# An Exceptionally Technical Discussion of AESToE

CarlB
Homework Helper
Another example of a cute theory that only gives one generation of the elementary fermions, see:

Symmetries of Nonrelativistic Phase Space and the Structure of Quark-Lepton Generation

Piotr Zenczykowski.

According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space singles out an element which might be associated with the concept of lepton mass. This element is transformed into a corresponding element for a single coloured quark, leading to a generalization of the concept of mass and a different starting point for the discussion of quark unobservability.
http://arxiv.org/abs/0901.2896

So does the above have anything to do with the way Garrett packs a single generation into E8? I don't think so but others understand his theory better than me.

P.S.

MTd2, when I had done this originally, it was based on assumptions which violated special relativity. That probably put Smolin off his feed. The latest version hides all that stuff by sticking to quantum information theory (where position and momentum are ignored, hence there is no need for special relativity or a replacement for it) and so that might get by better.

I seem to have given it an attractive abstract because some important people have written to me saying that they are very busy, especially this time of year, but they are going to take the time to read the paper. I think that basically, it's an attractive way of extending Regge trajectories to radial excitations and I wonder if I should give it a title that mentions Regge trajectories instead of Koide mass formulas. Hmmm.

I'm submitting this to Phys Math Central next week and would appreciate comments on it:
I quickly read through this and I'm afraid I don't
see the main point. It looks like you take these
masses three at a time and find a data fit for them
using three real parameters. You use 3x3 circulant
matrices to inspire the form of this fit. These matrices
(and their eigenvalues) are defined by 3 parameters.
It's well known that all circulant matrices (any size)
are diagonalized by the discrete fourier transform matrix,
so they will all have the same eigenvectors; I don't think
that adds anything. At the end, it's still just a fit of 3
numbers by three parameters. It doesn't look like there's any
relation between the different fits...each has it's own
set of 3 parameters (right?). It's also not apparent how
special these fits are. It seems there are enough degrees
of freedom to fit any randomly picked 3 numbers to this
form...

CarlB
Homework Helper
I quickly read through this ...
At the end, it's still just a fit of 3 numbers by three
parameters.
Thanks for reading! You are right that this is the effect of the discrete Fourier transform; it takes three real variables and turns them into three real variables (or one real variable and one complex variable). Whichever, it keeps 3 real degrees of freedom. But read on.

It doesn't look like there's any relation between the different fits. Each has it's own set of 3 parameters (right?).
No, there are only two parameters for each fit, "s" and "v". You're probably confused by the $$\mu_e$$ constant that is in front of each fit. This is a constant equal to 25.054 square root MeV and is not a parameter. It's value never changes. It's taken from the electron fit.

If it still isn't obvious that there are only two degrees of freedom, note that $$\mu_e$$ multiplies s and v. So you could define
$$s_e = \mu_e s, \;\;v_e = \mu_e v$$
and get each fit down to two real parameters.

By the way, you're not the only one to make this error. When my neutrino paper came out a few years ago it used similar notation and I had a professor of physics tell me that it used 4 parameters, LOL. It must be a natural mistake on a fast read. I've got the $$\mu_e$$ factored out because it's a natural scale.

By the way, if I had 3 real parameters to play around with, I wouldn't have errors, LOL. The third parameter becomes the angle delta. The claim is that the mass spectrum can be closely approximated by quantizing delta as $$2/9$$ or $$2/9 + \pi/12$$

I wouldn't be surprised if other people make the same error, but I don't think I'm going to eliminate the scale factor. From a sociological point of view, a paper that has not passed peer review gets read by people who don't expect anything good and really don't pay very close attention to the details. So they reject things as soon as they find the first detail that disagrees with them. But after a paper is past peer review this effect should go away.

arivero
Gold Member
http://www.slac.stanford.edu/spires/find/hep/www?c=ARXIV:0711.0770 [Broken]

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MTd2
Gold Member
Why did you point the citations for garrett's articles?

arivero
Gold Member
Why did you point the citations for garrett's articles?
First because it is interesting to remark that there are some :-)

Second, because of the second one in the list, Supersymmetry and Polytopes, which is an argument independent from Garret's (and from Tony's) but touching the same theme, plus susy.

MTd2
Gold Member
Arivero, did you know that an attemptive version of SUSY E(8) GUT exists since the 80's?

http://arxiv.org/abs/hep-ph/0201009

And also that recently it was found that F-Theory together with M-Theory with the usual standard model as a low energy limit, which might be need to be embeded in an E(8)?

http://arxiv.org/abs/0905.0142

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arivero
Gold Member
Arivero, did you know that an attemptive version of SUSY E(8) GUT exists since the 80's?

http://arxiv.org/abs/hep-ph/0201009
Yes, I knew It is only that the particle content seems, to me, excesive.

Does AESTOE make any new predictions, in terms of quantum gravity? Does it calculate black hole entropy?

It's not a quantum theory and not consistent anyway, as far as we know.