After giving a talk to A level physics teachers the other weekend, I stayed around to listen to a presentation about radioactivity: it really is a pleasure listening to other people teaching!
From my disinterested perch at the back of the class I was surprised to find that the process of beta decay was described by means of a Feynman Diagram.
I was then even more surprised when teachers asked detailed questions about which type of ‘vector boson’ was involved. I began to wonder how this could make any sense to ‘A’ level students. Do they really know what a ‘boson’ is? Or a ‘vector boson’?
And an e-mail today from an AS level student asking me about these diagrams crystallised my misgivings: I realised that teaching and examining this kind of thing as physics is potentially quite misleading.
At the heart of the matter is the fact that Feynman diagrams represent an ingenious way of describing a calculation: they do not describe the physics underlying the process. You can read an excellent article about their history here.
Let me explain:
- The diagram at the head of the page describes the way that the electrical interaction of two electrons – their mutual repulsion – is calculated in an advanced theory called quantum electrodynamics (QED). The lines and vertices each have a precise mathematical interpretation.
- QED describes the repulsion between the electrons in terms of the exchange of an infinite number of ‘virtual photons’. The diagram above summarises the way the exchange of a single ‘virtual photon’ - the wiggly line in the middle – is calculated.
Now QED is an astounding theory. It has been checked thoroughly and there is an astonishing correspondence between the results of its calculations and physical reality. In other words it is in some sense ‘correct’.
But nonetheless there are two problems when using these diagrams in schools.
- Firstly I underlined the word ‘infinite’ in the bullet point above because when you see that word you can be sure you are in the realm of maths, not physics. This is because there are no infinite quantities in physics.
- The second problem is that it involves the concept of a ‘virtual photon’. Despite 35 years of exposure to this concept – I haven’t a clue what it means physically. I suspect strongly that its role is calculational rather than physical.[I searched for a comprehensible 'link' but there are none! Try this as a typical example.]
Some people might argue that because ‘virtual photons’ are part of the way QED works, then the accuracy of QED is in itself evidence that virtual photons ‘exist’. To these people I have a one word rebuttal: ‘Epicycles‘: just because a calculational technique improves predictions does not mean that there is a physical counterpart to the ‘calculational entities’.
Now why does any of this matter?
It matters because this stuff is being taught for all the wrong reasons. It is being taught , I guess, because it looks like a cool cartoon, and also requires no numerical skills. We are asking students to simply imitate the marks made on blackboards by other physicists.This is bad.
Further, its inclusion has caused the exclusion of a really interesting feature of beta decay that students could appreciate directly.
Instead of electrons being emitted in the same way as alpha particles are - with a single characteristic energy and momentum, electrons emitted in beta decays have a wide range of energies, from a maximum characteristic value, all the way down to zero.
In the early days of nuclear physics this spectrum was puzzling because it seemed as though beta decay did not conserve energy or momentum. ‘A’ level students can readily appreciate both these conservation laws, and the potential significance of them being broken.
And the resolution of the apparent breakdown of the conservation laws was that there was a third particle involved – a particle with almost no mass called a neutrino. And the existence of this particle – not to be directly detected for 25 years after its existence was hypothesised – was based on the law of conservation of momentum.
So these diagrams look like physics, but they are not. And IMHO they don’t belong in an ‘A’ level physics syllabus.