On the Nature of Discrete Space-Time Part 2: Special Relativity in Discrete Space-Time

TL;DR

This paper develops a discrete spacetime model that incorporates special relativity principles, deriving Lorentz transformations and resolving classical paradoxes within a discrete framework.

Contribution

It introduces a new isotropic discrete spacetime model and derives relativistic equations, including Lorentz transformations, within this discrete setting.

Findings

Derived DST versions of Lorentz transformations

Constructed Minkowski spacetime in DST

Resolved Zeno's Stadium Paradox

Abstract

In this paper -- Part 2 of our series on discrete spacetime -- we first provide a review of the previously published Part 1 that included the first important steps in the development of a new model of discrete spacetime (DST): the Isotropic Model of DST. The review starts with a description of the most important and oft-cited problems associated with DST models and how the Isotropic Model of DST solves these problems. We then summarize the derivations of the equations describing time dilation, length contraction and spatial distances in DST that were developed in Part 1. Following the review is the main part of the paper that includes the development of the DST versions of the Lorentz transformation equations and the derivation of the relativistic velocity addition rule, the construction of Minkowski spacetime in DST, and the resolution of Zeno's Stadium Paradox. Important physical phenomena unique to the Isotropic Model are discussed: the fact that light experiences space and time in DST, and the uncertainty in the position of a particle upon the sudden termination of its travel.