Relativistic Doppler Shift

In special relativity, light propagates in vacuum at speed c in every inertial frame without requiring a mechanical medium. For one-dimensional radial motion with signed relative recession parameter β = v/c, combining kinematic wavefront travel time with Lorentz time dilation γ = 1/√(1 − β²) yields the observed wavelength λ_obs = λ_rest√((1 + β)/(1 − β)) and reciprocal frequency ratio f_obs/f_rest = √((1 − β)/(1 + β)).

Experiment

Explore the relativistic Doppler shift by comparing light frequency and wavelength ratios for approaching and receding sources in the Relativistic Doppler Shift module:

1. Set Recession beta to 3/5 and Rest wavelength nm to 500 to observe a receding redshift where observed wavelength doubles to 1000 nm.
2. Change Recession beta to −3/5 with Rest wavelength nm set to 400 to observe an approaching blueshift where the wavelength ratio drops to 0.5 (200 nm).
3. Compare 4/5 and −4/5 at 600 nm to verify reciprocal wavelength ratios (3 vs 1/3) while the Lorentz factor remains γ = 5/3 ≈ 1.66666666667.