Related papers: What `shape' is space-time?
We investigate measures of distance and redshift in cosmological space-times that admit a shear-free foliation, which we henceforth refer to as `quasi-Newtonian'. Space expands isotropically in this description, and small-scale…
The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static…
There are competing schools of thought about the question of whether spacetime is fundamentally either continuous or discrete. Here, we consider the possibility that spacetime could be simultaneously continuous and discrete, in the same…
We put forward a model of discrete physical space that can account for the structure of space- time, give an interpretation to the postulates of quantum mechanics and provide a possible explanation to the organization of the standard model…
General relativity describes the gravitational field geometrically and in a self-interacting way because it couples to all forms of energy, including its own. Both features make finding a quantum theory difficult, yet it is important in the…
An algebraic scheme is suggested in which discretized spacetime turns out to be a quantum observable. As an example, a toy model producing spacetimes of four points with different topologies is presented. The possibility of incorporating…
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…
The quantization of time-reparametrization invariant systems such as general relativity is plagued by an ambiguity relating to the role of time in the theory. If one parametrizes observables by the (unobservable) time, and then relies on…
It is plausible that quantum gravity effects may lead us to a description of Nature beyond the framework of special relativity. In this case, either the relativity principle is broken or it is maintained. These two scenarios (a violation or…
Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier.…
The Problem of Time in Quantum Gravity is analyzed from a classical presymplectic perspective. In the first part of the paper the Three Space Approach to General Relativity is introduced via the Barbour-Foster-\'O Murchadha action and the…
Shape dynamics is a classical theory of gravity which agrees with general relativity in many important cases, but possesses different gauge symmetries and constraints. Rather than spacetime diffeomorphism invariance, shape dynamics takes…
An introduction is given to discussions on the possiblity of fabricating spacetime geometries allowing time-travel scenarios with the help of matter possessing typically quantum features. Those scenarios are considered in the framework of…
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…
Background Independence is the modern form of the relational side of the Absolute versus Relational Debate. Difficulties with its implementation form the Problem of Time. Its 9 facets - Isham and Kucha\v{r}'s conceptual classification -…
The canonical formalism of general relativity affords a particularly interesting characterisation of the infamous hole argument. It also provides a natural formalism in which to relate the hole argument to the problem of time in classical…
Gravity is understood as a geometrization of spacetime. But spacetime is also the manifold of the boundary values of the spinless point particle in a variational approach. Since all known matter, baryons, leptons and gauge bosons are…
Superpositions of black holes can be described geometrically using a combined canonical formulation for space-time and quantum states. A previously introduced black-hole model that includes quantum fluctuations of metric components is shown…
Self-similar potentials generalize the concept of shape-invariance which was originally introduced to explore exactly-solvable potentials in quantum mechanics. In this article it is shown that previously introduced algebraic approach to the…
General relativity is unable to determine the topology of the Universe. We propose to apply quantum approach. Quantization of dynamics of a test particle is sensitive to the spacetime topology. Presented results for a particle in de Sitter…