Related papers: Mapping Cartesian Coordinates into Emission Coordi…
Flat space-time has not heretofore been thought a suitable locus in which to construct model universes because of the presumed necessity of incorporating gravitation in such models and because of the historical lack of a theory of…
Relativistic positioning systems provide tensors represented in $\{\ell\ell\ell\ell\}$-frames ($\ell$ for light) dual to systems of emission coordinates. We show that any Lorentzian metric field given in such a frame is isometrically…
We propose to derive deviation measures through the Minkowski gauge of a given set of acceptable positions. We show that, given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework. In…
We have recently proposed a simple relativistic theory which reduces to modified Newtonian dynamics for the weak-field quasistatic situations applied to galaxies, and to cosmological behavior as in the $\Lambda$CDM model, yielding a…
We discuss a new class of coordinate systems for a plane, which provide an analytical representation of arbitrary straightline, and then define the form of potential on the plane, under which the equations of motion of a mass point are…
The causal set program as well as the Wolfram physics project leave open the problem of how a graph that is a (3+1)-dimensional Minkowski-spacetime according to its simple geodesic distances, could be generated solely from simple…
P.A.M. Dirac had stated that the Cartesian coordinates are uniquely suited for expressing the canonical commutation relations in a simple form. By contrast, expressing these commutation relations in any other coordinate system is more…
Theoretical and observational challenges to standard cosmology such as the cosmological constant problem and tensions between cosmological model parameters inferred from different observations motivate the development and search of new…
A two-dimensional Minkowski spacetime diagram is neatly represented on a Euclidean ordinary plane. However the Euclidean lengths of the lines on the diagram do not correspond to the true values of physical quantities in spacetime, except…
Matrix models play an important role in studies of quantum gravity, being candidates for a formulation of M-theory, but are notoriously difficult to solve. In this work, we present a fresh approach by introducing a novel exact model…
We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of…
We develop a new approach to building cosmological models, in which small pieces of perturbed Minkowski space are joined together at reflection-symmetric boundaries in order to form a global, dynamical space-time. Each piece of this…
The aim of this set of lectures is a systematic presentation of a 1+3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic 1+3 covariant relations…
The theory of relativistic {\em location systems} is sketched. An interesting class of these systems is that of relativistic {\em positioning systems,} which consists in sets of four clocks broadcasting their proper time. Among them, the…
We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the…
Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of…
Flat space cosmology spacetimes are exact time-dependent solutions of 3-dimensional gravity theories, such as Einstein gravity or topologically massive gravity. We exhibit a novel kind of phase transition between these cosmological…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum…
The cosmological scale factor $a(t)$ of the flat-space Robertson-Walker geometry is examined from a Hamiltonian perspective wherein $a(t)$ is interpreted as an independent dynamical coordinate and the curvature density $\sqrt {- g(a)}…