Related papers: Algebraic description of spacetime foam
Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…
In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which do not have…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
There are not many tools to quantitatively monitor the emergence of classical geometric features from a quantum spacetime, whose microscopic structure may be a highly quantum-fluctuating "spacetime foam". To improve this situation, we…
I would like to consider the Beginning of space-time in this paper. First of all, we do consideration historical thought. A lot of philosophers have considered the relation between this real phenomenal world and the basic world in which the…
The problem of topology change description in gravitation theory is analized in detailes. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of boundary conditions (or…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
It is argued that a noncommutative geometry of spacetime leads to a reconciliation of electromagnetism and gravitation while providing an underpinning to Weyl's geometry. It also leads to a cosmology consistent with observation. A few other…
A recent paper (gr-qc/9909017) criticizes our work on the structure of spacetime foam. Its authors argue that the quantum uncertainty limit for the position of the quantum clock in a gedanken timing experiment, obtained by Wigner and used…
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in…
We perform a foliation of a four dimensional Riemannian space-time with respect to a discrete time which is an integer multiple of the Planck time. We find that the quantum fluctuations of the metric have a discrete energy spectrum. The…
Quantum fluctuations endow spacetime with a foamy texture. The degree of foaminess is dictated by blackhole physics to be of the holographic type. Applied to cosmology, the holographic foam model predicts the existence of dark energy with…
It is shown that high-energy astrophysics can provide information on the small-scale structure of spacetime.
Spacetime is modelled as a homogeneous manifold given by the classes of unitary $\U(2)$ operations in the general complex operations $\GL(\C^2)$. The residual representations of this noncompact symmetric space of rank two are characterized…
I propose a general geometric framework in which to discuss the existence of time observables. This frameworks allows one to describe a local sense in which time observables always exist, and a global sense in which they can sometimes exist…
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…
Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime; a topology…
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…