Related papers: Natural Coordinate System in Curved Space-time
Space-time symmetries are a crucial ingredient of any theoretical model in physics. Unlike internal symmetries, which may or may not be gauged and/or spontaneously broken, space-time symmetries do not admit any ambiguity: they are gauged by…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
Introduction of curvilinear coordinates might be very convenient in many cases. Theoretically, tensor analysis would be most suited. However, tensor notation can't be used in numerical procedure. For example, the strict discrimination of…
Quantum measurement is a physical process. What physical resources and constraints does quantum mechanics require for measurement to produce the classical world we observe? Treating measurement as a fully unitary quantum process, our goal…
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
Curvature is a key notion in General Relativity, characterizing the local physical properties of spacetime. By contrast, the concept of curvature has received scant attention in nonperturbative quantum gravity. One may even wonder whether…
We describe coordinate systems adapted for the space between two surfaces, such as those delineating the highly folded cortex in mammalian brains. These systems are estimated in order to satisfy geometric priors, including streamline…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in this paper we transfer the concept of atomic coherent state to the nuclear spin context, where it is referred to as pseudo-nuclear spin coherent state…
We show that proper time, when defined in the quantum theory of 2d gravity, becomes identical to the stochastic time associated with the stochastic quantization of space. This observation was first made by Kawai and collaborators in the…
Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein's relativity. Accordingly, a comparison between observational data and theoretical expectations might…
The motion of a compact body in space and time is commonly described by the world line of a point representing the instantaneous position of the body. In General Relativity such a world-line formalism is not quite straightforward because of…
Time crystals are quantum many-body systems which, due to interactions between particles, are able to spontaneously self-organize their motion in a periodic way in time by analogy with the formation of crystalline structures in space in…
In this work, we report the development of a spatially fourth order temporally second order compact scheme for incompressible Navier-Stokes (N-S) equations in time-varying domain. Sen [J. Comput. Phys. 251 (2013) 251-271] put forward an…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an ad hoc fashion. Here, instead, we start from the…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
The paper addresses the quantization of minisuperspace cosmological models by studying a possible solution to the problem of time and time asymmetries in quantum cosmology. Since General Relativity does not have a privileged time variable…