Related papers: The Chrono-Geometrical Structure of General Relati…
It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields…
Clocks in different heights or with different velocities run with different speeds. For global positioning systems these effects are much too large to be ignored. Nevertheless, in classical and quantum mechanics we get high accuracy using a…
The observable spacetime can be viewed as worldline coincidences (events) between a particle system and the observers of an extended (material) reference frame (ERF). Particle positions are then operationally well defined with respect to…
We study the conformal geometry of timelike curves in the (1+2)-Einstein universe, the conformal compactification of Minkowski 3-space defined as the quotient of the null cone of $\mathbb{R}^{2,3}$ by the action by positive scalar…
The notion of time is given a different footing in Quantum Mechanics and General Relativity, treated as a parameter in the former and being an observer dependent property in the later. From a operational point of view time is simply the…
In his Autobiographical Notes, Einstein mentioned that on his road to the final theory of general relativity it was a major difficulty to accustom himself to the idea that coordinates need not possess an immediate physical meaning in terms…
One of the main goal of large-scale structure surveys is to test the consistency of General Relativity at cosmological scales. In the $\Lambda$CDM model of cosmology, the relations between the fields describing the geometry and the content…
Time-like and space-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances defined by two spatially-separated clocks. The time dilatation effect is confirmed, but not `relativity of…
In my previous work, physics/0205011, I reported several observations on special relativity, its experimental facts and its relations to quantum mechanics and statistical mechanics. These observations made us conscious: Special relativity…
We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead…
In an apparently unexplored region of relativistic spacetime, a simple thought experiment demonstrates that conjoined Lorentz transformations predict a proper clock at rest will run backwards and that prediction violates the logical…
We consider three dimensional Einstein gravity non-minimally coupled to a real scalar field with a self-interacting scalar potential and present the exact black hole formation in three dimensions. Firstly we obtain an exact time-dependent…
Metric descriptions of gravitation, among them general relativity as today's established theory, are founded on assumptions summarized by the Einstein equivalence principle (EEP). Its violation would hint at unknown physics and could be a…
We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. These are systems where the kinematics of small perturbations are dominated by an effective…
We revisit conformal time $\eta$ in a spatially flat Friedmann--Robertson--Walker universe and use a $1+1$-dimensional setting as a technically transparent pedagogical arena. Our purpose is to clarify the relation among cosmic time $t$,…
Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter-wave interferometry. Yet, phase shifts can always be explained as arising due to an Aharonov-Bohm effect,…
By extending the framework of the gravitational clock compass we show how a suitably prepared set of clocks can be used to extract information about the gravitational field in the context of General Relativity. Conceptual differences…
In this paper, the modern theory of infinitesimals is applied to the General Relativity metric dS and its geometric and physical meanings are rigorously investigated. Employing results obtained via the time-dependent Schrodinger equation,…
Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computational efficiency. Here we study relationships…
Is the geometry of space a macroscopic manifestation of an underlying microscopic statistical structure? Is geometrodynamics - the theory of gravity - derivable from general principles of inductive inference? Tentative answers are suggested…