Redshift and Blueshift Simulator: Doppler, Gravitational and Cosmological
Free redshift and blueshift simulator: watch light shift near and far from a heavy mass (gravitational redshift, clocks and refractive-index view), moving sources with relativistic Doppler wavefronts, a spectrum shifter that combines motion, gravity and cosmic expansion, and an expanding-universe calculator with lookback time and distance.
Light that falls toward a heavy mass arrives blueshifted; light that climbs away from it arrives redshifted. In the picture below the mass is on the left: clocks run slower there, so a wave of fixed frequency has a shorter wavelength, as if the space were a medium with a higher refractive index n = 1 / (clock rate). Press Emit pulse.
Check it against real experiments
A moving source emits waves that bunch up ahead of it (blueshift) and spread out behind it (redshift). Each ring below is a light wavefront, coloured by the shift an observer in that direction would see. At high speed time dilation matters too: a source slows its own emission by γ, so even sideways light is redshifted.
Shift a real set of spectral lines by any mix of causes. The three sources of redshift multiply: (1+z) = (1+zmotion) × (1+zgravity) × (1+zexpansion). Lines that leave the coloured band turn into ultraviolet, infrared or radio waves.
Work out z from one line
Cosmological redshift is not a Doppler shift through space: the space light travels through stretches, so every wavelength is stretched by the same factor as the universe grows, 1 + z = anow / athen. Distances here use a flat ΛCDM universe (radiation neglected).
Redshift and blueshift explained
A redshift lengthens the wavelength of light, a blueshift shortens it. Astronomers measure it as z = (λobserved − λemitted) / λemitted; a positive z is red, a negative z is blue. There are three physical causes, and this page simulates all of them:
- Motion (Doppler shift). A source moving away is redshifted, one moving toward you is blueshifted: 1 + z = √((1 + β) / (1 − β)) along the line of sight, and the general formula fobs = fsrc / (γ(1 − β cos θ)). Even sideways motion gives a redshift 1 / γ because the moving source's clock runs slow.
- Gravity. Near a mass clocks run slow, by √(1 − rs/r) with rs = 2GM/c². Light climbing out of a gravity well is redshifted, light falling in is blueshifted: fobs/fsrc = √((1 − rs/rsrc) / (1 − rs/robs)). The 1959 Pound-Rebka experiment measured it across 22.5 metres; GPS satellites must correct for it every day.
- Expansion of space. Light from distant galaxies is stretched as the universe grows: 1 + z = anow/athen. At z = 1089 the light is the cosmic microwave background.
The refractive-index picture
Because clocks tick slower near a mass, a wave whose frequency is fixed in far-away time has a shorter wavelength nearby, just as light entering glass keeps its frequency and shortens its wavelength. Treating gravity as a medium with index n = 1 / (clock rate) reproduces the redshift, the slowing of light near a mass (the Shapiro delay) and light bending. It is an analogy for the Schwarzschild geometry, not a separate theory, and the animation exaggerates the tiny real numbers so you can see them (switch to True scale for the real picture).
Questions
- Is a cosmological redshift a Doppler shift?
- Not exactly. Galaxies are nearly at rest in their own patch of space; the space between them grows. For small z the two agree (z ≈ v/c); for large z they differ, and the recession speed in the table can even pass the speed of light, which is allowed because nothing moves through space that fast.
- Why does gravitational redshift matter for GPS?
- Satellite clocks run about 45.7 µs a day fast from gravity and 7.2 µs slow from their speed, a net 38.5 µs a day. Uncorrected, positions would drift by about 10 km a day.
- Why can nothing be seen leaving a black hole?
- As the emitter approaches the horizon (r = rs) the redshift grows without limit, so the light is stretched to nothing and arrives later and later.
Limits: static emitters and receivers in the Schwarzschild geometry (no spin, no orbital Doppler mixed in), a flat ΛCDM universe without radiation (the age at very high z is approximate), the spectral lines are laboratory values to 0.1 nm. For research use real ephemerides and models.