Relativistic relative velocities and relativistic acceleration

TL;DR

This paper identifies a gap in special relativity's four-vector formalism, showing it lacks a proper concept of relative velocity and introduces a relativistic acceleration through velocity subtraction operations.

Contribution

It highlights the absence of relative velocity in the four-vector formalism and proposes a differential approach to define relativistic acceleration.

Findings

Standard SR formalism only describes absolute velocity.

Velocity subtraction operations lead to a definition of relativistic acceleration.

The work clarifies the conceptual gap in relativistic velocity and acceleration.

Abstract

It turns out that the standard application of the four-vector SR formalism does not include the concept of relative velocity. Only the absolute velocity is described by the four-vector, and even the Lorentz transformation parameters is described by the three-dimensional velocity. This gap in the development of the SR formalism reflects the lack of some significant velocity subtraction operations. The differential application of these operations leads to a relativistic acceleration.