, an initially pure state will evolve in a nonlinear way to a mixed…