Related papers: An observer principle for general relativity
The equivalence principle is treated on a mathematically rigorous base on sufficiently general subsets of a differentiable manifold. This is carried out using the basis of derivations of the tensor algebra over that manifold. Necessary…
A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a sum of symmetric outer product of vectors. A rank-1 order-k…
The apparent discrepancy between the bending of light predicted by the equivalence principle and its corresponding value in general relativity is resolved by evaluating the deflection of light with respect to a direction that is parallel…
Uniqueness theorems are considered for various types of almost periodic objects: functions, measures, distributions, multisets, holomorphic and meromorphic functions.
We address the problem of observables in generally invariant spacetime theories such as Einstein's general relativity. Using the refined notion of an event as a ``point-coincidence'' between scalar fields that completely characterise a…
In this paper we introduce an observer design framework for ordinary differential equation (ODE) systems based on various types of existing or even novel one-parameter symmetries (exact, asymptotic and variational) ending up with a certain…
A general principle of non-equivalence for bodies and observers in different G potentials (GP) was derived from correspondence of the Einstein's equivalence principle either with optical physics or with gravitational experiments in which…
It is shown that the most important effects of special and general theory of relativity can be understood in a simple and straightforward way. The system of units in which the speed of light $c$ is the unit of velocity allows to cast all…
In a Lorentzian spacetime there exists a smooth regular line element field $(\bm{X},-\bm{X}) $ and a unit vector $ \bm{u} $ collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric…
In this paper we prove a number of exact relations between optical observables, such as trigonometric parallax, position drift and the proper motion of a luminous source in addition to the variations of redshift and the viewing angle. These…
The spectral theorem says that a real symmetric matrix has an orthogonal basis of eigenvectors and that, for a matrix with distinct eigenvalues, the basis is unique (up to signs). In this paper, we study the symmetric tensors with an…
There have been a number of papers proposing that the light speed of a homogeneous and isotropic universe is variable. This paper outlines a simple way that the vectors and tensors of special relativity can be extended to allow such a…
The objectivity is a basic requirement for the measurements in the classical world, namely, different observers must reach a consensus on their measurement results, so that they believe that the object exists "objectively" since whoever…
To resolve some unphysical interpretations related to velocity measurements by static observers, we discuss the use of generalized observer sets, give a prescription for defining the speed of test particles relative to those observers and…
In the framework of the teleparallel equivalent of general relativity it is possible to establish the energy-momentum tensor of the gravitational field. This tensor has the following essential features: (1) it is identified directly in…
We discuss the issue of defining and measuring conical deficits (conicity) in spacetimes with the torsion singularity such as the Misner string in Taub--NUT spacetime. We propose a geometric definition that generalizes the standard notion…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…
I prove an old unsolved conjecture, the hard part of its obvious sufficiency, namely that all identically conserved symmetric two-tensors are necessarily metric variations of invariant actions, thus sparing the world more alternative…
As a rule in General Relativity the spacetime metric fixes the Einstein tensor and through the Field Equations (FE) the energy-momentum tensor. However one cannot write the FE explicitly until a class of observers has been considered. Every…