The Doppler Effect, Hubble’s Law and the Big Bang

The Doppler effect — the change in observed wavelength when a source moves relative to an observer. For speeds well below c:

Δλ / λ = v / c

Redshift — a source moving away stretches the observed wavelength, shifting lines towards the red end. Blueshift is the reverse, for approaching sources.

Measuring it — the shift is found by comparing the observed wavelengths of known absorption lines with their laboratory values. Because the line pattern is a fingerprint, the whole set can be matched and the shift measured precisely even when the shift is large.

Hubble's discovery — almost all galaxies are redshifted, and the further away they are, the greater the redshift.

v = H₀ d

where H₀ is the Hubble constant, currently estimated at around 70 km s⁻¹ Mpc⁻¹, though measurements by different methods disagree by more than their stated uncertainties.

What the expansion actually is — not galaxies flying apart through space, but space itself expanding, carrying galaxies with it. There is no centre and no edge: from every galaxy, all the others appear to be receding. A common analogy is dots on an inflating balloon, where every dot sees every other moving away and none is at the centre.

Estimating the age of the universe — if the expansion rate had been constant, the time since everything was together is

t ≈ 1 / H₀

Example: with H₀ ≈ 2.2 × 10⁻¹⁸ s⁻¹, t ≈ 4.5 × 10¹⁷ s, about 14 billion years. That the figure agrees with the ages of the oldest stars, found by completely independent means, is a strong check on the whole picture.

Evidence for the Big Bang

Redshift of galaxies — consistent with expansion from a hot dense origin.

Cosmic microwave background — radiation at about 2.7 K from every direction, the highly redshifted remnant of radiation released when the universe first became transparent. It is remarkably uniform, and its spectrum is an almost perfect black body.

Abundance of light elements — the observed ratio of roughly 75% hydrogen to 25% helium matches what a hot early universe predicts.

Dark energy and acceleration — observations of distant supernovae in the late 1990s showed the expansion is accelerating, not slowing as gravity alone would require. The cause is termed dark energy. Its nature is unknown, which is worth stating plainly: it is a name for an observation, not an explanation of it.