Experiment 1
The κ Dial
The symmetry algebra generates a one-parameter family of universes, labelled by κ. Each choice produces a completely different geometry of spacetime. Select a value and see what kind of universe you get.
Lorentz Factor — γ = 1/√(1 − v²/V²)
Time dilation
0.8660 × normal
Length contraction
0.8660 × rest length
κ > 0 — The Lorentzian Universe (Ours)
When κ is positive, the transformation group is the Lorentz group. A universal speed limit V = 1/√κ emerges from the algebra. Lightcones structure spacetime. Causality is preserved. Moving clocks run slow. Moving rulers shrink. Space and time mix under boosts. This is the universe we actually live in — and the Killing form proves it must be so.
The Killing form B = diag(−4I₃, 4κI₃) with κ > 0 is indefinite — exactly the signature of the Minkowski metric. This is not a coincidence.
Experiment 2
The Lorentz Transformation Explorer
A train moves past a platform. As the velocity increases, time dilates, lengths contract, and the axes of spacetime tilt towards the lightcone. Watch the numbers and the diagram update in real time.
Train velocity (fraction of c)
Lorentz Factor
γ = 1/√(1 − v²)
1.154701
Moving clock rate
Runs at γ⁻¹ × normal speed
0.866025× normal
Length contraction
L = L₀/γ
0.866025 × rest length
Moving Frame (Train)
Train length: 0.8660L₀
Clock speed: 0.8660× normal
Rest Frame (Platform)
Platform length: L₀ (unchanged)
Clock speed: 1× normal
Minkowski spacetime diagram — axis tilting at v = 0.50c