Hi Ray,

Ray@:My model uses Special Unitary groups heavily. I equate the (N-1) rank of the SU(N) algebra with dimensionality (here, I imply mostly unseen space-like dimensions - not 'units' as you use the word). A classic example is the Georgi-Glashow SU(5) GUT. SU(5) has a rank of 4, with four 'charges':color g_3, color g_8, hypercolor, and weak isospin, that relate to the four dimensions of Spacetime. This is all we understand well: the strong, electromagnetic and weak forces, and Spacetime - all remnants of the first four observable dimensions. We do not understand gravity - of course, we have General Relativity but we still haven't confirmed the origin of mass or why mass doesn't seem to be quantized (dimensions 7-10 in my model). We do not understand the origin of generations (dimensions 11 and 12 in my model). Is there a symmetry rule that only 3 (or 4 or 5) generations exist, or can we keep making progressively heavier 'fundamental' particles as we can in nuclear physics? We simply haven't probed high enough energy scales yet. And we don't understand hyperspace (dimensions 5 and up). How can we? We have no direct evidence, but tons of theoretical implications. I have the following branes: Hyperflavor-brane (5th and 6th D), WIMP-Gravity-brane (8th-10th D), and Generation-brane (11th and 12th D), along with 'imaginary time' in the 7th D. Supersymmetry may convert my 12-D model into a 24 or 26-D model similar to Lawrence Crowell's. These branes are new spaces, but note that some are two dimensional, and one is three dimensional. Two dimensional spaces allow anyonic statistics, so the distinction between boson and fermion becomes blurred.

Peter: Last few days I red Penrose about fibre bundles and gauge connections. The picture I now have is that we have external and internal dimensions. The 16 dimensions of the general metric (generalized spacetime) are the external dimensions. The internal dimensions are part of a fibre bundle above the external dimensions. Therefore I think that they are completely separated from the external dimensions. They can't be ordinary spatial or temporal dimensions. So I think that electric charge and em-flux and weak charge e.d. or some combinations of them are internal dimensions. The internal dimensions are somehow described by the dimensions used by (Special)unitary groups. So I think that your WIMP-Gravity-brane if there is gravity involved can't be part of the internal dimensions. And also that 'imaginary time' can't be part of the internal dimensions.

Ray@:In my opinion, you need to separate 'electric charge' from 'mass charge' -they must be two different quantum numbers, and not intimately related. Also, I don't think the octonion is large enough to accomplish a TOE. If the octonion was large enough, we would be able to 'fix' Lisi's E8 TOE. I am playing with the union of an Octonion and a Quaternion, and might need even more dimensions...

Peter:Yes, maybe I must separate 'electric charge' from 'mass charge'. But I have to read Feijnman again about Lorenz and his opinion that the charges could be responsible for all the mass.

Ray@:You and Florin have sufficiently discussed the fine structure running coupling. It would imply a strange brane if Planck's constant varied with renormalization energy scale.

Peter:Yes, and some combination of the (internal dimensional) running planck charges will equal the classical planck constant at a specific temperature. I don't know what it means that at a certain temperature all forces become the same strenght. The many different charges don't disappear to become one charge, but the stay different charges, but they have the same strength.

Ray@:In my models, each new gauge 'charge' corresponds to a new (mostly space-like?) dimension. This is the similarity that I see with your model, where each new 'unit' corresponds to a new dimension. Abbreviations: HF=Hyperflavor (a left-right symmetric extension of the Weak force), WG=WIMP-Gravity (Weakly Interacting Massive Particle Gravity - a short-ranged tensor force similar to Gravity), Gen=Generaton=Generation-brane (a massive boson force responsible for the enforcement of generational structure).

Peter: I like to understand your model. But I have to read more about gauge groups.

Ray@:Supersymmetry will at least double the size of this, so I already have at least 24 dimensions. Recent conversations with Lawrence Crowell may be pushing this number up to 28 dimensions. I don't think you can quite accomplish a TOE with an 8-dimensional octonion plus its 8-dimensional Supersymmetric component. Lisi' E8 TOE was close...

Ray@: If it is supersymmetry, then your model is effectively the same size as a supersymmetric Lisi E8 model - and I don't think this is quite large enough. If your second octonion isn't supersymmetry, then you still need to double this model and you will have 32 dimensions (I'm not proposing 32 dimensions - just talking about theoretical consistency with supersymmetry).

Peter:I don't know about supersymmetry. In my essay I speculated that it could be part of the generalized spacetime, but after reading Penrose I don't know anymore. He suggest that some dimensions involved in supersymmetry are internal dimensions.

Peter: No I haven't seen Rick Lockyer's website, but I have red his article about octonions. I haven't understood all of it, but other things became clear to me.

Friendly regards, Peter

Dear Peter,

You said "Yes, and some combination of the (internal dimensional) running planck charges will equal the classical planck constant at a specific temperature. I don't know what it means that at a certain temperature all forces become the same strength. The many different charges don't disappear to become one charge, but the stay different charges, but they have the same strength."

In my book, I proposed the idea of a Grand Unified Mediating (GUM) Boson with different quantum states: n=1 -> Strong Nuclear (gluons), n=2 -> Electromagnetic (photons), n=3 -> Weak Nuclear (Intermediate Vector Bosons), n=4 -> Gravitational (gravitons), n=5 -> WIMP-Gravitational (WIMP-gravitons), etc...

At the original GUT, the temperature was approximately 'infinity' and the occupation probabilities (equivalent to relative coupling strengths) of these various quantum states were simple ratios of each other (not necessarily equal).

If we tie in your ideas of various Planck scales, then that implies that the Planck scales were all comparable at the GUT/ TOE. However, spontaneous symmetry breaking of the GUT and Inflation would have allowed those Planck scales to separate into a variety of Planck scales. This is speculation. It is awkward that everything varies with temperature/ energy scale and thus nothing seems to be a true constant (not even h?) if we consider this possibility.

Have Fun!

Ray Munroe

Hi Ray,

Ray@: I knew that you had two octonions. I interpreted the 2nd octonion as supersymmetry. If it is supersymmetry, then your model is effectively the same size as a supersymmetric Lisi E8 model - and I don't think this is quite large enough. If your second octonion isn't supersymmetry, then you still need to double this model and you will have 32 dimensions (I'm not proposing 32 dimensions - just talking about theoretical consistency with supersymmetry).

Supersymmetry is derived from the super-poincaré group. That group also contains Lorenz symmetry. Lorenz symmetry generates gravity. I think supergravity is wrong in that it uses the super-poincaregroup as a local symmetry like a Yang-Mills symmetry. The internal dimensions can't be ordinary spacetime dimensions. The planck constant is part of the spacetime dimensions. The internal dimensions maybe have their own planck constants and in that case according to Grgin that would be another reason that the internal dimensions are totally different physical systems. So indeed the two different octonions maybe already contain supersymmetry. And according to Jens Koeplinger at first sight it looks like that the general metric doesn't account for particles with spin 2, in that case there are no gravitons. That suggest spacetime is not quantized. And the gravitational force is inherently different from the other forces. Spinorial space is also part of the base manifold and not a part of the internal dimensions.

But if the second octonion is supersymmetry, then how is Grassmann algebra involved? Has it something to do with anticommuting spinor generators? Do you have any idea's?

Friendly regards,

Peter

Dear Peter,

I have seen Maxwell's four equations of Electromagnetism written as one Quaternion equation, so I know that tensors, cross (Grassman/ exterior) products and dot products are contained in the algebra. Also, my approach is very geometrical and should be quite consistent with differential geometry and algebraic geometry.

Similarly, an Octonion contains 10 symmetric tensor, and 10 anti-symmetric tensor components. I think sufficient structure exists for multiple particles of spin-2 (tensors), thus my Graviton and WIMP-Gravitons.

Certainly, details need to be fleshed out. Lawrence Crowell and I are still considering different foundational models. I think that having a universal foundation is most important, and the details will naturally fall out - its just a lot of algebra at that point.

After many conversations with Lawrence, I think that the Octonion is closely related to E8. In my models, bosonic and fermionic structures seem to be reciprocal lattices of each other. The reciprocal lattice of E8 is another E8, and I think this second E8 may be related to Supersymmetry.

Likewise, I think that the Quaternion may be related to H4. H4 represents the two reciprocal lattices: the 120-cell and 600-cell, so Supersymmetry gets more complicated (and looks less universal) at this stage of my model.

What 'units' have you ommitted thus far? I think you should separate electric and gravitational charges. This will give you more 'dimensions'.

Have Fun!

Ray Munroe

2 years later