I may have said this before, but the real problem of theoretical physics is that we haven’t got a definition of mass. This point was emphasised very strongly in Basil Hiley’s OSMU24 talk. Basil Hiley worked for many years with David Bohm on the foundations of quantum mechanics, and has clearly thought very very deeply on this subject, so you should listen to him. This point was the one that I identified in 2014 as the crucial point that needs to be resolved in order to create a unified theory of physics: we need a unified definition of mass. And this is the point I have focussed on ever since.
I would re-word the problem slightly – it is not so much that we have NO definition of mass, but rather that we have TWO. And these definitions are not compatible with each other. The first is Einstein’s mass equation, derived from the Special Theory of Relativity, which defines mass as a scalar of the Lorentz group SO(3,1). And the second is the Dirac equation, which defines mass as a scalar of the Lorentz group SL(2,C). So the reason we have TWO definitions of mass is precisely because we have TWO definitions of the Lorentz group.
Physicists ASSUME these two definitions of the Lorentz group are equivalent, or at least consistent with each other. But they are NOT. There are numerous mathematical reasons why they cannot possibly be equivalent, that I have been SHOUTING about for ten years, until I am blue in the face. Nobody listens. They KNOW what the Lorentz group is, and I don’t, apparently. CRAP. I have thought deeply about this problem, and about almost nothing else, for ten years. I know what I am talking about. You should listen to me.
Why I am writing like a CRACKPOT, with lots of CAPITAL LETTERS? Because I am SHOUTING to try and make myself heard.
Anyway, if you want an E8 theory of everything, then you have to grasp the difference between the Einstein version of the Lorentz group, and the Dirac version. They do not act in the same way on physical reality, and therefore you have to understand the difference. That’s what I do in my latest paper. There is only one way to embed the Standard Model of Particle Physics in E8, and there is only one way to embed General Relativity in E8. They are not compatible with each other, of course. Unless you accept that there are TWO copies of the Lorentz group, not one. Unless you accept that there are TWO definitions of mass, not one. Unless you accept that they are PHYSICALLY DIFFERENT.
The Dirac version is about Quantum Electrodynamics, and describes how particles of matter interact with photons. The Einstein version is about gravity, and describes how particles of matter interact with neutrinos. Neutrinos are not photons. Neutrinos do not behave like photons. Neutrinos do not interact with particles the same way that photons do. Quantum Electrodynamics describes how matter interacts with matter via exchange of photons. Matter also interacts with matter via exchange of neutrinos. What do you call that? Most physicists haven’t got a name for it, and say it isn’t a force, but I say it must be everything that isn’t electrodynamics, and therefore I call it gravity.
You can pretend gravity isn’t a force if you like, but common sense says it is. But I don’t care – if physicists tell me that exchange of neutrinos isn’t a force (which they do), and then tell me that gravity isn’t a force (which they do), they cannot then turn round and tell me that neutrinos don’t mediate gravity. Because if they do, then they suddenly admit that gravity is a force after all. And suddenly their argument falls to the ground. They want to have their cake and eat it. They can’t do that in the real world, although they might be able to in their fantasy worlds of string theory and the like.
Not even there, I think. The proof (i.e. test) of the pudding is in the eating, as they say, and string theory cannot be tested, which means it cannot be eaten. So they can have their cake (and they do – what a monstrous cake it is too!), but they cannot eat it. When I bake a cake (and I do), I bake one that is for eating, not for looking at and admiring. So that’s the difference between me and physicists – they HAVE some wonderful cakes to admire, but I EAT my cakes! My latest cake has just come out of the oven, and will be posted on the arXiv at midnight tonight, for you to eat, if you fancy a midnight feast. The fairy-tale coach of the Standard Models will then turn into a pumpkin, and the horses will turn back into mice. When you find the glass slipper, don’t forget about Cinderella.
And what will happen to Albert Einstein’s cakes? From what I heard, King Albert burnt the cakes.