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The developments of special relativity and quantum mechanics marked the beginning of the modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity -- the space-time interval --…
We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a…
Special relativity turns out to be more than coordinate transformations in which the constancy of the speed of light plays the central role between two inertial reference frames. Special relativity, in essence, is a theory of…
Based on a recent relational formulation of quantum reference frame transformations, especially with a case of quantum spatial translations in particular, we analyzed how the `value' of an observable for a fixed state change. That is the…
In this paper we introduce a proposal for the kinematics of bodies in uniform circular motion. This model could contribute for the explanation of the two main problems of contemporary cosmology: dark matter and dark energy. We use one of…
A new formulation of special relativity is described. It is based on a postulate that the universe is a vast Cellular Automata (CA). We show that any CA model automatically leads to a maximum speed limit for the transfer of information from…
We give a detailed exposition of the formalism of Kinetic Field Theory (KFT) with emphasis on the perturbative determination of observables. KFT is a statistical non-equilibrium classical field theory based on the path integral formulation…
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…
We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes…
Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
Relations between kinematics, geometry and law of reference frame motion are considered. We show, that kinematical tensors define geometry up to a space functional arbitrariness when integrability condition for spin tensor is satisfied.…
It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of…
Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).
The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…
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…
Treating reference frames fundamentally as quantum systems is inevitable in quantum gravity and also in quantum foundations once considering laboratories as physical systems. Both fields thereby face the question of how to describe physics…