With hindsight, my surprise probably comes from keeping my brain inactive and sticking to a rather conservative idea of how sciences should be taught at school; that idea is that understanding physics requires you to have some solid basis in maths, and that the explanation of phenomena should proceed along with quantitative calculations.
Now, of course the mathematical tools available to 16-year-old students are insufficient to describe the physical processes at work in complex quantum mechanical reactions; why, they do not even yet know what a derivative is. But do you really need differential calculus to understand what are alpha, beta, and gamma decays ? In truth, no. That is, you either need much more than that to do precise calculations, or much less if you only wish to appreciate the basic principles of the matter at hand.
In order to introduce neutrinos to my son, I took the matter from a historical point of view as I thought it was interesting to him to understand how a physical discovery can take place. So I explained that until the thirties of last century beta decay was imagined as a process whereby a nucleus emitted an energetic electron, thereby changing by one unit its electric charge. Something in that simple picture did not add up, though. To explain what that was I made an example.
Imagine a cannon set on wheels fires an iron ball. As the ball is shot in one direction, the cannon recoils in the opposite direction as momentum conservation must hold: the product of mass and speed of the ball must equal the product of mass and speed of the cannon. As the cannonball is much lighter than the cannon, it is fired away at a much higher speed; this is more or less what happens with a heavy nucleus, which weighs thousands of times the tiny electron.
What physicists observed when they measured the electron velocity - or rather, its kinetic energy - in beta decays, was that they did not get always the same value: sometimes the electron had a certain energy, some others it had twice less, or even three or four times less than that. This did not make sense: in the cannon analogy, it was as if filling the cannon with the same explosive charge every time produced sometimes very slow cannonballs, and other times very fast ones. The nuclei involved in the process were all equal, and yet they behaved differently. One had to imagine that energy was not conserved in the beta decay of nuclei. Or perhaps there was another possibility ?
Wolfgang Pauli was the physicist who put the alternative hypothesis forth: if the electron is carrying away variable fractions of the released energy, one could imagine this was due to the fact that some invisible other particle was being also shot out. Let us call this mysterious entity "neutrino". If electron and neutrino shared the released energy of the decaying nucleus, the puzzle was no more, as there was now no need for the electron to have always the same energy: energy conservation could be satisfied by any combination of the electron and neutrino energies, as long as their sum was the same.
By the way, the neutrino hypothesis is to me the best example of the way Conan Doyle made Sherlock Holmes extract deductions from his observations: once the impossible has been discarded, what remains - even if improbable, is the correct interpretation.
At the end of my explanation I was happy to have something awe-inspiring to show, to complement the discussion. I thus googled for Superkamiokande, and showed my son the pictures of that fantastic experiment, explained him how it was constructed and why, and finally showed him the way neutrinos are detected, by reconstructing Cerenkov light cones from the electrons produced in neutrino interactions. If those digitally reconstructed circles (showing photons emitted as electron travel faster than light in water) are not awesome to you, then studying physics at school must be a very, very boring thing!
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