How Does the Doppler Effect Show That Galaxies Are Moving and the Universe Is Expanding?

SL and HL: The wavelengths of identifiable spectral lines from galaxies are shifted relative to laboratory values. Most galaxies show a redshift, and more distant galaxies generally have larger redshifts, providing evidence that the universe is expanding.

The Reasoning

Atoms produce characteristic spectral lines at known wavelengths. Astronomers compare these rest wavelengths, $\lambda_0$, with the wavelengths observed from a galaxy, $\lambda$.

The redshift is defined as

$$z=\frac{\Delta\lambda}{\lambda_0}=\frac{\lambda-\lambda_0}{\lambda_0}.$$

For relative speeds much smaller than the speed of light, the IB Doppler approximation gives

$$\frac{\Delta\lambda}{\lambda_0}\approx\frac{v}{c}.$$

For example, if a spectral line normally at $500\text{ nm}$ is observed at $505\text{ nm}$, then

$$z=\frac{505-500}{500}=0.010,$$

so $v\approx zc=0.010(3.00\times10^8)=3.0\times10^6\text{ m s}^{-1}$ away from Earth.

A single displaced line could be misidentified, so astronomers match several lines from the same element. If all lines have the same fractional shift, the pattern is strong evidence that the shift is real. The observation gives line-of-sight motion only, not transverse motion.

Observations show that most distant galaxies are redshifted. The Hubble and Lemaître law, $v=H_0d$, also shows that recession speed $v$ increases with distance $d$. This systematic relationship is evidence that space itself is expanding, rather than Earth simply being at the centre of galaxies moving through static space.

A common misconception is that every redshift is an ordinary Doppler shift caused by motion through space. For nearby galaxies, the Doppler approximation is useful; at cosmological distances, the redshift is more accurately understood as the stretching of light as the universe expands.

Exam Technique

For an IB Explain question, link three points: spectral lines shift toward longer wavelengths, redshift indicates recession, and increasing redshift with distance supports expansion. Do not claim that all galaxies recede: some nearby galaxies can be blueshifted because local gravitational motion can exceed the expansion effect.