Can Baez's new paper explain SM gauge in higher dimensions?

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In summary, the conversation discusses a paper by John Baez that presents two propositions and a corollary about the gauge group of the Standard Model. The conversation also includes an attack on the paper by Luboš Motl and a response from John Baez defending his work. The conversation also briefly mentions a previous exchange between Motl and Baez on sci.physics.research.
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  • #2
There has been quite a discussion on Woit's about this paper:

http://www.math.columbia.edu/~woit/wordpress/?p=291#comments


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... :smile:


Regards, Hans
 
  • #4
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,

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

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

[tex](1,1,1)[/tex] 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:

[tex]\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}[/tex]

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).

[tex]\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)[/tex]

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
 
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  • #5
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:

[URL='https://www.physicsforums.com/insights/author/john-baez/' said:
John Baez[/URL]]particle physicists are a touchy bunch! Give ‘em a 4-page paper with two propositions and a corollary - I save the word “theorem” for things that are hard to prove - and they’ll complain you didn’t explain why the universe must be the way it is.
 
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  • #6
Hans de Vries said:
In my opinion this attack merely shows how Luboš underestimates other people.

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.

Hans de Vries said:
Surely John was well aware, when he wrote the paper, of all the points Luboš brings forward.

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
 
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  • #7
CarlB said:
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.

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.

:smile:
 
  • #8
Kea said:
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.
:smile:

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.
 

1. What is the main topic of Baez's new paper?

The main topic of Baez's new paper is quantum gravity and its relationship to higher category theory.

2. Who is Baez and why is their paper significant in the scientific community?

Baez is a famous mathematician and physicist known for his work in category theory and quantum gravity. His paper is significant because it presents a new approach to understanding the connection between these two fields, which has been a long-standing challenge in physics.

3. What is the key finding of Baez's new paper?

The key finding of Baez's new paper is the development of a mathematical framework that unifies quantum gravity and higher category theory, providing a deeper understanding of the fundamental nature of space and time.

4. How does Baez's new paper contribute to the current understanding of quantum gravity?

Baez's new paper offers a novel perspective on the relationship between quantum gravity and higher category theory, which has the potential to advance our current understanding of quantum gravity and potentially lead to new breakthroughs in the field.

5. What implications does Baez's new paper have for future research in physics?

Baez's new paper opens up new avenues for research in the fields of quantum gravity and higher category theory, and has the potential to inspire new ideas and approaches to understanding the fundamental laws of the universe.

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