On a New Alternative Mathematical Model for Special Relativity

TL;DR

This paper introduces a new generalized transformation for coordinate systems in special relativity, addressing inconsistencies in Lorentz Transformation and maintaining key relativistic effects like time dilation and length contraction.

Contribution

It proposes a novel mathematical model that generalizes Lorentz Transformation, resolving its limitations and aligning with established relativistic phenomena.

Findings

Resolves mathematical inconsistencies of Lorentz Transformation.

Maintains the same predictions for time dilation and length contraction.

Yields the same velocity addition law as Lorentz Transformation.

Abstract

In this paper, it is shown why Lorentz Transformation implies the general case where observed events are not necessarily in the inertia frame of any observer but assumes a special scenario when determining the length contraction and time dilation factors. It is shown that this limitation has led to mathematical and physical inconsistencies. The paper explains the conditions for a successful theory of time dilation and length contraction, and provides a simple proof to a new generalized transformation of coordinate systems as the only possible solution that meets those conditions. It discusses inconsistencies of Lorentz Transformation, and shows how the new generalized transformation resolves those apparent inconsistencies. The new transformation agrees with Special Relativity on its conclusions of time dilation and space contraction, and yields the same law of addition of velocities as proposed in Lorentz Transformation.