There is an old saying that “the proof of the pudding is in the eating”. Nowadays you never hear this said properly, because people say “the proof is in the pudding” without understanding that this is a completely meaningless phrase. Much the same applies to the fundamental principle of mathematical physics: “the proof of the mathematics is in the physics”. Too many people say “the proof is in the mathematics” without understanding that this is a completely meaningless phrase.
It has always always always been the case that the proof of the mathematics is in the physics. If the mathematics do not describe the physics that are observed by experiment, then the mathematics are completely worthless. Somehow, somewhen, a misunderstanding has arisen, and the attitude has taken hold that “the proof is in the mathematics”. No, no, no. This is complete nonsense. If the proof is in the mathematics – as it is, for example, in the Coleman-Mandula Theorem that the gauge groups commute with the Lorentz group, or the Distler-Garibaldi Theorem that there is no E8 theory of everything, then it isn’t a proof at all. These are completely theoretical assertions about how you should combine the ingredients in your pudding recipe. They have nothing whatever to do with the physical proof of the pudding – that is, the eating.
I have read the recipe books for puddings, and I have tried those recipes. I have eaten those puddings, and they do not taste right. There is something wrong somewhere. They look like delicious puddings, but the proof is in the eating – they do not taste like delicious puddings. I have tried my own recipes – many of them – but what has been clear from the early days is that you have to separate your eggs. The white of the egg, and the yolk of the egg, have completely different physical attributes, and must be treated separately. In the Standard Model, the egg represents the Lorentz group, which separates into a white SO(3,1) and the yolk SL(2,C). As long as you make your pudding without separating the yolk from the white, you will never have a recipe that gives you the right texture, the right colour and the right flavour.
All the standard models, without exception, treat the egg as an indivisible whole. Never is the white separated from the yolk. I have worked with many recipes of this type, and I have never been satisfied with any of them. But if you separate the egg whites, and whisk them vigorously, you can make a souffle. And then you can use the yolks for a custard. Or there are many other recipes I am sure you know better than I do.
Anyway, my latest recipes experiment with quaternions, as do many of my earlier recipes. The basic quaternionic structure of a cake is clear to every baker – equal quantities of butter, sugar, flour and eggs – so it is hard to understand how anyone would contemplate baking a cake without this quaternionic structure. But there are various ways of breaking the symmetry: you can mix the flour with ground almonds, or coconut flour, or coca powder, or ground rice, etc etc, and the sugar with treacle, or maple syrup, or sultanas, or apricots, etc etc, mix the eggs with milk, rum, orange juice, etc etc, mix the butter with oil – the sky’s the limit.
OK, joking apart, the point is to make sure the mathematics match up to the experimental physics. I don’t give a damn about the “standard model” mathematics, and I focus especially on the points where the standard mathematics doesn’t meet the experimental reality. This is mainly the three generations, including neutrino oscillations, the definition of mass, and the quantisation of gravity. I take the standard recipe as something to work with, to modify as necessary, not as a God-given commandment. I am not prepared to tie myself to a fundamentalist literal interpretation of the Coleman-Mandula Theorem, and I am not prepared to whisk my egg-whites and yolks together without thinking about it first.
And what I really don’t understand about the models people seem to be producing left, right and centre is that they think all they have to do is lay out the standard model ingredients. That is the first step. Then you have to mix them together. You’ve got to get the mixing right, and nobody seems to have the first clue how to go about this. That is what I have always focussed on, because there is relatively little disagreement about what the ingredients are. And then you have to bake it in the oven of experimental reality. Only then will you be able to unify your souffle and custard.