25.3 Hubble’s law and the Big Bang theory
- Syllabus
- 9702–2028–2029
- Topic
- 25.3
- Level
- A2
Learning objectives
25.3.1The lines in the emission and absorption spectra• understand that the lines in the emission and absorption spectra from distant objects show an increase in wavelength from their known values25.3.2Redshift of electromagnetic radiation• use ∆λ / λ ≈ ∆f / f ≈ v / c for the redshift of electromagnetic radiation from a source moving relative to an observer25.3.3Why redshift leads to the idea that the universe is expanding• explain why redshift leads to the idea that the universe is expanding25.3.4Hubble’s law v ≈ H0d and explain how this leads to the Big Bang theory• recall and use Hubble’s law v ≈ H0d and explain how this leads to the Big Bang theory (candidates will only be required to use SI units)
Distant-object spectral lines are redshifted from their known laboratory wavelengths
Identify an element by the distinctive spacing pattern of its emission or absorption lines, then compare the distant object's line wavelengths with the same lines measured in a laboratory/rest spectrum.
If the whole matching pattern appears at larger observed wavelengths than its known values, it is redshifted; the corresponding observed frequencies are lower.
A shift to shorter wavelength/higher frequency is blueshift. The direction of shift is judged from corresponding lines, not the overall colour alone.
Redshift also moves a thermal spectrum's observed peak to a larger wavelength than the emitted peak, so it must be corrected before using Wien's law for true surface temperature.
Do not compare unrelated spectral features. The evidence is a common fractional displacement of an identifiable line pattern from known rest values.
Use fractional redshift to estimate radial speed
Forrecession:Δλ=λobs−λemit>0Δf=femit−fobs>0
z≈Δλ/λemit≈Δf/femit≈v/c(v≪c)
A line shifts from 4.62×10⁻⁷ m to 4.91×10⁻⁷ m: z=(4.91−4.62)/4.62=0.0628, so v=zc=1.88×10⁷ m s⁻¹ away from Earth.
For a source approaching the observer, λobs<λemit and the wavelength change is negative; its speed magnitude may be calculated from |Δλ|/λ.
State how Δf is defined: redshift lowers frequency, so f_emit−f_obs is positive. This approximation is for speeds much smaller than c and uses the emitted/rest value in the denominator.
Systematic galaxy redshift is evidence that the universe is expanding
Spectra from many distant galaxies show identifiable lines at larger wavelengths/lower frequencies than their known rest values.
This redshift indicates that those galaxies are receding and that, on large scales, galaxy separations are increasing.
If distant galaxies are generally moving apart, the universe's large-scale geometry is expanding rather than remaining static.
Observers in different galaxies would see the same large-scale pattern: expansion does not require Earth to be a unique central point.
One nearby galaxy can have local motion toward us. The expansion inference comes from the systematic large-scale redshift pattern of distant galaxies.
Hubble's law links recession to distance and points back to a dense early universe
v≈H0dH0=v/d;d=v/H0
The recession speed v of a distant galaxy is approximately proportional to its distance d from the observer. In SI, v is m s⁻¹, d is m and H0 is s⁻¹.
A graph of recession speed v against distance d is approximately a straight line through the origin with gradient H0.
For v=1.9×10⁷ m s⁻¹ and H0=2.3×10⁻¹⁸ s⁻¹, d=v/H0=8.3×10²⁴ m.
More distant galaxies recede faster. Running this expansion backward means separations were smaller in the past, leading to the idea that the universe began in an extremely hot, dense state and expanded—the Big Bang model.
simpleexpansiontimescale≈1/H0forH0=2.3×10−18s−1:1/H0≈4.3×1017s≈1.4×1010years
Use H0 in s⁻¹ with SI data. Backward extrapolation supports a common dense past; it is not evidence for an explosion from one location into pre-existing empty space.