Related papers: On the Relativity in Configuration Space: A Renewe…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
Some examples from the mathematics of shape are presented that question some of the almost hidden assumptions behind results on limiting behaviour of finitary approximations to space-time. These are presented so as to focus attention on the…
The concept of time-space defined in an earlier paper of the author is a certain generalization of the so-called space-time. In this paper we introduce the concept of time-space manifolds. In the homogeneous case, a time-space manifold is a…
The contemporary physics has revealed growing evidences that the emergence can be applied to not only biology and condensed matter systems but also gravity and spacetime. We observe that noncommutative spacetime necessarily implies emergent…
Relational particle mechanics is useful for modelling whole-universe issues such as quantum cosmology or the problem of time in quantum gravity, including some aspects outside the reach of comparably complex minisuperspace models. In this…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space" is the complement of an arrangement of…
The concepts of relative velocity and acceleration, deviation velocity and acceleration and relative momentum of point particles in spaces (manifolds), the tangent bundle of which is equipped with a transport along paths, are introduced. If…
It is suggested, that a curved 4-dimensional space-time manifold is a strained elastic plate in multidimensional embedding space-time. Its thicknesses along extradimensions are much less than 4-dimensional sizes. Reduced 4-dimensional free…
We review how reparametrization of space and time, namely the procedure where both are made to depend on yet another parameter, can be used to formulate quantum physics in a way that is naturally conducive to relativity. This leads us to a…
Our main purpose here is to study some qualitative aspects of space and time. These include the notion of space and time regarded as the containers of respectively bodies and events, the divisibility of space, and the unrepeatability of…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
The higher-dimensional generalization of Randall-Sundrum approach with additional positive curvature $n$-dimensional and Ricci-flat $m$-dimensional compuct subspaces is considered in pure gravity theory with metric of space-time and…
Finitely many hypersurfaces are removed from unordered configuration spaces of $n$ points in $\mathbb{C}$ to obtain a fibration over unordered configuration spaces of $n-1$ complex points. Fundamental groups of these restricted…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
All gauge theories need ``something fixed'' even as ``something changes.'' Underlying the implementation of these ideas all major physical theories make indispensable use of an elaborately designed spacetime model as the ``something…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
We develop a theory for describing composite objects in physics. These can be static objects, such as tables, or things that happen in spacetime (such as a region of spacetime with fields on it regarded as being composed of smaller such…
We note that the existence of physical states which are coherent superpositions of states with even and odd numbers of fermions means the existence, together with x,y,z,t, of additional spinor dimensions of space-time. A system with…
The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these…