Abstract Coordinate Transforms in Kinematic Changeable Sets and their Properties

TL;DR

This paper develops an abstract mathematical theory of coordinate transforms in kinematic changeable sets, exploring conditions under which universal transforms exist or do not, with implications for physical system simulations.

Contribution

It introduces a formal framework for coordinate transforms in kinematic changeable sets and proves the possibility of kinematics without universal transforms.

Findings

Existence of coordinate transforms in kinematic sets is formally established.

Kinematics without universal transforms are possible under certain conditions.

Implications for simulating physical systems with particle-dependent light speed.

Abstract

One of the fundamental postulates of the special relativity theory is existence of a single system of universal coordinate transforms for inertial reference frames, that is coordinate transforms, which are uniquely determined by space-time coordinates of a material point. In this paper the abstract mathematical theory of coordinate transforms in kinematic changeable sets is developed. In particular it is proved the formal possibility of existence of kinematics, which do not allow universal coordinate transforms. Such kinematics may be applied for simulation the evolution of physical systems under the condition of hypothesis on existence of particle-dependent velocity of light.