iris
Experiment

Special Relativity

A Minkowski spacetime diagram where the vertical axis is time and the horizontal axis is space. Drag the velocity slider to apply a Lorentz boost and watch worldlines, simultaneity, and light cones transform. The twin paradox emerges naturally from the geometry.

Light cones (45°) Stationary observer Moving observer / twin Simultaneity lines
Velocity (v/c)0.00c

Relativistic Effects

Lorentz factor γ 1.000
Time dilation factor 1.000
Length contraction 1.000
Twin stay-home age 10.0 yr
Twin traveler age 10.0 yr

Minkowski spacetime

In special relativity, space and time are unified into spacetime. The Minkowski diagram plots ct (time times the speed of light) on the vertical axis and x (space) on the horizontal axis. Light always travels at 45° — these form the light cones.

The Lorentz boost is a rotation-like transformation that mixes space and time. When you boost to a moving frame, the time axis tilts toward the light cone, and the space axis tilts symmetrically. This geometric tilt is time dilation and length contraction, visible.

The twin paradox: One twin stays home (vertical worldline). The other travels away at velocity v, turns around, and returns. The traveler’s worldline has a kink — acceleration breaks the symmetry. The proper time along the kinked path is shorter: the traveler ages less. This is not a paradox but a consequence of spacetime geometry.