Universal Relativity and Its Mathematical Requirements

In this presentation, I review physical principles behind a recently proposed \cite{smw-utr} Universal Theory of Relativity and speculate on the mathematical requirements implied by these physical principles. Some unresolved issues will also be discussed.Comment: 8 pages, Talk presented at the South African Mathematical Society's 48th Meeting, October 31 - November 2, 2005, Rhodes University, Grahamstown, South Afric

Mach's Principle and Spatial Scale-Invariance of Gravity

Gravity does not provide any scale for matter properties. We argue that this is also the implication of Mach's hypothesis of the relativity of inertia. The most general spacetime compatible with this property of gravity is that admitting three, independent spatial homothetic Killing vectors generating an arbitrary function of each one of the three spatial coordinates. The matter properties for such a spacetime are (spatially) arbitrary and the matter generating the spacetime admits {\it any} equation of state. This is also the most general spacetime containing the weak gravity physics in its entirety. This spacetime is machian in that it is {\em globally} degenerate for anti-machian situations such as vacuum, a single matter particle etc. and, hence, has no meaning in the absence of matter.Comment: Revtex4, No figure

Some fundamental issues in General Relativity and their resolution

The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution of Einstein's field equations to be of relevance to some, hypothetical or not, physical situation. Hence, to resolve the considered problems of the standard approach to general relativity, one must go beyond it. A possible approach, a theory of everything, is outlined in the present article and will be developed in details subsequently.Comment: 30 pages, double colum

Einsteinian Field Theory as a Program in Fundamental Physics

I summarize here the logic that leads us to a program for the Theory of the Total Field in Einstein's sense. The purpose is to show that this theory is a logical culmination of the developments of (fundamental) physical concepts and, hence, to initiate a discussion of these issues.Comment: 28 pages, double spaced, comments and criticisms most welcom

Towards a Universal Theory of Relativity

We discuss here the significance of the generalization of the newtonian concept of force by that of a transformation of a certain Standard Borel Space of cardinality $\mathbf{c}$ of the continuum as the ``cause'' behind motions of material bodies that are representable as Borel measurable subsets of this space. This generalization forms the basis for a Universal Theory of Relativity in which, importantly, the fundamental physical constants can only arise from mutual relationships of the so-defined physical bodies. This Universal Relativity also has the potential to explain the quantum nature of the physical world.Comment: Essay for Gravity Research Foundation competition - 200

On the continuum origin of Heisenberg's indeterminacy relations

If space is indistinguishable from the extension of a physical body, as is Descartes's conception, then transformations of space become transformations of physical bodies. Every point of space then has properties of physical bodies in some suitable non-singular sense of average over the space. Every point of space is then thinkable as a non-singular point particle possessing such (averaged) physical properties. Then, the location of such a point particle is, relative to another (similar) point particle, {\em indeterminate} over the extension of the physical body. Further, transformations of the space may ``move'' such a point particle in relation to another such point particle. These notions then provide a non-probabilistic explanation of Heisenberg's indeterminacy relations.Comment: 5 pages, double spaced. to be submitted to General Relativity & Gravitation, Comments and Criticisms would be most welcom

On the significance of the Braxmaier et al. Laser Interferometry Experiment of 2002 for a Theory of Relativity

A recent laser interferometry experiment [Phys. Rev. Lett., Vol. 88, 10401 (2002)] registered a non-detection of a frequency shift that amounts to a fractional change in the speed of light $\delta c/c \approx (4.8\pm5.3)\times10^{-12}$. We comment here on the theoretical significance of this experimental result.Comment: 4 pages, submitted for publicatio

Explaining Michelson-Morley without Special Relativity

In this paper, we first discuss the concept of an emission wave. In the history of science, this is the first time we have discovered a new way in which (transverse) waves are realized in nature. It can therefore be expected to lead to important changes in the perspective about the nature of light or radiation. Then, we point out that the null result of the Michelson-Morley experiment is a natural and straightforward consequence of light being an emission wave. Concepts of special relativity, of length contraction and of time dilation, are not required for this explanation, however.Comment: 3 pages, no figures, comments would be most welcom

The Significance of the General Principle of Relativity

In this note, we discuss the significance of the general principle of relativity for a physical theory that abandons the newtonian concept of force and, hence, uses an entirely different conception for the ``cause'' behind motions of material bodies.Comment: Presented as a Poster during the IAGRG Conference held at Jaipur, India during December 200

Inhomogeneous Big Bang Cosmology

In this letter, we outline an inhomogeneous model of the Big Bang cosmology. For the inhomogeneous spacetime used here, the universe originates in the infinite past as the one dominated by vacuum energy and ends in the infinite future as the one consisting of "hot and relativistic" matter. The spatial distribution of matter in the considered inhomogeneous spacetime is {\em arbitrary}. Hence, observed structures can arise in this cosmology from suitable "initial" density contrast. Different problems of the standard model of Big Bang cosmology are also resolved in the present inhomogeneous model. This inhomogeneous model of the Big Bang Cosmology predicts "hot death" for the universe.Comment: Revtex4, No figure