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We describe the space-time model of a uniformly rotating frame of reference satisfying the Helmholtz free mobility postulate, as we implemented it in a preceding article \cite{Bel1}, and we discuss the implications of this model as it…
Newton seems to have stated a quantitative relationship between the position of a body in relative space and the position of the body in absolute space in the first scholium of his Principia. We show that if this suspected relationship is…
We discuss some fundamental issues underlying gravitational physics and point out some of the main shortcomings of Einstein's General Relativity. In particular, after taking into account the role of the two main objects of relativistic…
There exists some confusion, as evidenced in the literature, regarding the nature of the gravitational field in Einstein's General Theory of Relativity. It is argued here the this confusion is a result of a change in interpretation of the…
There is ongoing interest in adopting various tools and ideas from general relativity for optical applications and the study of light propagation through natural or engineered media. Here, the covariant kinematics of light propagating…
We explain in a very concise way the basic principles that lead from Galilean to General Relativity to make them understandable to students or general audience, even with little knowledge in physics and mathematics.
This article investigates an extension of General Relativity based upon a class of lifted metrics on the cotangent bundle of space-time. The dynamics of the theory is determined by a fixed section of the cotangent bundle, representing the…
We introduce the theory of thermodynamic relativity, a unified framework for describing both entropies and velocities, and their respective disciplines of thermodynamics and kinematics, which share a surprisingly identical description with…
The most general form of transformations of spacetime coordinates in Special Theory of Relativity based solely on physical assumptions are described. Only the linearity of spacetime transformations and the constancy of the speed of light…
The deflection of light rays near gravitating objects can be influenced not only by gravity itself but also by the surrounding medium. Analytical studies of such effects are possible within the geometrical optics approximation, where the…
We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.
I show the decisive difference between genuine transverse Fresnel drag of light in a moving medium and the "spatial shift" measured with a time dependent interference pattern of light traversing a homogeneous finite medium (J. Leach et al.,…
The Equivalence Principle (EP) is at the heart of General Relativity (GR), tested in many aspects. It is often used to discuss qualitatively the influence of gravity on physical phenomena. But can this be made more precise? We compare clock…
First, we extend the special relativity into the superluminal case and put forward a superluminal theory of kinematics, in which we show that the temporal coordinate need exchanging with one of the spatial coordinates in a superluminal…
We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the…
A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along…
We examine two far-reaching and somewhat heretic consequences of General Relativity. (i) It requires a cosmology which includes a preferred rest frame, absolute space and time. (ii) A rotating universe and time travel are strict solutions…
We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…
Relativistic rotation is considered in the limit of angular velocity approaching zero and radial distance approaching infinity, such that centrifugal acceleration is immeasurably small while tangent velocity remains close to the speed of…
General relativity differs from other forces in nature in that it can be made to disappear locally. This is the essence of the equivalence principle. In general relativity the equivalence principle is implemented using differential…