God spins coins

The whole reason for inventing spinors was to explain how electrons “spin”. Experiment made it clear that they do not spin like cricket balls (or baseballs, or tennis balls, or golf balls, or whatever your preferred game is), so they had to invent these spinors to distinguish between two states, called spin up and spin down, that these electrons came in when you looked at them closely. But now that I’ve translated the spinors into spinners, the electron must behave like some physical object that spins in ordinary classical Hamiltonian phase space. So how do electrons spin? I worked through the calculations in my head last night, and I found the answer – they spin like coins.

They really should have realised that 100 years ago when they were building quantum theory in the first place. A spinning coin can land either heads (spin up) or tails (spin down) when you measure it. And that really is all there is to it. The two sides of the coin are different, and if you put the electrons in a magnetic field their spins tend to line up in the same direction. Now my 8-year-old self wants to know how electricity works, and how magnets work, so I explain. Electricity is made of these miniature coins, and they are so small they can get through metal really easily, though there is some resistance, because there’s heaps and heaps of these coins and they have to keep pushing each other along. And how does a battery work? Well there’s this thing inside that keeps pushing the coins one way, so when you join up the terminals with wires they start running along the wires. But why is there resistance, why don’t they form an orderly queue? Why couldn’t you have electrons whizzing along without anything getting in the way? Well, actually you can, you just have to get things cold enough so that electrons start to freeze, and then they stick together in pairs, sticky sides inside, smooth sides outside. And then they do form an orderly queue, and the resistance disappears completely. And the magnetism disappears completely as well, because you can’t have magnetism if you can’t see both sides of the coins. That’s called superconductivity.

What sticks the electrons together in a superconductor? Superglue? No, supersymmetry does not exist, as experiment has conclusively demonstrated, they are stuck together by gluons. Yes, really! I looked at the mathematics, and that’s what they are, real honest-to-goodness Standard Model common or garden gluons. Superconductors are essential for making things like the Large Hadron Collider, which smashes protons together at 99.9999% of the speed of light, or thereabouts. At that speed, protons are squashed as flat as pancakes by Lorentz contraction, so they spin like coins too. If you understand electrons in a magnetic field, then you understand protons in the LHC.

But under more normal circumstances protons and neutrons are much rounder than electrons, and they roll like dice instead. Who said God doesn’t play dice? Of course They do. When you fire a proton or neutron round the LHC, they go point first, and they flatten so you’ve got three sides in front and the opposite three sides behind. The total number of spots is 6+5+4+3+2+1=21 (which happens to be the dimension of the gauge group Sp(3,R), don’t forget that!), so that you have an even number on side and an odd number on the other side. Each side consists of three sides of the original cube, and the three parts of one side are called quarks. Dice are arranged with opposite sides adding up to 7, and the 8 gluons glue the corners of the cube together. There is always one corner between the sides 1/2/3, and this can in principle count upwards in clockwise order or anti-clockwise order. In ordinary gaming dice, there is a standard convention (I forget which one it is), but the difference between the two is the difference between a proton and a neutron.

So God spins coins, and God rolls dice. Do They also play cards? You bet They do. Why do you think there are 13 cards in each suit? Because there are 13 bosons in the Standard Model, of course. The 2 represents the photon, and 3 to 10 represent the 8 gluons, and together these form the compact gauge group SU(3). Then you’ve got the Jack, Queen and King (three intermediate vector bosons, distinguished by having charge +1 (the King?), 0 (the Queen?) and -1 (the Jack). And finally, the Ace is the Higgs boson. Why are there four suits, two black and two red? Well, it’s all about polarisation. Polarisation of photons (and all fundamental bosons) works by looking at the four directions perpendicular to the momentum, say up, down, left and right. These are the four suits. Two are horizontal (say red) and two are vertical (say black). And when God plays bridge, They play against two physicists, who have to agree on the polarisation of entangled photons. God always wins, of course (that’s Bell’s Theorem), and plays both hands (including Dummy). Dummy – that’s me. I don’t play my hand. God is playing it for me!

So don’t tell me there’s only one game in town! There’s coin-tossing, dice-rolling, card-playing going on everywhere. And the rules are very simple, laid down by Hamilton in the mid 19th century. Physicists have changed the rules, moved the goalposts, biased the coins, lied and cheated to get rich on crooked games, but God still plays by the old rules, revealed to Hamilton on Broom Bridge, and carved in tablets of stone.