Relativity · undergrad

Complete Special Relativity

A structured path through Lorentz symmetry, intervals, and proper time.

Published Apr 26, 2026 · 1 min

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Postulates

The laws of physics are the same in inertial frames, and the speed of light is invariant.

For motion along $x$ ,

t'=\gamma\left(t-\frac{vx}{c^2}\right), \qquad x'=\gamma(x-vt).

The invariant interval is

ds^2=-c^2dt^2+dx^2+dy^2+dz^2.

The symmetry of spacetime itself, derived from the constancy of the speed of light.

The invariant spacetime distance preserved by Lorentz transformations.

The time measured by a clock moving along a worldline.