The Gravity and The Quantum: A Bohr-inspired Synthesis

An effective angular momentum quantization condition of the form $mvr=n\hbar(m/m_F)$ is used to obtain a Bohr-like model of Hydrogen-type atoms and a modified Schr\"{o}dinger equation. Newton's constant, $G$, of Gravitation gets explicitly involved through the fundamental mass $m_F$ as defined in the sequel. This non-relativistic formalism may be looked upon as a ``testing ground'' for the more general synthesis of the gravity and the quantum.Comment: 4 pages, RevTex. Rejected: Reviewer's comments: ``This paper does not reach the standards needed for publication on an international journal. It contains some naive and poorly motivated speculations, and shows no awarness of the vast literature on the problem. The Authors should get a more comprehensive knowledge of the literature, before trying to work with simple ideas as in this paper.'' We would be grateful if anyone can point out whether equations (6) and (7) appear in the literature and are well know

Maass space for lifting to GL(2) over a division quaternion algebra

Muto, Narita and Pitale construct counterexamples to the Generalized Ramanujan Conjecture for GL(2,B) over the division quaternion algebra B with discriminant two via a lift from SL(2). In this paper, we try to exactly characterize the image of this lift. The previous methods of Maass, Kohnen or Kojima do not apply here, hence we approach this problem via a combination of classical and representation theory techniques to identify the image. Crucially, we use the Jacquet Langlands correspondence described by Badulescu and Renard to characterize the representations

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

Progress with a Universal Theory of Relativity

In this presentation, I will summarize the present status of the developments with a Universal Theory of Relativity \cite{smw-utr}. Some general challenges to be overcome will also be discussed.Comment: 5 pages, 4 figures, Talk Presented at the South African Relativity Society's Einstein Centennial Meeting, September 25 - 26, 2005, Durban, South Afric

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

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

Emission Origin for the Wave of Quanta

We argue that certain assumptions about the process of the emission of the quanta by their (oscillating) emitter provide for their changing (oscillatory) flux at any location. This mechanism underlying (such) wave phenomena is not based, both, on the newtonian notion of force and the field concept (of Faraday, Maxwell, Lorentz and Einstein). When applied to the case of thermal radiation, this emission origin for the wave of quanta is shown here to be consistent with the laws of the black body radiation. We conclude therefore also that a conceptual framework, which is not rooted in the notion of force and in the field concept, may provide a deterministic basis underlying the probabilistic methods of the quantum theory.Comment: 13 page

Categorical Foundations for Physics - I: Program at a Glance

Measures in the context of Category Theory lead to various relations, even differential relations, of categories that are independent of the mathematical structure forming objects of a category. Such relations, which are independent of mathematical structure that we may represent a physical body or a system of reference with, are, precisely, demanded to be the Laws of Physics by the General Principle of Relativity. This framework leads to a theory for the physical entirety.Comment: title changed, substantial changes to include mathematical detail