Related papers: Reciprocity Independent Lorentz Transformation
We have defined slowness (or reciprocal velocity) corresponding to v as cc/v, where c is the speed of light and v is the corresponding velocity. Velocity and slowness are images of each other. Reciprocal symmetric law of addition of…
Each of the two moving observers observes the relative velocity of the other. The two velocities should be equal and opposite. We have shown that this relativistic requirement is not fulfilled by Lorentz transformation. We have also shown…
We have shown that Lorentz transformation is not necessary to present relativistic relative velocity. A modified definition of velocity together with Galilean transformation is equivalent to relativistic relative velocity. On the other…
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…
A new relativistic transformation in the velocity space (here named the differential Lorentz transformation) is formulated solely from the principle of relativity and the invariance of the speed of light. The differential Lorentz…
The shortening of bodies in the direction of motion, Lorentz contraction, follows from the solution of Maxwell's equations. Moving light clocks will tick slower than those at rest because the speed of light does not depend on a source of…
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…
The Lorentz Transformation is traditionally derived requiring the Principle of Relativity and light-speed universality. While the latter can be relaxed, the Principle of Relativity is seen as core to the transformation. The present letter…
After a short Historical bibliographical note, in the Starting points attention will be focused on some postulates common to classical mechanics and special relativity. Starting from these premises, in the sections The deduction of the form…
The reciprocal velocity force, $F(v)=\frac{C}{v}$, despite its theoretical and practical importance, is often neglected in mechanics courses. We use graphical methods to explain how such a force naturally arises from a device called a…
The Lorentz Transformations are derived without any linearity assumptions and without assuming that y and z coordinates transform in a Galilean manner. Status of the invariance of the speed of light is reduced from a foundation of the…
We show that starting with the addition law of parallel speeds derived as a consequence of the invariance of the speed of light, the Lorentz transformations for the space-time coordinates can be derived.
We propose definitions for covariance and local Lorentz invariance applicable when the speed of light $c$ is allowed to vary. They have the merit of retaining only those aspects of the usual definitions which are invariant under unit…
In this extended note a critical discussion of an extension of the Lorentz transformations for velocities faster than the speed of light given recently by Hill and Cox is provided. The presented approach reveals the connection between…
This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross…
Lorentz Transformation is reinterpreted. It is shown that by admitting the existence of a frame of reference with synchronized clocks, we conclude that any other frame of reference that moves related to the first has desynchronized clocks.…
We begin by admitting the following: (i) there is a frame of reference where the speed of light is the same in any direction (that speed is c) (ii) the average speed of light on a two-way journey is c in every frame of reference. From this…
Generalized Lorentz transformations with modified velocity parameter are considered. Lorentz transformations depending on the mass of the observer are suggested.The modified formula for the addition of velocities remarkably preserves the…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
We have defined a slowness, s, as the reciprocal conjugate of velocity, v. s = -ih/v. We have shown that Einstein's postulate (v has an upper limit) implies that s is discrete. A velocity operator is defined as the derivative with respect…