Length Contraction (Lorentz)
This interactive simulator explores Length Contraction (Lorentz) in Астрономия и небо. 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. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Для кого: Best once you already know the basic definitions and want to build intuition. Typical context: Астрономия и небо.
Ключевые понятия
- length
- contraction
- lorentz
- length contraction
- astronomy
Как это работает
Compare a ruler in its rest frame S′ with the same ruler measured in the lab S where it moves at v = βc. The lab measurement is shorter by exactly 1/γ: L = L₀√(1 − β²). Animated fly-by, ruler ticks and proper-length reference make the contraction visually unambiguous.
Ещё из «Астрономия и небо»
Другие симуляторы в этой категории — или все 45.
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.
Pair Production Threshold & σ(E_γ)
Pair creation channels γ + nucleus → e⁺e⁻ (Bethe–Heitler, σ ∝ Z²), the higher-threshold triplet γ + e⁻ → e⁻e⁺e⁻, and Breit–Wheeler γγ → e⁺e⁻ that limits TeV photons against the cosmic background. Live threshold marker, log-σ curve, and material presets (H, C, Al, Cu, Pb) make the 1.022 MeV / 4 m_e c² thresholds intuitive.
CMB Power Spectrum (Acoustic Peaks)
Cosmic Microwave Background temperature D_ℓ vs ℓ with Sakharov peaks: tune Ω_b h², Ω_c h², n_s, A_s, τ, h and watch the parity flip between odd / even peaks, the Silk damping tail, and the Sachs–Wolfe plateau move. Pedagogical parametric ΛCDM model.
Big Bang Nucleosynthesis (BBN)
Light-element abundance curves H, ⁴He, D, ³He, ⁷Li vs cosmic time / temperature. Weak freeze-out, neutron decay gap, deuterium bottleneck → Y_p ≈ 0.245. Slide η₁₀ and N_eff over the classic BBN curves; observed values overlaid.