Hubble's law and the Big Bang
The stretched light of galaxies
- Light from distant galaxies arrives redder than it left — stretched to longer wavelengths.
- Read as a Doppler shift, those galaxies are rushing away from us.
- This single clue reveals an expanding Universe.
Redshift
- Redshift: a galaxy's spectral lines shift toward longer wavelengths.
- For $v \ll c$: $\dfrac{\Delta\lambda}{\lambda} \approx \dfrac{v}{c}$, where $v$ is the recession speed.
Redshift means a galaxy's spectral lines are shifted to:
A receding source stretches the wavelengths — a redshift, with $\dfrac{\Delta\lambda}{\lambda} \approx \dfrac{v}{c}$.
A galaxy's lines show $\dfrac{\Delta\lambda}{\lambda} = 0.020$. What is its recession speed, as a fraction of $c$?
For $v \ll c$, $\dfrac{v}{c} = \dfrac{\Delta\lambda}{\lambda} = 0.020$.
An expanding Universe
- Almost every distant galaxy is redshifted — they are all moving apart.
- Space itself is stretching, and farther galaxies are redshifted more.
Almost all distant galaxies are redshifted, which shows the Universe is expanding.
They are moving apart on average — the space between them is stretching.
Hubble's law
- Recession speed is proportional to distance: $v \approx H_0 d$.
- A graph of $v$ against $d$ is a straight line; its gradient is the Hubble constant $H_0$.
Hubble's law: recession speed $= H_0 \times$ ____.
$v = H_0 d$ — speed grows in proportion to distance.
Galaxy B is 3 times as far away as galaxy A. By Hubble's law, B recedes how many times as fast?
$v \propto d$, so 3 times the distance means 3 times the recession speed.
The Big Bang
- Run the expansion backwards and everything was once together — the Big Bang.
- The age of the Universe is roughly $\dfrac{1}{H_0} \approx 14$ billion years.
The approximate age of the Universe is:
Running the expansion back at a steady rate, all distances reach zero after a time $\dfrac{1}{H_0} \approx 14$ billion years.
You've got it
- redshift: lines stretched longer; $\dfrac{\Delta\lambda}{\lambda} \approx \dfrac{v}{c}$
- Hubble's law: $v \approx H_0 d$ — farther galaxies recede faster (an expanding Universe)
- rewind the expansion → the Big Bang; age $\approx \dfrac{1}{H_0}$