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A logic of reciprocity between inertial frames in relative uniform motion is investigated. Relativity allows any reference frame to apply Lorentz Transformation while reciprocity would require the relative frame to use Inverse…

We are proving that the Lorentz boost entails the relative velocity to be ternary: ternary relative velocity is a velocity of a body with respect to an interior observer as seen by a preferred exterior-observer. The Lorentz boosts imply…

Time-like and space-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances defined by two spatially-separated clocks. The time dilatation effect is confirmed, but not `relativity of…

Given two observers, we define the "relative velocity" of one observer with respect to the other in four different ways. All four definitions are given intrinsically, i.e. independently of any coordinate system. Two of them are given in the…

In this work, we introduce the Law of Closest Approach which is derived from the properties of conic orbits and can be considered an addendum to the laws of Kepler. It states that on the closest approach, the distance between the objects is…

We propose a generalisation of the local causality principle of space-time, asserting that it holds for all regimes of motion, including superluminal motions. It assumes the existence of a countably infinite set of metrical null cone…

We consider three possible approaches to formulating coordinate transformations on position space associated with non-linear Lorentz transformations on momentum space. The first approach uses the definition of velocity and gives the…

A modification of the accepted relativistic energy momentum relation is suggested. The new relation allows massive particles to have a maximum velocity c(m) greater than the velocity of light c. The effect of the modification suggested here…

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory…

The law of balance of angular momentum is shown to imply the existence of absolute time, a fundamental physical quantity that is independent of the motion or position of the observer. Absolute time implies the notion of absolute…

A phenomenological explanation is presented for the physics of aberration, which is in contrast with special relativity physics. The effect of relativity is identified with an effect due to the velocity of observation being affected by the…

In \cite{2} it was shown that Einstein's special theory of relativity and Maxwell's field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact…

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…

The purpose of this paper is to explain clearly why nonlocality must be an essential part of the theory of relativity. In the standard local version of this theory, Lorentz invariance is extended to accelerated observers by assuming that…

It is shown that a generalized special theory of relativity (GSTR) with an arbitrary limiting velocity of a particle different or equal to the speed of light in vacuum can be constructed from the canonical equation of the 4-dimensional…

According to the postulates of the special theory of relativity (STR), physical quantities such as proper times and Doppler shifts can be obtained from any inertial frame by regarding it as isotropic. Nonetheless many inconsistencies arise…

The principles of the special theory of relativity are extremely simple. A knowledge of the Pythagorean theorem and an ability to perform the simplest algebraic operations are sufficient to be conversant with the kinematics of the special…

The algebra of the relativistic composition of velocities is shown to be isomorphic to an algebraic loop defined on division algebras. This makes calculations in special relativity effortless and straightforward, unlike the standard…

It is shown how a Doubly-Special Relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a one-dimensional automaton that spawns the Dirac…

The central concept of the theory of relativity is the relativity of velocity. The velocity of a material body is not an intrinsic property of the body; it depends on a free choice of reference system. Relative velocity is thus…