# Relativity for games

## TL;DR

This paper details a method to implement special relativity in computer games, accurately modeling relativistic effects like time dilation, Lorentz contraction, and causality for all entities, including nonplayer characters.

## Contribution

It introduces a comprehensive approach to simulate special relativity in games, including relativistic physics, scene projection, and Doppler effect approximation, ensuring consistency for all objects.

## Key findings

- Relativistic effects are accurately modeled for all game entities.
- Causality is maintained using covariant velocities and light cones.
- A method to approximate rigid bodies and Doppler effects in games is proposed.

## Abstract

We present how to implement special relativity in computer games. The resultant relativistic world shows the time dilation and Lorentz contraction exactly, not only for the player but also for all the nonplayer characters, who obey the correct relativistic equation of motion according to their own accelerations. Causality is explicitly maintained in our formulation by use of the covariant velocities, proper times, worldlines, and light cones. Faraway relativistic scenes can be accurately projected onto the skydome. We show how to approximate a rigid body consisting of polygons, which is ubiquitous in computer games but itself is not a relativistically invariant object. We also give a simple idea to mimic the Doppler effect within the RGB color scheme.