Simulation of Kinematics of Special Theory of Relativity

TL;DR

This paper presents a simple, classical physics-based simulation of special relativity effects like time dilation and length contraction, using intuitive examples without dismissing common sense.

Contribution

It introduces elementary methods to simulate relativistic phenomena within classical physics, making the concepts more accessible and reconciling them with everyday intuition.

Findings

Successfully simulated Lorentz contraction and time dilation

Derived Lorentz transformations from simple models

Showed how to simulate four-dimensional spacetime visually

Abstract

The principles of the special theory of relativity are extremely simple. A knowledge of the Pythagorean theorem and an ability to perform the simplest algebraic operations are sufficient to be conversant with the kinematics of the special theory of relativity, as well as the time dilation and contraction of the longitudinal dimensions of moving bodies that are associated with relative motion. However, the simplicity of the fundamentals of the theory of relativity are in surprising contrast with the difficulty of the perception and at times the total nonacceptance of the consequences of the special theory of relativity by skeptics based on ordinary common sense. The authors of certain popular books on the theory of relativity explain the existence of this contrast by way of the fact that the common sense of skeptics cut its teeth on a "stark notion of our everyday life". The special theory of relativity is simulated in this article based on the simplest examples of the movement of barges, shuttles, and boats in an aquatic environment. It has been simulated without rejecting the customary ordinary common sense. In this article, relativistic time and the relativistic effects of Einstein's special theory of relativity - Lorentz contraction, time dilation, relativistic Doppler effects, the Skobeltsyn-Bell effect, and the relativistic addition of velocities - are simulated using elementary methods of classical physics. They have been simulated without rejecting the customary ordinary common sense that was squashed in the past century by the celebration of "mad ideas". Lorentz transformations are obtained. Means for simulating four-dimensional space-time are shown.