Related papers: What `shape' is space-time?
Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian…
`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…
A new approach to the dynamics of the universe based on work by O Murchadha, Foster, Anderson and the author is presented. The only kinematics presupposed is the spatial geometry needed to define configuration spaces in purely relational…
Shape theory works nice for (Hausdorff) paracompact spaces, but for spaces with no separation axioms, it seems to be quite poor. However, for finite and locally finite spaces their weak homotopy type is rather rich, and is equivalent to the…
The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is…
Physical time intervals are attributes of single physical object whereas physical space intervals are a relational attribute of two physical objects. Some consequences of the breaking of the space-time exchange symmetry inherent in the…
Counterfactuals in quantum theory are briefly reviewed and it is argued that they are very different from counterfactuals considered in the general philosophical literature. The issue of time symmetry of quantum counterfactuals is…
Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about…
We consider the possibility that the basic space of physics is not spacetime, but configuration space. We illustrate this on the example with a system of gravitationally interacting point particles. It turns out that such system can be…
With the theory of special relativity, time has been linked with space into a four-dimensional space-time from which a basic question must be asked: can space be really transformed into time and vice-versa? The response is affirmative if…
General Relativity can be reformulated as a geometrodynamical theory, called Shape Dynamics, that is not based on spacetime (in particular refoliation) symmetry but on spatial diffeomorphism and local spatial conformal symmetry. This leads…
Discussion of some aspects of the concept of time for a general audience: nature of time, A- and B-series, time in physics, the "now", measurement of time, definition of time units, time's arrow, relativity of time, relativity of…
The absence of unique time evolution in Einstein's spacetime description of gravity leads to the hitherto unresolved `problem of time' in quantum gravity. Shape Dynamics is an objectively equivalent representation of gravity that trades…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
Quantum theory depends on an external classical time, and there ought to exist an equivalent reformulation of the theory which does not depend on such a time. The demand for the existence of such a reformulation suggests that quantum theory…
Some ideas aimed to understand that time is one-dimensional are briefly reviewed. Some attempts to construct theories in varieties with more spatial and temporal components are presented. It is discussed, from the epistemological point of…
The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth…
Over the last decade a growing number of quantum-gravity researchers has been looking for opportunities for the first ever experimental evidence of a Planck-length quantum property of spacetime. These studies are usually based on the…
Our purpose here is to introduce the idea of viewing the spacetime as a macroscopic complex system which, consequently, cannot be directly quantized. It should be thought of as a collection of more fundamental "microscopical" entities…