We first show that Doppler’s effect implies that the time runs identically in the frames of reference of the source of light and the observer. Furthermore, we then show that the frequency shift due to the (assumed) expansion of space, if any, is “indistinguishable” from that due to the motion of the source with respect to the observer; and that the shift does not depend on the distance to the source. Observed frequency shifts of cosmological sources then need to be interpreted as being only due to their motions with respect to us. This has important implications for our ideas in cosmology.

Abstract:
General Principle of Relativity unequivocally supports the notion of momentum-less energy for bodies (energy-quanta) moving at the {\em same} or {\em constant} speed relative to all the reference systems. In this communication, we point out that whether energy-quantum is a momentum-less body or not is verifiable using ultra-cold atoms trapped in an optical lattice, perhaps with some minor modifications to the existing such experimental setups.

Abstract:
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.

Abstract:
The equality of the inertia and the gravitational mass of a body is explained in a very general manner. We also motivate this explanation by providing analogous examples

Abstract:
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.

Abstract:
A modest aim of this pedagogical presentation is to analyze, critically, certain fundamental physical concepts to illustrate the physical principles behind the special theory of relativity and, hence, to also illustrate the limitations of its applicability.

Abstract:
Spacetimes admitting appropriate spatial homothetic Killing vectors are called spatially homothetic spacetimes. Such spacetimes conform to the fact that gravity has no length-scale for matter inhomogeneities. The matter density for such spacetimes is (spatially) arbitrary and the matter generating the spacetime admits {\it any} equation of state. Spatially homothetic spacetimes necessarily possess energy-momentum fluxes. We first discuss spherically symmetric and axially symmetric examples of such spacetimes that do not form naked singularities for regular initial data. We then show that the Cosmic Censorship Hypothesis is {\em equivalent} to the statement that gravity has no length-scale for matter properties.

Abstract:
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.

Abstract:
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.

Abstract:
The ``unification'' of fundamental physical forces (interactions) imagines a ``single'' conceptual entity using which {\em all} the observable or physical phenomena, {\em ie}, changes to physical bodies, would be suitably describable. The physical, conceptual and mathematical, framework which achieves this is that of the recently proposed Universal Theory of Relativity \cite{smw-utr}. Here, we argue that the mathematical framework required to achieve the ``unification'' should be that of the general Category Theory. There are certain unanswered mathematical questions arising out of this context. In the sequel, we also point out these issues for the wider attention.