Related papers: Abstract Coordinate Transforms in Kinematic Change…
We discuss implications of the cosmological frame principle which states that cosmological effects of modified gravity must be stable as solutions of each of the corresponding sets of dynamical equations holding in the two…
A transition of focus from state space to frames of reference and their transformations is argued as being the appropriate setup for ensuring the covariance of physical laws. Such an approach can not only simplify and clarify aspects of…
It is shown that physical mechanics for pointlike bodies can be effectively modeled in terms of the action of transformation groups that act as symmetries of the solutions of systems of differential equations that describe the integrability…
We show that starting with the fact that special relativity theory is concerned with a distortion of the observed length of a moving rod, without mentioning if it is a "contraction" or "dilation", we can derive the Lorentz transformations…
It is proved that local Lorentz transformations for different systems cannot derive varying speed of light. Based on the special relativity principle, an invariant speed is necessarily obtained. Therefore, the exact basic principles of the…
It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…
In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized…
The term integrable asymptotically conformal at a point for a quasiconformal map defined on a domain is defined. Furthermore, we prove that there is a normal form for this kind attracting or repelling or super-attracting fixed point with…
This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…
Special relativity is reformulated as a symmetry property of space-time: Space-Time Exchange Invariance. The additional hypothesis of spatial homogeneity is then sufficient to derive the Lorentz transformation without reference to the…
A free system, considered to be a comparison system, allows for the notion of objective existence and inertial frame. Transformations connecting inertial frames are shown to be either Lorentz or generalized Galilei.
This is a short note to announce the availability of some movies that may be useful in classroom discussions on the photographic appearance of objects moving at relativistic speeds. The images are based on special relativity with no account…
In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M, we derive the constraints that the relativity principle imposes between coefficients of a deformed…
We determine the nonlinear transformations between coordinate systems which are mutually in a constant symmetrical accelerated motion. The maximal acceleration limit follows from the kinematical origin and it is an analogue of the maximal…
We encode dynamical symmetries of Born-Infeld theory in a geometry on the tangent bundle of generally curved spacetime manifolds. The resulting covariant formulation of a maximal acceleration extension of special and general relativity is…
In the article, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory were re-stated. And, the addition of velocity laws were derived and used…
The FRT quantum group and space theory is reformulated from the standard mathematical basis to an arbitrary one. The $N$-dimensional quantum vector Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of…
We present a covariant framework of kinematics in the dS spacetime, which is a natural postulate of recent astronomical observations ($\Lambda>0)$. One-particle states are presented explicitly. It is noticed that the dispersion relation of…
This article explores the differences between frame and coordinate transformations in relativistic theories. We highlight the key role of tetrad fields in connecting spacetime and frame indices. Using Maxwell's electrodynamics as an…
The locality hypothesis is generally considered necessary for the study of the kinematics of non-inertial systems in special relativity. In this paper we discuss this hypothesis, showing the necessity of an improvement, in order to get a…