Compton scattering

While we are talking about relativity, what about evidence for special relativity? That’s the area of physics which talks about the way things move at very high speeds (close to the speed of light).   For example, we talk about things contracting as they get faster (Lorentz contraction) and time slowing down (time dilation). Neither of these things are naturally demonstratable in the lab (although time slowing can be demonstrated with atomic clocks flown on aircraft)

But one lovely experimental verification of special relativity is through the phenomenon of Compton scattering.

Basically, the idea is that a high energy photon (e.g. a gamma ray or X-ray) can interact with an electron (e.g. in a metal) and be scattered (change its direction of travel). At the same time as being scattered, the photon loses energy. Compton’s formula neatly describes the connection between the loss in energy of the photon and the angle through which it is scattered. It’s important in medical radiation physics – e.g. radiotherapy – it means your beam doesn’t go exclusively where you point it.

Deriving the Compton equation is actually not all that hard for a physics student. All you need to do is to apply the concepts of conservation of energy and conservation of momentum, to a collision between a photon and electron.  But you have to do them relativistically – so you need to use the relativistic relationship between energy and momentum.

(For those of you who want a go at it – the relationship is energy squared, minus momentum squared times speed of light squared, equals mass squared times speed of light to the power four:  E^2 -p^2 c^2 = m^2 c^4.  Note that when we have zero momentum p, this equation just gives the famous  E = mc^2.  Wikipedia gives a worked derivation.  You’ll also need to remember that the photon is a quantummy thing – so its energy is proportional to its frequency. )

Measuring the Compton scattering distribution experimentally is also not all that hard if you have the facilities – we get our third-year undergraduate physics students to do it. You just need a suitable source of high-energy photons (e.g. a nice big lump of radioactive caesium 137 – please don’t put one in your garage) a metal rod to scatter the photons and a spectrometer to measure the energy of the photons (the expensive bit). Doing this experiment is great – it gives me a real feeling that what Einstein was talking about isn’t utter rubbish – it actually works – relativity happening before my very eyes.

Arthur Compton was awarded the Nobel Prize for physics in 1927. A good choice, in my opinion.

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