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Звёздный параллакс
Угол орбиты Земли против кажущегося смещения ближней звезды на фоне далёких звёзд; π = 1/d(пк) угл. сек., показано с преувеличением.
Light Clock & Time Dilation
Two side-by-side light clocks — one at rest, one moving at v = βc — show why a moving clock ticks slower. The photon zig-zag traces a longer Pythagorean hypotenuse cT/2 vs the rest hypotenuse cT₀/2, giving T = γT₀ with γ = 1/√(1 − β²) live. The Pythagorean diagram and the running tick ratio make the special-relativistic time-dilation derivation visual rather than algebraic.
Length Contraction (Lorentz)
A ruler of proper length L₀ in S′ flies past the lab S at v = βc and is measured to be L = L₀/γ — only in the direction of motion. Animated fly-by with on-board ruler ticks and a dotted L₀ baseline makes the contraction L = L₀ √(1 − β²) immediately readable; same factor explains why GeV cosmic-ray muons reach the ground despite their ≈ 2 μs lifetime.
Minkowski Spacetime Diagram (Lorentz Boost)
Interactive (x, ct) spacetime diagram: a Lorentz boost at v = βc rotates the (x′, ct′) axes inward by atan(β) toward the 45° light cone — relativity of simultaneity, time dilation and length contraction become pure geometry. Click events with Shift / Alt to read the invariant interval Δs² = (cΔt)² − (Δx)² and its time-/light-/space-like classification.
Relativistic Doppler Effect
Source emits at rest frequency f₀ and moves at v = βc; observer at angle θ measures f_obs = f₀ √(1 − β²) / (1 − β cos θ). Animated lab-frame wavefronts, observer at any angle, and a 380–700 nm spectrum strip showing the apparent colour shift of a 555 nm reference line — including the purely relativistic transverse Doppler (θ = 90°) red-shift f₀/γ.
Relativistic Energy–Momentum Hyperbola
Energy–momentum relation E² = (pc)² + (mc²)². The green hyperbola E = √(p² + 1) is bracketed by the Newtonian parabola E ≈ 1 + p²/2 (low-momentum limit) and the photon-like asymptote E = pc (ultra-relativistic). Pick β, p or T as the independent slider and watch all four quantities (β, γ, p, T) lock together — the operational core of accelerator and cosmic-ray physics.