Baez's new paper.

1. Nov 16, 2005

CarlB

2. Nov 16, 2005

Hans de Vries

Starting with an attack from Luboš Motl. In my opinion this attack merely
shows how Luboš underestimates other people. Surely John was well aware,
when he wrote the paper, of all the points Luboš brings forward.

There is the issue that some of the symmetries in the SU(3) x SU(2) x U(1)/N
are internal symmetries which would not be related to real dimensions.

But do we really know? For instance, the internal part of the probability
density and current of the Dirac field after Gordon decomposition still
has a relation to the spatial dimensions, even being "internal"

On the other hand. There's more needed than this to turn me into a
proponent of string theory. But then, I don't think that was John's
goal. He merely posted this as an interesting note. A sort of numerical
coincidence, so to speak....

Regards, Hans

3. Nov 16, 2005

Hans de Vries

Last edited: Nov 16, 2005
4. Nov 17, 2005

CarlB

Well Hans, I can't help but feel superior to these efforts. As several of the Woit commenters stated, the real problem is why SU(3)x etc. I think the way to solve the problem is to come up with a very simple preon dynamics and then work backwards to the symmetry.

I'm busily connecting together the Koide mass formula and the Cabibbo mixing angle. The notion right now is going down this path:

There are three eigenvectors to the square root mass matrix,

$$(1,e^{+2i\pi/3},e^{-2i\pi/3})$$ electron

$$(1,e^{-2i\pi/3},e^{+2i\pi/3})$$ muon

$$(1,1,1)$$ tau

Now the thing to note about the above eigenvectors is that if you swap any two elements of the electron eigenvector you get a muon eigenvector (and vice versa). But the tau eigenvector is unaffected by such a swap. I'm thinking that this relationship explains why it is that the Cabibbo angle relates electron family quarks with muon family quarks (and the tau family mixing angles are relatively suppressed).

The mass matrix can be thought of as giving the branching ratios for transitions among the preons. The above eigenvectors give the relative phases for the three preons. The Cabibbo angle is also a phase, and indicates what happens when you move from one orientation preon to another. There are three preons and their orientations are 1, 2, and 3. The branching ratios and Cabibbo angle phases are:

$$\begin{array}{ccc} 1 -> 1; & 2/3; & e^0 \\ 1 -> 2; & 1/6; & e^{+2i/9} \\ 1 -> 3; & 1/6; & e^{-2i/9} \end{array}$$

with 2->xx appropriate. The matrix for this set of branching ratios and phase angles is the square root mass matrix for the leptons (where I'm using 2/9 for the Cabibbo angle).

$$\left( \begin{array}{ccc} \sqrt{2} & e^{+2i/9} &e^{-2i/9} \\ e^{-2i/9} &\sqrt{2} & e^{+2i/9} \\ e^{+2i/9} & e^{-2i/9} &\sqrt{2}\end{array}\right)$$

If you make the assumption that phases are preserved (as you have to in order to use the square root mass matrix as a table of branching ratios for the preons), it becomes very natural that the weak force crosses between the electron and muon families at a high rate (i.e. with the Cabibbo angle) but to get to the tau family you have to change phases which is apparently much more difficult.

What I'm saying here is that I expect to see explanations for the standard model that depend on very simple dyanmics for preons rather than symmetry theory. My guess is that the SU(3) is purely due to there being three preons per fermion, while the rest of the symmetry comes from geometry.

Carl

Last edited: Nov 17, 2005
5. Nov 17, 2005

ahrkron

Staff Emeritus
Wow! I really liked JB's paper.

I've been reading the exchange in http://www.math.columbia.edu/~woit/wordpress/?p=291#comments", and I was quite surprised by some of the replies (starting from the first one, from Lubos Motl). I very much enjoyed one of John Baez' replies in there:

Last edited by a moderator: Apr 21, 2017
6. Nov 17, 2005

George Jones

Staff Emeritus
I think that there is more to it than this. I think Motl's attacks on John are personal - as much about style and political ideology as physics/math. Whether on not this is true, Motl goes out of his way to try and make John, in particular, look ignorant. I suspect most people who followed the exchanges over the last several years between Motl and John on sci.physics.research will agree.

As an example, consider this http://groups.google.ca/group/sci.p...sics.research&rnum=19&hl=en#13284e9bf071fe2a", in which Motl patronizingly lectures John about the properties of separable Hilbert spaces. At a techincal level, I'm sure that John knows at least as much as, if not more than, Motl about the sublties of operators on separable Hilbert spaces and their spectra.

I agree, and I can provide documentary evidence with respect to Motl's first point: "As far as I understand, John: * rediscovered that the Standard Model group is SU(3) x SU(2) x U(1) divided by a certain Z_6 group"

First, in his paper, John says "The gauge group of the Standard Model is often said to be SU(3) × SU(2) × U(1), but it is well known that a smaller group is sufficient."

Secondly, in a http://math.ucr.edu/home/baez/week133.html" [Broken] of his net column, John talks about this and gives O'Raifeartaigh's 1986 book "Group structure of gauge theories" book as a reference.

Anybody know who the commenter andy.s over on Not Even Wrong is? I can hazard a guess, but I'm not sure at all.

Regards,
George

Last edited by a moderator: May 2, 2017
7. Nov 17, 2005

Kea

This seems like a pretty good bet to me! However, I believe the correct explanation should be able to explain SM gauge both as preon dynamics and in terms of a higher dimensional M-theoretic description.

8. Nov 18, 2005

arivero

Yeah, there was some work from Nima Arkani time ago in this sense, about composites in extra dimensions. Sometimes they used it simply to substitute the Higgs sector, but there was also an amazing proposal of getting one chirality of fermions as elementary, the another chirality as composite.

I am browsing the ArXiV but I can not locate the concrete papers just now, sorry.