String theory is what?

[lpetrich]

Another bit of evidence for the quark structure of protons: Parton (particle physics) (Wikipedia) -- from collision experiments, one finds lots of evidence that protons are composite.

Farsight, what is your opinion of the success of the Standard Model of particle physics?

[Nautilidae]

Another bit of evidence for the quark structure of protons: Parton (particle physics) (Wikipedia) -- from collision experiments, one finds lots of evidence that protons are composite.

Farsight, what is your opinion of the success of the Standard Model of particle physics?

That was first observed at SLAC, correct?

[lpetrich]

Another bit of evidence for the quark structure of protons: Parton (particle physics) (Wikipedia) -- from collision experiments, one finds lots of evidence that protons are composite.

That was first observed at SLAC, correct?

Yes, that's right.

Over at books.google.com there is some of Constructing quarks: a sociological history of particle physics, by Andrew Pickering, which describes how quarks were discovered. Physicists worked from different directions, like symmetries in hadrons and proton-structure collision experiments, and the paths ended up at the same destination: quarks.

(Edited to note gaps in what books.google.com reveals of that book)

[lpetrich]

As I'd mentioned, the discovery of quarks proceeded along two paths - hadron symmetries and nucleon structure.

The first hadron symmetry recognized was a result of studying strong interactions. They were discovered to treat protons and neutrons essentially alike, as if they were like the two spin states of a spin-1/2 particle. Noting a mathematical similarity with angular momentum, they named a new quantum number, "isotopic spin" or "isospin". Nucleons are thus an isospin doublet with total isospin I equal to 1/2 and individual isospin components
Protons: I3 = +1/2
Neutrons: I3 = -1/2

Pions have I = 1:
Pi+ : I3 = +1, Pi0 : I3 = 0, Pi- : I3 = -1

As with angular momentum, total multiplicity = 2*I + 1

Electromagnetism and weak interactions break isospin symmetry, of course.

In the 1950's, some strongly-interacting particles were discovered to live unusually long, a property that seemed very strange. Thus some physicists introduced a quantum number that they called "strangeness".

But strangeness seemed almost interchangeable with isospin, and Murray Gell-Mann and George Zweig proposed extending isospin to a bigger symmetry that included strangeness. They thus went from isospin SU(2) to "Eightfold Way" SU(3).

They thus identified three quarks, up, down, and strange; isospin is the up vs. down symmetry.

But were quarks real particles? They had electric charges 2/3, -1/3, and -1/3, and weak interactions could do up <-> down and up <-> strange. But they could not be shaken loose from hadrons, and their spin of 1/2 caused problems. They acted like they have integer spin, with symmetric rather than antisymmetric wavefunctions. Otherwise, it would be hard for the hadrons to have the patterns they did, and for the proton and neutron magnetic moments to have the ratio that they do. The delta++ is uuu, the delta- is ddd, and the omega is sss, but they did not seem to be excited compared to other mixtures of quarks -- were all the quarks in the same orbit states?

-

Then along comes SLAC's electrons and CERN's neutrinos, smashing protons and neutrons to bits. They were clearly composite, but what were the "partons" that they contained? They have spin 1/2, and the neutron-to-proton ratios were what one would expect of protons being uud and neutrons being udd. That seemed to clinch the identification, except for the pesky problem of wavefunction (anti)symmetry.

Except that these "valence quarks" carried only some of nucleons' momentum at high energies. Another part was carried by quark-antiquark "sea quark" pairs, and still another part was electrically and weak-interaction neutral.

In 1965, Moo-Young Han, Yoichiro Nambu and Oscar W. Greenberg proposed a solution to the symmetry problem: that quarks have an additional degree of freedom that also follows SU(3). It was named "color" for there being three degrees of freedom in it. Three quarks could form an antisymmetric colorless combined state that would solve the symmetry problem. They'd be antisymmetric in color but symmetric in everything else.

Han and Nambu then went on to propose that quarks interact by exchanging "gluons", which have color-anticolor degrees of freedom. One of the possible 9 mixes is colorless, so they would have 8 color degrees of freedom, the "Eightfold Way" again.

-

Independent evidence for this extra triplicity of quarks? Or gluons? I can't find any dates, but I recall that electron-positron collider experiments were able to verify this extra triplicity -- the quark-antiquark pair production is 3 times higher than what one would otherwise calculate.

Gluons? Collisions at high enough energies were producing quarks that moved close to freely until they separated by about 10^(-15) m. They then pulled lots of quark-antiquark pairs out of the vacuum, making jets of hadrons. In 1979, three-jet events were observed, where the extra jet was due to an energetic gluon leaving the quark-antiquark pair.

It turned out that the gluon coupling constant increased with distance in a fashion that agreed with experiments like these, slowly for small separations and high energies, then rapidly for about 10^(-15) m and a few hundred MeV. This explained the lack of free quarks and free gluons, and why jets formed. A gluon string would form, which would repeatedly pull quark-antiquark pairs out of the vacuum, making hadrons.

Returning to isospin and the original "Eightfold Way", they were side effects of the low masses of the up, down, and strange quarks. Three other quarks have since been discovered: charm, bottom, and top, and not surprisingly, they are much more massive.


Farsight, isn't real science great? Good theories get supported from several sources.

[Farsight]

Another bit of evidence for the quark structure of protons: Parton (particle physics) (Wikipedia) -- from collision experiments, one finds lots of evidence that protons are composite.

Yes, they're composite, but look at the title of your link. It says Partons. That's what quarks are, they're parts, like Feynman said. That's why we've never seen a free quark.

Farsight, what is your opinion of the success of the Standard Model of particle physics?

Good. But it will evolve rather more than you might expect. Some aspects of it are solid, other aspects less so. For example see A Zeptospace Odyssey: A Journey into the Physics of the LHC by Gian Francesco Giudice. He's a legit CERN guy, and he talks about the Higgs sector being relatively weak. If you've bought books from Amazon.co.uk you can do a search-inside on "higgs sector" in quotes. See http://www.amazon.co.uk/gp/product/0199 ... sib_rdr_dp and look at page 174. What you read is this:

"The Higgs sector is that part of the theory that describes the Higgs mechanism and contains the Higgs boson. Unlike the rest of the theory, the Higgs sector is rather arbitrary, and its form is not dicated by any deep fundamental principle. For this reason the structure looks frightfully ad-hoc".

He goes on to talk about 13 adjustable parameters, and lower down on the page gives a qualification for "the mystery of mass" that IMHO is used rather excessively in promotional material. It's actually "the mystery of 1% of mass". There are some other issues too. QED is what's called a perturbative theory where higher order terms get smaller and smaller and you can safely neglect them. However QCD is non-perturbative, and this will have an impact on the quark model. It won't be dispensed with, but again will evolve into something rather different to current understanding.

[Farsight]

The problem is that you don't exactly explain your points. For instance, you claim that the electron isn't well understood. You don't provide any evidence for this. So I will ask you this; why is it that the electron isn't well understood? What about it don't we understand? I don't want to make it seem that your opinion is meaningless. I'm simply trying to understand why you make the objections that you do and then decide wether or not those objections are misguided. I do respect your points, but I merely wish to see why you make them.

It's usually considered to be an elementary pointlike particle with instrinsic spin, which doesn't adequately address pair production and annihilation or electron angular momentum or magnetic dipole moment along with finer details. Have a look at the Stern-Gerlach experiment and see where it says:

"If the particles are classical, "spinning" particles, then the distribution of their spin angular momentum vectors is taken to be truly random and each particle would be deflected up or down by a different amount..."

The experiment shows that this doesn't happen, so we know the particles aren't spinning spheres. However the article goes on to say:

"Electrons are spin-1⁄2 particles. These have only two possible spin angular momentum values, called spin-up and spin-down. The exact value in the z direction is +ħ/2 or −ħ/2. If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast."

There's actually nothing wrong with that, but there then follows a non-sequitur:

"The speed of rotation would be in excess of the speed of light, 2.998×10^8 m/s, and is thus impossible. Thus, the spin angular momentum has nothing to do with rotation and is a purely quantum mechanical phenomenon. That is why it is sometimes known as the "intrinsic angular momentum."

It's fair enough to say that the electron isn't rotating like a planet, but there is no justification for asserting that spin angular momentum has nothing to do with rotation at all. The rotation might take a different form. For example, imagine a particle as something like a globe, the sort of thing you'd see in a geography classroom. Give it a spin so it's spinning like a planet. Now give it another spin in another orientation. You have two choices as regards this new spin direction, this way ↓O↑ or that way ↑O↓. After this you can't really say which way its spinning, because the spin axis is spinning. Throw it through the Stern-Gerlach inhomogeneous magnetic field, and there's only two outcomes, not the range of outcomes you would expect from planets spinning on an axis with a variety of orientations. Another example of this complex spin is given by the moebius strip, which demands two trips round the strip to return to the original orientation and position. There's papers on this sort of thing which IMHO have not received adequate attention. See http://arxiv.org/abs/physics/0512265 or http://www.cybsoc.org/electron.pdf and http://www.cybsoc.org/electremdense2008v4.pdf. I'm not saying these answer all the questions, but I do think they offer a coherent outline that's worth pursuing as opposed to settling for elementary and intrinsic.

[newolder]

(electron) It's usually considered to be an elementary pointlike particle with instrinsic spin ...

(electron) that is generated by circulatory motion of a mass-less particle at the speed of light.

Okay... where does electron rest mass and Coulomb electric charge emerge as testable predictions from this 'theory of many symbols'?

[Farsight]

In that form, topological field theory cannot be correct -- the quark model is VERY well-established.

It's been possible to calculate the proton and neutron masses with it to within about 2%:
[0906.3599]Ab-initio Determination of Light Hadron Masses

It's also possible to get the proton and neutron magnetic-dipole moments to within about 10%:
[1001.1131] Extracting Nucleon Magnetic Moments and Electric Polarizabilities from Lattice QCD in Background Electric Fields

There have been efforts to determine other observable features, like the "axial charge" (involved in weak interactions) and the "charge radius" (average spread of electric charge), though they have not been as successful:
[1002.0925]Status and prospects for the calculation of hadron structure from lattice QCD

Can topological field theory come close in either case?

To be honest, I don't know. But note that the first paper says "The ψ fields also have an additional “color” index in QCD, which runs from 1 to 3" and later says "only three input parameters are required: the light and strange quark masses and the coupling g." This is talking about wavefunction, and those input parameters mean it isn't quite "from the beginning". The way I think it will play out is that quarks gradually morph back into partons or "elements of wavefunction topology", and the standard model gets improved physical meaning that makes it better all round. The big step is to say the wavefunction is what the particle is, not the probability of where a particle can be found. Here's an illustration to try to get this across:



That's the trefoil knot. If you look in a table of knots, it's the next-simplest knot after the trivial knot. Trace it round starting from the bottom left and look at the directions of the crossing-over points. (I say crossing-over rather just crossing points so you don't double-count). The crossing-over directions are up, up, and down, just like the quarks in a proton. Now imagine it's made of rubber, grab it, and pull at one of the loops. It gets harder and harder to stretch it out. That's rather like the bag model of quark confinement. If you threw a rock at it, it might catch in one of the loops which is deformed elastically into a v before the rock bounces back, so the loop looks pointlike in a scattering experiment. If you throw a machete at it and cut one of the loops, none of the loops persist. Hence no free quarks.

I'd say string theory started off well in that it took a step away from point particles, and it introduced open and closed things. But rather than seeing bosons and fermions as open and closed elements of wavefunction, it went too far into tiny vibrating strings and later 11-dimensional branes. It's like it missed the turn-off that says "this way to complete the standard model". IMHO if somebody had looked harder at the electron and pair production in the early days, things might have turned out very different.

[newolder]

The big step is to say the wavefunction is what the particle is

What is the particle? The particle is the wavefunction.
What is the wavefunction? Numbers.
The particle is numbers?
Probably.

What natural length scale emerges when this theory sets g = 1?

[Nautilidae]

It's usually considered to be an elementary pointlike particle with instrinsic spin, which doesn't adequately address pair production and annihilation or electron angular momentum or magnetic dipole moment along with finer details. Have a look at the Stern-Gerlach experiment and see where it says:

"If the particles are classical, "spinning" particles, then the distribution of their spin angular momentum vectors is taken to be truly random and each particle would be deflected up or down by a different amount..."

The experiment shows that this doesn't happen, so we know the particles aren't spinning spheres. However the article goes on to say:

"Electrons are spin-1⁄2 particles. These have only two possible spin angular momentum values, called spin-up and spin-down. The exact value in the z direction is +ħ/2 or −ħ/2. If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast."

There's actually nothing wrong with that, but there then follows a non-sequitur:

"The speed of rotation would be in excess of the speed of light, 2.998×10^8 m/s, and is thus impossible. Thus, the spin angular momentum has nothing to do with rotation and is a purely quantum mechanical phenomenon. That is why it is sometimes known as the "intrinsic angular momentum."

It's fair enough to say that the electron isn't rotating like a planet, but there is no justification for asserting that spin angular momentum has nothing to do with rotation at all. The rotation might take a different form. For example, imagine a particle as something like a globe, the sort of thing you'd see in a geography classroom. Give it a spin so it's spinning like a planet. Now give it another spin in another orientation. You have two choices as regards this new spin direction, this way ↓O↑ or that way ↑O↓. After this you can't really say which way its spinning, because the spin axis is spinning. Throw it through the Stern-Gerlach inhomogeneous magnetic field, and there's only two outcomes, not the range of outcomes you would expect from planets spinning on an axis with a variety of orientations. Another example of this complex spin is given by the moebius strip, which demands two trips round the strip to return to the original orientation and position. There's papers on this sort of thing which IMHO have not received adequate attention. See http://arxiv.org/abs/physics/0512265 or http://www.cybsoc.org/electron.pdf and http://www.cybsoc.org/electremdense2008v4.pdf. I'm not saying these answer all the questions, but I do think they offer a coherent outline that's worth pursuing as opposed to settling for elementary and intrinsic.

I don't understand how this shows that electrons aren't well understood. All you've shown is that electrons aren't well understood classically. This is the entire point of quantum mechanics. You're attempting to show that because you cannot describe electron spin in terms of classical angular momentu, spin isn't well understood. Wrong. The problem with your argument is that electrons aren't spinning spheres; they are points. The precession of the electron can't be described by a spinning globe; a spinning globe is a classical object. In QED, the electron spin, or the quantum mechanical EQUIVALENT of classical angular momentum, is describe by virtual photons affecting the motion of the electron. This is why spin is intrinsic; it's the result of the electron's own electromagnetic field. As for the direction of the spin: of course there aren't a range of spin directions like in the situation of a spinning globe; globes are not quantum objects. The reason that spin can only be up or down is due to quantum mechanical probabilities. This isn't experienced by the spinning globe.

You've not shown that electrons aren't well understood. You've shown that you don't approve of our current explanations. This isn't to say that your opinion is invalid, but you certainly haven't shown that the electron isn't well understood.

[Nautilidae]

To be honest, I don't know. But note that the first paper says "The ψ fields also have an additional “color” index in QCD, which runs from 1 to 3" and later says "only three input parameters are required: the light and strange quark masses and the coupling g." This is talking about wavefunction, and those input parameters mean it isn't quite "from the beginning". The way I think it will play out is that quarks gradually morph back into partons or "elements of wavefunction topology", and the standard model gets improved physical meaning that makes it better all round. The big step is to say the wavefunction is what the particle is, not the probability of where a particle can be found. Here's an illustration to try to get this across:



That's the trefoil knot. If you look in a table of knots, it's the next-simplest knot after the trivial knot. Trace it round starting from the bottom left and look at the directions of the crossing-over points. (I say crossing-over rather just crossing points so you don't double-count). The crossing-over directions are up, up, and down, just like the quarks in a proton. Now imagine it's made of rubber, grab it, and pull at one of the loops. It gets harder and harder to stretch it out. That's rather like the bag model of quark confinement. If you threw a rock at it, it might catch in one of the loops which is deformed elastically into a v before the rock bounces back, so the loop looks pointlike in a scattering experiment. If you throw a machete at it and cut one of the loops, none of the loops persist. Hence no free quarks.

I'd say string theory started off well in that it took a step away from point particles, and it introduced open and closed things. But rather than seeing bosons and fermions as open and closed elements of wavefunction, it went too far into tiny vibrating strings and later 11-dimensional branes. It's like it missed the turn-off that says "this way to complete the standard model". IMHO if somebody had looked harder at the electron and pair production in the early days, things might have turned out very different.

What exactly can topological field theory accomplish that string theory cannot accomplish? What can topological quantum field theory accomplish that normal quantum field theory cannot in terms of completing the standard model?

EDIT: I should probably thank you. It is quite pleasant to have some present reasonable arguments rather than ignoring the arguments that I make. It was much needed

[Farsight]

Okay... where does electron rest mass and Coulomb electric charge emerge as testable predictions from this 'theory of many symbols'?

This is where it gets interesting. They don't, they come out as variable, along with all the constants. The fine structure constant is a good example of this. See http://physics.nist.gov/cuu/Constants/alpha.html:

"Thus α depends upon the energy at which it is measured, increasing with increasing energy, and is considered an effective or running coupling constant. Indeed, due to e+e- and other vacuum polarization processes, at an energy corresponding to the mass of the W boson (approximately 81 GeV, equivalent to a distance of approximately 2 x 10^-18 m), (mW) is approximately 1/128 compared with its zero-energy value of approximately 1/137. Thus the famous number 1/137 is not unique or especially fundamental."

The fine structure constant is usually expressed as α = e²/4πε0hc where e is the "effective charge". This e varies. The effect of the electron's charge varies with energy, or in other words, according to the environment it's in. Sounds unusual, but it's true. In QED it's explained in terms of "screening". But flip it around and say that the electron has always got unit charge because of the spin 1/2. Then if α varies and e doesn't because you've pegged it at -1, things like the vacuum permittivity of free space ε0 must secretly vary. Now take a look at Mordehai Milgrom's New Physics at Low Accelerations (MOND): an Alternative to Dark Matter at http://arxiv.org/abs/0912.2678 and note this line on page 5:

"We see that the modification of GR entailed by MOND does not enter here by modifying the ‘elasticity’ of spacetime (except perhaps its strength), as is done in f(R) theories and the like."

I don't think Milgrom is quite right with MOND, but the point is that here's talk of gravity and "the strength of space". That's what everything else hangs on. If space is stronger, then in the topological interpretation, it's "harder to tie a knot in it". In this respect, proton mass is essentially a relic. Note that the fine structure constant gives the relative strength of the electromagnetic force as opposed to the strong force. See http://hyperphysics.phy-astr.gsu.edu/HB ... ouple.html re coupling constants for a bit more on this. Now look at the wiki article where it says the fine structure constant is also:

"The ratio of two energies: (i) the energy needed to overcome the electrostatic repulsion between two electrons when the distance between them is reduced from infinity to some finite d, and (ii) the energy of a single photon of wavelength λ = 2πd"

That's a signal indicator that the strong force is lurking there even in photons and electrons. Hence when you conduct low-energy proton-antiproton annihilation into two neutral pions which promptly decay into two photons, the strong force doesn't disappear, it just becomes invisible, in "the strength of space". The reference to gravity is of crucial importance here, because if the fine structure constant changes ever so slightly with gravitational potential, that means gravity is merely a gradient in the relative strength of the electromagnetic force and the strong force. IMHO that's how it unifies, which will fill in another box for the standard model.

Sorry for rabbiting on. It's just that this is interesting stuff.

[newolder]

Okay... where does electron rest mass and Coulomb electric charge emerge as testable predictions from this 'theory of many symbols'?

This is where it gets interesting. They don't, they come out as variable, along with all the constants. The fine structure constant is a good example of this. See http://physics.nist.gov/cuu/Constants/alpha.html:

"Thus α depends upon the energy at which it is measured, increasing with increasing energy, and is considered an effective or running coupling constant. Indeed, due to e+e- and other vacuum polarization processes, at an energy corresponding to the mass of the W boson (approximately 81 GeV, equivalent to a distance of approximately 2 x 10^-18 m), (mW) is approximately 1/128 compared with its zero-energy value of approximately 1/137. Thus the famous number 1/137 is not unique or especially fundamental."

The fine structure constant is usually expressed as α = e²/4πε0hc where e is the "effective charge". This e varies. The effect of the electron's charge varies with energy, or in other words, according to the environment it's in. Sounds unusual, but it's true. In QED it's explained in terms of "screening". But flip it around and say that the electron has always got unit charge because of the spin 1/2. Then if α varies and e doesn't because you've pegged it at -1, things like the vacuum permittivity of free space ε0 must secretly vary. Now take a look at Mordehai Milgrom's New Physics at Low Accelerations (MOND): an Alternative to Dark Matter at http://arxiv.org/abs/0912.2678 and note this line on page 5:

"We see that the modification of GR entailed by MOND does not enter here by modifying the ‘elasticity’ of spacetime (except perhaps its strength), as is done in f(R) theories and the like."

I don't think Milgrom is quite right with MOND, but the point is that here's talk of gravity and "the strength of space". That's what everything else hangs on. If space is stronger, then in the topological interpretation, it's "harder to tie a knot in it". In this respect, proton mass is essentially a relic. Note that the fine structure constant gives the relative strength of the electromagnetic force as opposed to the strong force. See http://hyperphysics.phy-astr.gsu.edu/HB ... ouple.html re coupling constants for a bit more on this. Now look at the wiki article where it says the fine structure constant is also:

"The ratio of two energies: (i) the energy needed to overcome the electrostatic repulsion between two electrons when the distance between them is reduced from infinity to some finite d, and (ii) the energy of a single photon of wavelength λ = 2πd"

That's a signal indicator that the strong force is lurking there even in photons and electrons. Hence when you conduct low-energy proton-antiproton annihilation into two neutral pions which promptly decay into two photons, the strong force doesn't disappear, it just becomes invisible, in "the strength of space". The reference to gravity is of crucial importance here, because if the fine structure constant changes ever so slightly with gravitational potential, that means gravity is merely a gradient in the relative strength of the electromagnetic force and the strong force. IMHO that's how it unifies, which will fill in another box for the standard model.

Sorry for rabbiting on. It's just that this is interesting stuff.

The constants of nature measured since Galileo are an interesting read. But you may have misunderstood. I asked for the mass and charge of an electron. What does your wibble predict in kilogrammes and Coulombs for these things?

[lpetrich]

Another bit of evidence for the quark structure of protons: Parton (particle physics) (Wikipedia) -- from collision experiments, one finds lots of evidence that protons are composite.

Yes, they're composite, but look at the title of your link. It says Partons. That's what quarks are, they're parts, like Feynman said. That's why we've never seen a free quark.

We don't see free quarks because the QCD force becomes very strong at distances above 10-15 m, around the sizes of the light hadrons. When one tries to separate quarks by that distance, it becomes energetically favorable to pull ordinary-quark-antiquark pairs out of the vacuum. That's been demonstrated numerous times in collisions with energies much greater than 1 GeV. Quarks and gluons make jets of hadrons behind them. Free quarks and gluons have never been observed, and this strong-force-becoming-superstrong effect is likely responsible for producing this "quark confinement".

Furthermore, the QCD interaction's "charge" declines enough at distances much less than 10-15 m to allow quarks to travel nearly freely -- asymptotic freedom. At energies of about 100 GeV, the QCD equivalent of the electromagnetic fine-structure constant is about 1/9. Not quite 1/137, but still much less than 1.

That's been abundantly observed in the more energetic particle accelerators.

(the Higgs sector...)
I will concede that that's still unconfirmed, but that does not affect the success of the rest of the Standard Model.

He goes on to talk about 13 adjustable parameters, and lower down on the page gives a qualification for "the mystery of mass" that IMHO is used rather excessively in promotional material. It's actually "the mystery of 1% of mass".

The Standard Model has 19 free parameters:
The Higgs mass and self-interaction parameters: 2
The Higgs couplings with the elementary fermions (eigenvalues and mixing angles): 13
The gauge couplings: 3
The QCD CP-violation phase: 1
Total: 19

There are some other issues too. QED is what's called a perturbative theory where higher order terms get smaller and smaller and you can safely neglect them. However QCD is non-perturbative, and this will have an impact on the quark model. It won't be dispensed with, but again will evolve into something rather different to current understanding.

QCD is mostly perturbative at small-enough distances, but its nonperturbative effects become significant at 10-15 m. Furthermore, nonperturbative QCD can be handled with Lattice Gauge Theory, which requires an enormous amount of number crunching to get results.

From the Standard Model:

• Lattice QCD successes
• Quark confinement
  [*}Quark asymptotic freedom
• Hadron jets
• Deep-inelastic-scattering results
• Electromagnetic and weak properties of hadrons

By contrast, the trefoil model of the proton is a dismal failure.

[lpetrich]

It's fair enough to say that the electron isn't rotating like a planet, but there is no justification for asserting that spin angular momentum has nothing to do with rotation at all. The rotation might take a different form. ...

Farsight, electrons are MUCH better understood than what you seem to think.

In particular, electrons are very well described by the Dirac equation, the electrons' counterpart of Maxwell's equations. So how does one get the Dirac equation and Maxwell's equations out of topological field theory. Don't do a lot of hand-waving; give us the derivation.