M Theory Lesson 86
Smolin's slides from Loops07 are now available. Skip the stuff about The Dark Force and look in particular at slide number 38. The important thing to note here is that (a) The Loopies have enlisted the help of none other than Louis Kauffman, an absolutely brilliant knot theorist, and (b) Kauffman has invented something called the Kauffman numbers for three stranded braids, which do this: 
turning elementary braids into codes of the kind that appear in Carl Brannen's version of the Standard Model (eg. see Carl's comment here). Thus it appears there is a growing consensus that the three generations arise not from more complicated knots, as originally proposed, but rather from the kind of combinatorics that appear in M Theory. Category Theory is not mentioned at all in this work, despite the increasing usage of both knot theory and quantum information language.
Update: Carl Brannen points out that his scheme for the generations is far more advanced than the one outlined in Smolin's talk in later slides. I would have to agree.
turning elementary braids into codes of the kind that appear in Carl Brannen's version of the Standard Model (eg. see Carl's comment here). Thus it appears there is a growing consensus that the three generations arise not from more complicated knots, as originally proposed, but rather from the kind of combinatorics that appear in M Theory. Category Theory is not mentioned at all in this work, despite the increasing usage of both knot theory and quantum information language.Update: Carl Brannen points out that his scheme for the generations is far more advanced than the one outlined in Smolin's talk in later slides. I would have to agree.
posted by Kea | 10:01 AM
19 Comments:
Hi Kea,
One might almost suspect that braids and ribbons are playing mathematical games?
Here is a newsworthy item:
Hot gas in space mimics life
Scientists say it's an example of how difficult it is to define life
"Electrically charged specks of interstellar dust organize into DNA-like double helixes and display properties normally attributed to living systems, such as evolving and reproducing, new computer simulations show." ...
http://www.msnbc.msn.com/id/20264620/
Solenoid-like activity?
"... I think that linear superposition is a principle that should go all the way down. For example, the proton is not a uud, but instead is a linear combination uud+udu+duu. This assumption makes the generations show up naturally because when you combine three distinct preons, you naturally end up with three orthogonal linear combinations, hence exactly three generations. (This is why the structure of the excitations of the uds spin-3/2 baryons can be an exact analogue to the generation structure of the charged fermions.) ..." - Carl Brannen
This is an extremely interesting idea. How is the mainstream interpretation of SU(3) colour charges affected by having each quark composed of 3 preons?
I'm thinking about the colour charge of each quark in a baryon. Would the 3 preons comprising a quark have colour charges, or is the colour charge an emergent property of the combination of preons?
Obviously in a proton, the set of quarks (uud) have red, blue, and green colour charges, which all cancel out as seen from a large distance (compared to the size of a proton).
What is the difference (physically in terms of preons) between a u quark with a red colour charge and another u quark (in the same proton) which has a blue colour charge?
I think that SU(3) implies that there is a triplet preon structure to a quark, so that each quark has three possible values of colour charges that it can take.
The colour charge for a fermion remains neutral until you get two or three particles confined in a small enough space that their fields interact with one another, and then colour charge emerges.
This is physically like the mechanism of induced electric charge or induced magnetism (paramagnetism) caused by polarization.
Magnetism in iron is due to electron spin in iron atoms not being completely cancelled out by the Pauli exclusion principle which aligns opposing electron spins in pairs. So each iron atom is a small magnet, but the random alignment of iron atoms normally cancels out this magnetism.
But bring a magnet near a small piece of iron, and paramagnetism is produced because some start aligning.
Similarly, an electron has zero or neutral colour charge, but that may be because preons comprising an electron and causing colour charge cancel out the colour charge. Only when you bring together two or three fermions, you get some kind of polarization at short range which gives each of those fermions a net colour charge with respect to the others, causing the strong nuclear force to appear. (I'll copy this comment to my blog just in case it's out of place here.)
As to generations, my view of why there are three generations, with combinatorics that explain why the T-quark is a lot heavier than the B-quark even though the up and down quark massses are similar, looks sort of like a 2-strand braid in this way:
Consider an Octonion Basis representation of fermion particles:
1 = neutrino
i,j,k = rgb up quarks
E = electron
I,J,K = rgb down quarks
Consider Kaluza-Klein type physics
with M being 4-dim Minkowski Physical Spacetime
and I being 4-dim Internal Symmetry Space.
Consider the Planck-length Lattice path segments of a fermion particle travelling along its world-line string.
There are 3 cases, giving 3 generations:
(The diagrams below look bad. They might have looked better if I knew how to use in this comment a monospaced font that recognized a blank space as a blank space, but I don't know how to do that.)
1 -
If the fermion particle lives in M,
that is, each path segment begins and ends in M:
I -------------------
M ooooooooooooooooooo
then the fermion is represented by a Single Octonion
( o alone )
and is First Generation.
2 -
If the fermion particle lives partly in M and partly in I,
that is, each path segment begins (or ends) in M and ends (or begins) in I:
I ----- oooooooooooo
\o
o\
M ooooo ------------
or
I ooooo ------------
o/
/o
M ----- oooooooooooo
then the fermion is represented by Pairs of Octonions
( o plus one crossing )
and is Second Generation.
3 -
If the fermion particle lives in I
( only visiting M to find its location in spacetime ),
that is, each path segment begins and ends in I:
I ooooo - ooooooooo
o/ \o
/o o\
M ----- o ---------
then the fermion is represented by Triple of Octonions
( o plus two crossings )
and is Third Generation.
Tony Smith
Nige, about Carl Brannen's picture of a proton, said:
"... How is the mainstream interpretation of SU(3) colour charges affected by having each quark composed of 3 preons? ...
is the colour charge an emergent property of the combination of preons? ...".
In my model,
you can represent the 8 Octonion basis elements as triples of binary 0 and 1,
with the 0 and 1 being like preons, as follows:
1 = 000 = neutrino
i = 100 = red up quark
j = 010 = blue up quark
k = 001 = green up quark
E = 111 = electron
I = 011 = red down quark
J = 101 = blue down quark
K = 110 = green down quark
As is evident from the list, the color (red, blue, green) comes from the position of the singleton ( 0 or 1 ) in the given binary triple.
Then the generation structure comes as in my previous comment, and as I said there, the combinatorics gives the correct quark constituent masses. Details of the combinatoric calculations are on my web site.
Tony Smith
Tony,
Thank you very much for your suggestion to represent 8 particles using 3 bits of information (2^3 = 8), which is an extremely neat pattern. It also looks as if this correlates with electric charges:
If 000 represents a neutrino with three preons having electric charges of 0, 0 and 0 respectively, then the electric charge of a neutrino is 0 + 0 + 0 = 0.
If 111 represents an electron with three preons having electric charges of 1, 1 and 1, then the electric charge of an electron is 1 + 1 + 1 = 3 units.
For quarks represented by numbers like 001 or 011, they give electric charges of 1 or 2 units, i.e., 1/3 or 2/3 of the electron's charge?
Taking the distinction of colour charges, e.g. 100 and 010 are two quarks which are different only by the colour charge they carry, what interests me is the geometry involved.
If a quark is composed of three preons, then perhaps the effective colour charge it exhibits is physically due to the way it is geometrically aligned with respect to the other quark (in a meson) or the other two quarks (in a baryon)?
If you imagine each quark as a triangle of preons, one side of the triangle red, another blue and the third green, then three quarks in close confinement will can exhibit an effective colour charge if the side facing the other two quarks is a particular colour.
This could easily be explained by attraction between different colour charges, causing the quarks to rotate until each displays a different colour than the other two.
I'm interested in whether there are real mechanisms behind the mathematics. In quantum mechanics, the fact that in every pair of electrons in an atom the electrons have opposite spin directions to each other seems to be associated with magnetism. If electrons could spin in the same directions the magnetism resulting would be immense. It's fairly clear that electrons align themselves with opposite spins when added to a charged nucleus (say an alpha particle) because they repel one another electrically. Having opposite spins means that similar magnetic poles of each electron in the pair is generally pointed towards the other, causing magnetic repulsion. The Pauli exclusion principle concerning this is thus providing a repulsive force, which keeps the electron structure in the atom stable and prevents all electrons from piling up in the innermost shell.
Maybe the colour charge is an emergent effect similar in principle to the "spin" states of confined electrons in atoms (which are given by Pauli exclusion principle), with the emerging colour charge dependent upon the geometry that confined particles assume in close proximity?
Just as electron spin's cease being random (or in a "superposition" of states, for those who believe without objective evidence that wavefunctions collapse to definite states only when someone makes a measurement) when electrons are added to an alpha particle to form a helium atom, maybe the nature of colour charge is that it emerges in the same way due to some rotation of quarks inside a hadron?
Nige, in my version the preons don't take "color" charge, ...
Ah heck, let me type up a quick blog note instead of running this out here. Give me maybe an hour.
Nige said "... Maybe the colour charge is an emergent effect ... with the emerging colour charge dependent upon the geometry that confined particles assume in close proximity? ...".
Since my view is that "... the color (red, blue, green) comes from the position of the singleton ( 0 or 1 ) in the given binary triple ...[such as]...
i = 100 = red up quark
j = 010 = blue up quark
k = 001 = green up quark
...
I = 011 = red down quark
J = 101 = blue down quark
K = 110 = green down quark ...",
I agree that color emerges from "... the geometry that confined particles assume in close proximity ...".
Consider the proton as a superposition of the three color-neutral sets of its valence quarks as first-generation fermions:
100 = red up quark
010 = blue up quark
110 = green down quark
100 = red up quark
101 = blue down quark
001 = green up quark
011 = red down quark
010 = blue up quark
001 = green up quark
However, when you look at the neutron the same way (two downs instead of two ups) you don't get a realistic proton-neutron mass difference, especially if you do as I do in my model and consider the first-generation up and down quark constituent masses to be equal,
effectively giving a zero (wrong) proton-neutron mass difference.
To get the correct mass difference, you have to look more closely at the constituent valence quarks in the superposition.
Since first-generation quarks in a superposition are effectively virtual particles, they can for a short time live as similar quarks in higher generations, but the time they spend there is suppressed by the mass difference.
Since the third generation quarks are MUCH heavier than the first, ignore the third generation virtual contribution.
For the up quark, the corresponding second generation quark is the charm, which is also much heavier so that the up quark does not get much of any efffective mass increase due to spending time as a virtual charm (or T) quark.
However, the down quark corresponds to the strange quark, whose constituent mass is not so much heavier than that of the down itself, so the down quark effectively gains mass by spending a non-trivial amount of time as a virtual strange quark.
When you run the numbers (using Kobayashi-Maskawa parameters for generation mixing), you see that the down quark gains some mass while the up quark does not gain much mass,
so that
the proton (two ups and a down) is lighter
than
the neutron (two downs and an up).
The calculation gives a neutron mass that is about 1.1 MeV greater than the proton mass,
which is fairly close to experimental results.
See my web site, particularly
www.valdostamuseum.org/hamsmith/2002SESAPS.html#pnmd
Tony Smith
PS - Kea, I apologize if my comments here are too detailed and long about model details. Please feel free to delete them.
However, thank you for allowing me to post the comments so far, especially since I am blacklisted by the Cornell arXiv and since blogs like Peter Woit's refuse to allow comments about alternatives to superstring theory.
It is sort of puzzling to me that Peter attacks superstring theory as being "Not Even Wrong", but refuses to attempt to evaluate alternatives.
Lee Smolin also attacks superstring theory, and promotes his favorite alternative Loop Quantum Gravity, but he too refuses to attempt to evaluate any other alternatives.
Lee's position is somewhat understandable in terms of plain-old dollar self-interest in trying to get money away from superstrings into Loop Quantum Gravity,
but
Peter's position is very hard for me to understand.
Only a few blogs (such as this one) seem to be open to fair-minded discussion of a wide range of alternatives, and for them I am very grateful.
Goodness, Tony, no need to apologise: this is wonderful stuff!
It is sort of puzzling to me that Peter attacks superstring theory as being "Not Even Wrong", but refuses to attempt to evaluate alternatives...
My guess is that Peter is quite convinced that we are all just crackpots, because he takes the Standard Model in its usual guise far too seriously, as do many mathematicians who have been enthralled over the last decade or two by the structure of QFT.
The physics discussion posts are very valuable. Woit's philosophy for moderating his own blog, and deciding what to discuss and evaluate, is proudly elitist (see this link for "... I’m a lot more elitist and willing to see suppression of crackpottery than many of my commenters..."), but you're wrong to suggest that this is sole reason why he refuses to discuss/evaluate alternatives.
Dr Woit has his own ideas (see especially pp 50-51 of this linked paper, also he has some papers as unpublished PDF files on his home page) about how to proceed in developing a better understanding of the Standard Model, and he doesn't think the Higgs field sector of the Standard Model (and thus the usual electroweak symmetry breaking), is solid physics.
He chooses not to blog about or critically evaluate any alternatives to string theory, including his own. Probably he feels that if he did discuss alternative ideas on his blog too seriously, his attack on the failure of string theory would be ignored or even back-fire.
The mainstream groupthink has the hypocrisy to say without any embarrassment the contradictory sentences: "M-theory is the only self-consistent theory of quantum gravity. Alternative ideas need not be considered. All alternative ideas are failures."
To discuss alternative ideas on a blog about the failure of the mainstream model would confuse the issue. Instead of the mainstream people sulking away silently, or arguing the mainstream case, all the mainstream people would have to do is to criticise or ridicule the alternatives in comparison (ignoring the fact that the mainstream has had over 20 years of serious full-time effort invested in it by many people).
So the failures of the mainstream would become invisible to both the amateurs and to the media behind a smokescreen of abuse directed toward alternative ideas. They would be left with the false and mistaken impression that alternative ideas are as bad or worse than the mainstream (when this is wrong, because the mainstream has failed after being carefully developed for 20 years, and the alternative ideas haven't been that carefully developed).
The real hypocrisy is the mainstream call for more time, more experiments, more resources, when its past failures are pointed out.
Do you seriously expect that a lot of progress could be made if Dr Woit started to discuss alternative theories to string?
For a proof of what happens when alternative ideas are discussed on a blog dedicated to string controversy, see the 3rd ever post of Not Even Wrong, especially the attacks by Prof. Mark Srednicki, e.g. "I came to your web site because I was told that you are a critic of string theory, and I wanted to see what you had to say about it. What I find is appalling ignorance. You really ought to spend some time learning some physics before you attack it. I recommend starting with Weinberg’s three-volume text on quantum field theory. ..." What you find as you read that post is that someone misunderstands (accidentally through carelessness) and ridicules the alternative:
http://www.math.columbia.edu/~woit/wordpress/?p=3
It's like the problem of trying to get rid of flat earth theory by arguing for the alternative theory that the earth is approximately a sphere. The flat earther's simply ridiculed the spherical earth theory by making up absurd lies that the ignorant crowd and media believed: "if the earth was spherical, all the water in the oceans would be able to spill down to the bottom!"
It was the same with the spin of the earth (which replaced the sun's motion around the earth). Ptolemy ridiculed Aristarchus's solar system (proposed in 250 BC) in his "Almagest" of 150 AD, on the basis that "the winds would have to blow constantly 1000 miles/hour towards the west at the equator", and winds would always be blowing towards the west at other latitudes (although at lower speeds) apart from the poles. (The correct laws of motion, required for understanding the behaviour of air masses realistically, weren't available until 1687.)
This kind of problem (false attacks based on ignorant belief systems or assumptions which someone tries to sneak into a criticism under the label of "common sense", not hard facts), is very destructive and holds up progress. The lay person (and some mainstream peer-reviewers, who should know better) are likely very impressed by such vicious (non-scientific) attacks and think falsely that the alternative has been well-and-truly ridiculed and effectively debunked.
Dr Woit has his own ideas (see especially pp 50-51 of this linked paper, also he has some papers as unpublished PDF files on his home page) about how to proceed in developing a better understanding of the Standard Model...
Yup, pp 50-51 includes a discussion on K-theory and Bott periodicity and the statement, "This may indicate that one’s fundamental variables can be taken to be geometrical structures on R^8." R^8 is also manifest in Tony's model, yet with additional algebraic structure (Jordan algebras, Freudenthal triple systems, quasiconformal groups) to show how the "favorite experimentally unobserved internal symmetry groups" of GUTs and string theories arise (e.g. SU(5), SO(10), E6, SO(32), E8).
This is still work in progress, and some young string theorists like Andrew Neitzke, have made explicit connections between Jordan algebras, topological strings and twistor theory (arxiv.org/abs/0707.1669).
OK, Nigel, thanks. I hadn't looked at that link before. You are probably right.
Nige said "... Woit's philosophy ... is proudly elitist ... but you're wrong to suggest that this is sole reason why he refuses to discuss/evaluate alternatives. ...".
Only Peter Woit would know his own reasons for
"... refus[ing] to discuss/evaluate alternatives ...",
but
I feel that a major reason is that he is indeed "proudly elitist".
For instance, Kneemo noted that Peter Woit said
"... This may indicate that one’s fundamental variables can be taken to be geometrical structures on R^8. ..."
and
Kneemo also noted that "R^8 is also manifest in Tony's model".
However,
my attempts to engage Peter Woit in substantive discussion about such similar structures were unsuccesful,
and my personal feeling is that
my lack of success was primarily due to the fact that I am an outcast with respect to the establishment
and
he would have welcomed such discussion with Witten or a Witten protege at IAS.
My feeling is reinforced by Peter Woit's reluctance to entertain discussion critical of Ed Witten (particularly evident when I mentioned an episode at IAS in which IAS attempted to attack the tenure status of a non-superstringer, Piet Hut).
I should also note that my attempts to discuss the physics of the exceptional Jordan algebra with Lee Smolin (who had written a paper about the subject) were also unsuccessful,
and my personal feeling is that in that case as well my lack of success was primarily due to the fact that I am an outcast.
Nige also said "... To discuss alternative ideas on a blog about the failure of the mainstream model would confuse the issue ...".
I disagree.
Failing to discuss alternatives allows the mainstreamers to get away with saying that they are the only game in town,
since it allows them to say that the failure to present alternatives for discussion is prima facie evidence that they are indeed the only game in town.
Since some alternative models are MORE explicitly consistent with observations than ANY version of the superstring mainstream
(for instance, my model gives quantitative particle masses and force strengths)
discussion of such alternative models would be a much more forceful exposure of the deficiencies of the superstring mainstream models.
As Nige points out,
"... mainstream people ..." could then "... criticise or ridicule the alternatives ..."
but
to do that, they would have to do at least one of the following:
1 - show how the physics of the alternative model is less realistic than the superstring mainstream models (obviously not true with respect to my model)
or
2 - show that the alternative model is internally inconsistent (also not true of my model)
or
3 - do as Oppenheimer did to Bohm, that is, to engage in ad hominem attacks unrelated to substantive physics (in fact, that is what has been done and is being done with respect to my model).
Forcing the superstring mainstream to engage in type-3 behaviour, by open discussion of alternative models, would increase the exposure of the superstring mainstreamers as Naked Emperors.
In summary:
Nige asks ".. Do you seriously expect that a lot of progress could be made if Dr Woit started to discuss alternative theories to string? ...".
Yes,
I do, because IF MODERATED FAIRLY (which might take more effort than Peter Woit is willing to expend) it would expose more specific deficiencies of the superstring mainstream,
and would increase awareness of the good parts of the alternative models.
Tony Smith
PS - I am NOT saying that my model is the only alternative. There are many others, but I use my model as an example because I am familiar with it.
Hi Tony. Although we know you are correct about the experimental evidence, the difficulty is in convincing the mathematicians (and Woit's elitism is mostly based upon mathematical, not physical, knowledge). A vast gulf has developed between those who focus on theoretical physics and the mathematical physicists, who appear to be largely under the impression that new physics will just easily fall out of abstracting QFT far enough into n-cat land. There's not much that can be done about this: we must just keep plugging away at things.
Kea, you said
"... the mathematical physicists ... appear to be largely under the impression that new physics will just easily fall out of abstracting QFT far enough ...".
It seems to me that your characterization of the QFT Feldverein people is similar to that of the "Cynical observers" in the following quote:
"... the Main Problem of quantum field theory ...[is]... either
to show that the idealizations involved in ...[its]... fundamental notions ... are incompatible in some physical sense
or
to recast the theory in such a form that it provides a practical language for the description of elementary particle dynamics.
...
The physicists who have engaged in this kind of work are sometimes dubbed the Feldverein.
Cynical observers have compared them to the Shakers, a religious sect of New England who build solid barns and led celibate lives,
a non-scientific equivalent of proving rigorous theorems and calculating no cross sections. ...".
The quote is from the book "PCT, Spin and Statistics, and All That"
by Streater and Wightman (Benjamin 1964).
Maybe the Feldverein have not really changed much in over 40 years,
so maybe you are right that "... There's not much that can be done about this ...",
and
maybe you are mistaken in thinking that we will do any good if we "... just keep plugging away at things ...".
Maybe we should leave western theoretical physics to its New Dark Age and move to China and make money in Earth's new Center of Power.
Tony Smith
Alas, I see little evidence that things are any different in China. And to me the U.S. is just as 'foreign' as China (although they do speak better English there).
Over on Peter Woit's blog, recently ( I just now read the commments, dated August 17th, 2007 at 9:31 pm and 10:37 pm in its time zone )
solar-neutrino said directly to Peter Woit pretty much what I was saying in my comments here
"... If you would like to do what I am led to assume you are trying to do (i.e. help bring ‘physical’ research back into physical research endevours) why not highlight works of those who share the very same point of view as you, viz. Roger Penrose, et. al. This can be more valuable for the purpose in question than simply more of the same remarks, since it adds a further layer of reasoning to cast doubt on string theory’s mis-perceived status as the ‘only game in town’, and frees more young people to engage and analyze the research frontier for themselves. ..."
to which Peter Woit replied
"... I believe what is needed is as much new mathematical ideas as new physical ones. I will try and do more to write about what I see as promising new ideas here on the blog, although unfortunately these remain difficult to come by and few and far between. ...".
So, Peter Woit himself has now (on his own blog) answered a question raised in this thread in this blog, and his answer supports your
"... guess is that Peter is quite convinced that we are all just crackpots ...".
Tony Smith
"Failing to discuss alternatives allows the mainstreamers to get away with saying that they are the only game in town,
since it allows them to say that the failure to present alternatives for discussion is prima facie evidence that they are indeed the only game in town."
- Tony Smith
You are right, but the level of opposition to alternatives is directly proportional to the level of threat they pose. Where the alternatives are ignored, the mainstream will be gentle in dismissing them (in order to appear to be nice, wonderfully gracious people). But if the alternative idea - claiming to be more realistic than the mainstream M-theory - starts getting too much serious attention, then the steel fist inside the velvet glove appears.
We saw the widespread toleration of LM's behaviour against authors LS and PW last year, by most string theorists, which is a hint of the sort of thing to expect: mob or gang behaviour, tolerating those who fire personal attacks at others while ignoring the real science!
We can't be too hard on these people. Most of them really believe they are doing the best thing by getting on with their 'science' and by ignoring the shouting matches. If they are a little too sure of their 'science' it is because the Ivory Tower of the Dark Age shelters them from reality. We all suffer from delusions of some kind or another, and if we have been a bit luckier in spotting a few of those it is thanks to criticism.
The failure to interest a particular person (Peter Woit, for example) in an alternative view of physics is not much of an indictment of physics in general.
If a new physics is going to succeed, it must do what every new physics has done through history, convince later generations of physicists to use it.
One does this by providing methods of calculation that are better than the alternatives. And those converted will, by and large, be (a small number of) those who are early in their careers, not any one particular person.
As Kea says, if we get enough of a congregation, this is a sign in itself. All you can ask is that the congregation grows, not that any particular sinner get saved.
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