Special Relativity Spacetime Lab

Special relativity made physical. A rod-train moves at speed $\beta = v/c$ and is Lorentz-contracted to $L_0/\gamma$ against its dashed rest length, while two twin clocks tick: on a round trip the travelling twin returns having aged only $2L/(\gamma\beta)$ against the stay-home $2L/\beta$. The side panel is the Minkowski diagram with the 45-degree light cone, the boosted lines of simultaneity, and the bent twin worldline.

Figure 1. Lorentz contraction, the desynchronising twin clocks, the contraction ratio, the Minkowski worldlines, and a textual reading.

WHAT TO TRY

Push beta = v/c toward 1: the moving rod contracts to L0/gamma, the travelling clock visibly falls behind the home clock, and the worldline on the Minkowski diagram tilts toward the light cone. All three effects share the one gamma factor.
Read the twin clocks side by side: the traveller ages less, the elapsed-time gap widening as you approach c. This is time dilation, not an illusion of signalling delay.
Watch the Minkowski diagram: the home twin runs straight up the ct axis while the traveller leans over, and the 45-degree light cone is the speed limit neither can cross.