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Hubble's law states that galaxies recede from us at velocities proportional to their distances: v = H₀d, where H₀ is the Hubble constant (~70 km/s/Mpc). Discovered in 1929, this proportionality implies the universe is uniformly expanding — every galaxy moves away from every other, like raisins in rising bread. The spectral shift of galaxies is a cosmological redshift caused by the stretching of space itself, not by galaxies moving through static space. Measuring H₀ precisely requires the cosmic distance ladder: parallax → Cepheid variable stars → Type Ia supernovae; current precision measurements of H₀ reveal a tension that may signal new physics.
Plot recession velocity versus distance for a sample of galaxies and fit a line to recover H₀. Use the inverse of the Hubble constant as a rough estimate of the universe's age and compare to other age estimates.
From your understanding of the Doppler effect, you know that the wavelength of light shifts when the source and observer are in relative motion — blueshift for approach, redshift for recession. In the 1920s, Edwin Hubble combined Vesto Slipher's measurements of galaxy redshifts with his own distance estimates (using Cepheid variable stars in nearby galaxies) and discovered a striking pattern: the farther a galaxy is, the faster it appears to be receding. This proportionality, v = H₀d, is Hubble's law. The constant of proportionality, H₀ (the Hubble constant), has units of km/s per megaparsec and is currently measured at roughly 70 km/s/Mpc — meaning a galaxy 100 Mpc away recedes at about 7,000 km/s.
The profound implication is that the universe is expanding. But the expansion is not galaxies flying apart through static space like shrapnel from an explosion. Instead, the fabric of space itself is stretching, carrying galaxies along with it. The classic analogy is raisins in baking bread: as the dough rises, every raisin moves away from every other raisin, and the farther apart two raisins are, the faster they separate — not because they are moving through the dough, but because more dough is expanding between them. This means there is no center of expansion. Every galaxy sees all others receding, exactly as Hubble's law predicts.
The cosmological redshift of distant galaxies reflects this expansion directly. A photon emitted by a distant galaxy travels through space that is stretching during the journey. The photon's wavelength stretches along with it, arriving redder than when it was emitted. This is subtly different from a classical Doppler shift, which arises from relative motion through space. For nearby galaxies the distinction is negligible, but for distant objects the cosmological interpretation is essential — a galaxy at redshift z = 1 is not "moving" at the speed of light; rather, space has doubled in scale since the photon was emitted.
Measuring H₀ precisely requires the cosmic distance ladder, a chain of calibrated distance indicators that bootstrap from nearby to cosmological scales. Geometric parallax works for stars within a few kiloparsecs. Cepheid variable stars — whose pulsation periods correlate with luminosity — extend the reach to tens of megaparsecs. Type Ia supernovae, which explode with a standardizable peak luminosity, reach billions of light-years. Each rung calibrates the next. Current measurements from the distance ladder (the SH0ES project) give H₀ ≈ 73 km/s/Mpc, while measurements from the cosmic microwave background (Planck satellite) give H₀ ≈ 67 km/s/Mpc. This Hubble tension — a statistically significant disagreement between early-universe and late-universe measurements — is one of the most active problems in modern cosmology and may point to new physics beyond the standard model.