The Special Theory of Relativity

What is special relativity?

The special theory of relativity is a theory about how space and time relate to one another, based on the following two postulates:

  1. The laws of physics are identical in all inertial frames of reference.
  2. The speed of light in a vacuum is measured to be the same (c = 299,792,458 m/s) for all observers.

What is the Lorentz transformation?

The Lorentz transformation is a linear transformation that relates spacetime (x, y, z, t) for two observers moving relative to one another that is consistent with the special theory of relativity. This interactive site shows a version of the Lorentz transformation for a spacetime with one space dimension (x) and one time dimension (t).

What's wrong with classical relativity?

In classical physics, relativity relates two observers moving relative to one another by simply adding their velocities. This approach, called classical relativity, works well enough for low velocities but encounters issues for velocities approaching the speed of light.

For example, an observer moving at 80% the speed of light with respect to another observer could throw a ball at 70% the speed of light with respect to themself. The stationary observer, according to classical relativity, would see the ball move at 150% the speed of light, which is not possible. Special relativity accounts for this properly, predicting the observer would see the ball moving at 96% the speed of light (try the "Motorcycle" example to see the spacetime diagram).

About this site

This site was created for fun in January 2022 by Christian Bernier. Please feel free to view the source code, or learn more about me.

Spacetime Diagram


Horizonal axis: Displacement

Vertical axis: Time

Gray Grid: your spacetime

Red grid: Red Observer's spacetime

Orange lines: Speed of Light (c)

Δx = 299,792,458 m

Δt = 1 s

What is a spacetime diagram?

A spacetime diagram relates a particle's position versus time. Time is typically represented on the vertical axis, and position is typically represented on the horizontal axis.

By using segments of 1 second on the vertical axis and segments of exactly 299,792,458 meters on the horizontal axis, the speed of light will make a 45 degree angle with the axes.

The different lines you see above are called worldlines, and they each represent a different particle's movement. Straight lines represent particles with constant velocity, with the velocity being proportional to the tangent of the angle the worldline makes with the vertical axis.

Two worldlines on the spacetime diagram, the two orange ones above, never move under special relativity. They represent particles traveling at the speed of light (in accordance with the second postulate of special relativity).


Velocity relative to the Red Observer

0.0000 c ≈ 0 km/s

Type of relativity



Apparent velocity: 0.0000 c