In particular, mass in a classical theory of gravity *must* be treated as a variable, not a constant. Even today, no-one takes seriously the vast amount of experimental evidence that has been accumulating for decades, that proves beyond a shadow of doubt that mass is a variable. Its variations are detected here, there and everywhere.

]]>Thanks for the vote of confidence! But at the end of the day, I do not believe that this Spin(6,4) model is the real “theory of everything”. The splitting so(5) + so(1,4) is really a splitting of representations of the finite group 5+1+4, and the Einstein equations (or what they become) are equating the anti-symmetric squares of 5 and 1+4, not the adjoint representations of so(5) and so(1,4). Both these anti-symmetric squares split as 3a+3b+4, which gives the splitting into EM 3a+3b (photons) and gravity 4 = 2a x 2b (neutrinos x antineutrinos) at the fundamental level.

But it is impossible to explain all this at once, so I’m trying to write up the QFT version on its own, with one or two quantitative predictions if I can manage it.

The so(3) + so(3,4) splitting is also intriguing, because that describes the “ordinary” matter that we see everyday, and in the context of E8, so(3,4) splits as adjoint+vector G2. The importance of G2 is that it acts in the same way on vectors, LH spinors and RH spinors, so it sticks the classical particles (vectors) onto their quantum wave-functions (spinors). Hence we get wave-particle duality without having to give the particles and the waves separate ontological existence. Very important for the interpretation of QM. But there are also lots of different ways to split 6 into 3+3, so which one do we want to put into G2?! My vote is to split leptons from baryons, but this takes away our Lorentz group, which is not likely to be a popular move!

Some while ago I described how it is possible to use SL(3,R) in place of the Lorentz group, but it didn’t go down well. Perhaps in this more general context it might be taken more seriously: the basic idea is that one doesn’t need a concept of energy if one has a variable concept of mass, and if we have three generations of electrons then we have a variable concept of mass that can be quantised. We still have a vector representation of SL(3,R) which can replace the adjoint representation of the Lorentz group in all calculations. One half of the vector describes three generations (of negative charge) and the other half three colours (of positive charge). So the vector describes electromagnetism, and the adjoint describes how different observers can give different mass coordinates to the four basic charged particles, and still describe the same physical theory of electromagnetism. It’s exactly the same as the way the Lorentz group is used in Special Relativity, but extended to three generations of electrons.

]]>I meant Lie group, not Lie algebra, and no, it is nothing like reducing to a finite field. What I do is take a suitable copy of the binary icosahedral group 2I inside the Weyl group of E8, and use that to split up the Lie algebra. What I get (in the enveloping algebra) is more or less the same as the complex group algebra of 2I. But in fact the real group algebra seems to have all the necessary structures – which are all orthogonal or symplectic, never unitary.

]]>(I mean the Lie algebra.)

]]>I have seen many theories of everything, both mainstream and alternative. For me, this post marks the emergence of “your” theory of everything. A degree of mathematical and philosophical specificity has been reached which makes it concrete, comprehensive, and unique. In some sense I suppose it is an “E8 graviGUT”, but with so many unusual features that, when they are all taken into account, it might really be something else.

I do have one immediate question – when you talk about “break[ing] the symmetry from the Lie group to a finite group”, does that involve something like, considering the algebra over a finite field?

]]>Just looking at the Dirac spinors, the Dirac algebra is a complex tensor product of two Dirac spinors, and is therefore a complex 16-dimensional space, but the complex structure contains no physics, and only 16 real dimensions contain observable properties. If you simply take the correct mathematical definition of Dirac spinors as quaternionic 2-spaces, and take the quaternionic tensor product instead, then you lose the irrelevant complex structure, but at the same time you gain something much more important – you gain a measurable consequence of a relationship between the spin directions of two particles. Neither spin direction can be measured, but the relationship between them can. This is a huge gain over Born probabilities.

]]>Or, to put it another way, the unitary representations give you the Born probabilities, but the symplectic representations tell you what is actually happening.

]]>And I say this really seriously, because with symplectic representations you *can* explain the polarisation of light – I know because I’ve done it.

]]>I mean, you can’t even explain the polarisation of light with that model.

]]>Yes, I understand that. What I don’t understand is what that has to do with physics. With those assumptions, you can’t explain entanglement, and you can’t solve the measurement problem. Therefore it is fantasy, not physics.

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