Red-shift and distance
Definition
Galaxy
A galaxy is a very large collection of stars, gas and dust held together by gravity.
Definition
Red-shift
Red-shift is the increase in the observed wavelength, and decrease in the observed frequency, of light from a source that is moving away from the observer.
- When the light from a distant galaxy is compared with a laboratory spectrum, every absorption line is found at a longer wavelength than it should be.
- This red-shift is seen in almost every galaxy that has been measured, in whichever part of the sky the telescope is pointed.
- The size of the shift is not the same for every galaxy, and the further away a galaxy is, the larger its red-shift.
- The pattern is close to a proportional one, so a galaxy twice as far away shows roughly twice the shift.
- Since a larger shift means a faster speed along the line of sight, the more distant galaxies are moving away from us more quickly.
- A few of the nearest galaxies are blue-shifted instead, because their own motion within the local group of galaxies is larger than the general recession at such small distances.
Why this shows expansion
- The red-shift measurements show that the distance between our galaxy and almost every other galaxy is increasing.
- The same pattern would be measured from any galaxy, so there is no galaxy at the centre and our own position is nothing special.
- Galaxies flying outwards through fixed space from one point would put us at the centre of the motion, and the observations rule that picture out.
- What fits instead is that space itself is expanding, stretching the gaps between the galaxies and carrying them apart with it.
- Expanding space also stretches the light waves travelling through it, which is why the wavelength arriving at the telescope is longer than the wavelength that left the galaxy.
- Light from a more distant galaxy spends longer crossing the expanding space, so it is stretched more, which is exactly why distance and red-shift rise together.
- The expansion is a property of the whole Universe rather than of one region, so red-shift is evidence about the Universe as a whole.
How both theories explain it
Definition
Big Bang theory
The Big Bang theory states that the Universe began from a very small, extremely hot and dense region that has been expanding and cooling ever since.
Definition
Steady State theory
The Steady State theory states that the Universe has always existed and always looks much the same, because new matter is created continuously as it expands.
- Red-shift on its own does not decide between the two theories, because both of them include an expanding Universe.
- The Big Bang theory explains it as expansion that started at a single event, so the galaxies have been separating ever since and the light between them has been stretched throughout.
- On that account the red-shift is a record of an expansion with a beginning, which is why it can be traced back to a hot, dense start.
- The Steady State theory explains the same red-shift as expansion that has always been going on and always will, with no beginning to trace back to.
- New matter forms new galaxies in the widening gaps, so the galaxies still separate and still show red-shift while the Universe as a whole looks unchanged.
- Both theories therefore predict red-shift that increases with distance, and both match the measurements equally well.
- Separating them needs an observation the two theories disagree about, which is why red-shift is quoted as evidence for expansion rather than as evidence for the Big Bang alone.
Example
Comparing two galaxy spectra
- A hydrogen line measured at 656 nm656\ \text{nm}656 nm in the laboratory is recorded at 666 nm666\ \text{nm}666 nm from galaxy A and at 696 nm696\ \text{nm}696 nm from galaxy B.
- The change for galaxy A is 666−656=10 nm666 - 656 = 10\ \text{nm}666−656=10 nm, giving a fractional shift of 10656=0.015\dfrac{10}{656} = 0.01565610=0.015.
- The change for galaxy B is 696−656=40 nm696 - 656 = 40\ \text{nm}696−656=40 nm, giving a fractional shift of 40656=0.061\dfrac{40}{656} = 0.06165640=0.061.
- Galaxy B has about four times the red-shift of galaxy A, so it is receding about four times as quickly.
- Because speed of recession rises with distance, galaxy B must also be roughly four times as far away.
Example
Dots on an inflating balloon
- Draw dots on a deflated balloon to stand for galaxies, with one dot 2 cm2\ \text{cm}2 cm from a chosen dot and another 6 cm6\ \text{cm}6 cm away.
- Inflate the balloon until every distance has doubled, so the near dot is now 4 cm4\ \text{cm}4 cm away and the far dot is 12 cm12\ \text{cm}12 cm away.
- The near dot has moved 2 cm2\ \text{cm}2 cm and the far dot has moved 6 cm6\ \text{cm}6 cm in the same time, so the more distant dot has moved away faster.
- No dot was pushed and no dot is at the centre, because the rubber between them stretched, which is what expanding space does.
- Choosing any other dot as the starting point gives exactly the same result, which is why every galaxy sees the others receding.
Exam technique
Building the expansion argument
- Work through the chain in order, from lines shifted to longer wavelengths, to galaxies moving away, to more distant galaxies moving away faster, to an expanding Universe.
- Include the distance relationship, because an answer that only says galaxies are receding misses the step that shows the whole Universe is expanding.
- Add that the same view would be seen from any galaxy when a question asks why the Earth is not at the centre.
- For a question about both theories, give a separate sentence to each and state clearly that neither is ruled out by red-shift.
- Read data tables carefully, since the galaxy with the largest wavelength change is the one furthest away.
Common Mistake
- Do not say that red-shift proves the Big Bang theory, because the Steady State theory explains red-shift too.
- Do not place the Earth at the centre of the expansion, since observers in every galaxy see the same recession.
- Do not describe galaxies as moving through space away from a central point, because the space between them is stretching.
- Do not claim every galaxy is red-shifted, since a few nearby galaxies are approaching and are blue-shifted.
Self review
- Describe how the red-shift of a galaxy depends on its distance from the Earth.
- Explain why red-shift shows that the Universe is expanding.
- Explain why the Earth is not at the centre of the expansion.
- State how the Steady State theory accounts for the red-shift of galaxies.
- Explain why red-shift alone cannot decide between the two theories.
