Relativity

Build special relativity from reference frames and Einstein's postulates, then apply Lorentz transformations, time dilation, length contraction, velocity addition, and spacetime diagrams to interpret real measurements.

Physics HL, chapter 6. 1 simulations.

Simulation: Relativity Clock Lab

Vary beta = v/c and compare proper-time and coordinate-time intervals through the gamma factor.

In the textbook: 6.2 Time Dilation and Length Contraction, 6.3 Velocity Addition and Simultaneity, 6.4 Spacetime Diagrams and Causality

Relativity Clock + Spacetime Lab

γ

1.4003

v

0.700 c

v (m/s)

2.099e+8

t from τ

14.00 s

If the ship measures τ = 10.0 s, the lab measures t = γτ = 14.00 s. If the lab measures t = 10.0 s, ship proper time is τ = t/γ = 7.14 s.

Minkowski diagram (x, ct)

light conect′ axis (ship worldline)x′ axissimultaneous in Ssimultaneous in S′A (origin event)B (transformed event)xct

This diagram is coordinate-based: the same event pair gets different simultaneity slices in S and S′, while light-cone boundaries preserve causal structure.