# Dynamics of a Relativistic Particle in Discrete Mechanics

## TL;DR

This paper compares relativistic and discrete mechanics approaches for a particle's dynamics, showing that discrete mechanics conserves energy and aligns with Newtonian behavior at low velocities, unlike traditional relativistic theory.

## Contribution

It introduces a discrete mechanics framework that accurately models relativistic particle dynamics, conserving energy and matching Newtonian limits at low velocities.

## Key findings

- Discrete mechanics conserves energy at theoretical values.
- Velocity tends towards light speed with increasing time.
- Behavior aligns with Newtonian mechanics at low velocities.

## Abstract

The study of the evolution of the dynamics of a massive or massless particle shows that in special relativity theory, the energy is not conserved. From the law of evolution of the velocity over time of a particle subjected to a constant acceleration, it is possible to calculate the total energy acquired by this particle during its movement when its velocity tends towards the celerity of light. The energy transferred to the particle in relativistic mechanics overestimates the theoretical value. Discrete mechanics applied to this same problem makes it possible to show that the movement reflects that of Newtonian mechanics at low velocity, to obtain a velocity which tends well towards the celerity of the medium when the time increases, but also to conserve the energy at its theoretical value. This consistent behavior is due to the proposed physical analysis based on the compressible nature of light propagation.