Related papers: A logic road from special relativity to general re…
We show the first simple, systematic and direct approach to decoupling gravitational sources in general relativity. As a direct application, a robust and simple way to generate anisotropic solutions for self-gravitating systems from perfect…
The conceptual evolution of principle of relativity in the theory of special relativity is discussed in detail. It is intimately related to a series of difficulties in quantum mechanics,relativistic quantum mechanics and quantum field…
In the gauge natural bundle framework a new space is introduced and a first-order purely frame-formulation of General Relativity is obtained.
In this paper we present some of our school's results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain first-order logic (FOL) as in the foundation of mathematics (FOM) and we…
For the special theory of relativity, the normalization problem is formulated as the question how observers in constant relative motion may reach an agreement on space and time scales. As the normalization problem does not receive a…
The special theory of relativity is constructed demanding the retention of the rectilinear form of a trajectory and invariance of the wave equation under linear transformations of space and time coordinates. The usual approach to relativity…
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…
First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility".…
We discuss how the finiteness and universality of the speed of light arise in the theoretical framework introduced in [1], and derive generalized coordinate transformations, that allow to investigate physical systems in a non-classical…
We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein…
Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…
Under the assumption of closed-path velocity of light invariant, we show both the general expression of velocity of light in an ordinary inertial reference frame and the generalized Lorentz transformation between the ordinary inertial…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
We describe the non-minimal Standard Model, consisting of minimalistic extensions of the Standard Model, which for all we know is the theory of the universe, able to describe all of the universe from the beginning of time. Extensions…
This paper has pedagogical motivation. It is not uncommon that students have great difficulty in accepting the new concepts of standard special relativity, since these seem contrary to common sense. Experience shows that geometrical or…
We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin. We call such systems projective systems of rational difference equations and we…
An approach to special relativity is outlined which emphasizes the wave and field mechanisms which physically produce the relativistic effects, with the goal of making them seem more natural to students by connecting more explicitly with…
A new method of derivation of Lorentz Transformation (LT) is given based on both axioms of special relativity (SR) and physical intuitions. The essence of the transformation is established and the crucial role played by the presumptions is…
We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This…
By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear…