Recall that the Bilson-Thompson braid diagrams define neutrinos and antineutrinos with three neutral strands. There are four such pictures, with one mirror pair shown below. This is not obvious with $3 \times 3$ circulant permutation matrices, so one does need the braiding. These are Graham D's four neutrinos, and with generation number that makes $12$. Thus there are $8$ lepton and $8$ quark pictures per generation.

8 years ago

The braid group B_3 is embedded into the sl(2,R) as a discrete subgroup. The diagram chase is

ReplyDeleteZ - -> B_3 - -> SL(2,R) <- -π- - PSL(2,R),

where the first two right directed arrows are hook arrows to mean subset embedding. There is also the fibration of a discrete PSL(2Z) into the braid group.

The physical interpretation is a bit troublesome though. If leptons and quarks are composed of preons, or their related cousins called rishons, the binding potential on these particles is very large. The problem is these particles would be difficult to renormalize. This is one problem with QCD, where the “glue” is composed of vector bosons with a field energy comparable to the mass of the quarks. If nature has smaller components which make up leptons and quarks then due to the tiny size and E_{Δx} = ħ/Δx means this energy is much larger than the masses of the particles.

Maybe, if Δx is comparable to the Planck scale then holography takes over so that this high energy physics is equivalent to low energy physics. This might prevent this sort of catastrophe. Mathematically, maybe in the adjoint representation of the SL(2,R) the metaplectic or symplectic elements corresponding to B_3 are some symplectic or canonical transformation of standard U(1)xSU(2)xSU(3) physics.

ReplyDeleteThe physical interpretation is a bit troublesome though ...If you like, you can picture a holographic mechanism going on. This is not supposed to be gauge theory: it is about quantum gravity.

I have seen these in Baez blog. I want to try to understand what it is about, sry if I take place.

ReplyDelete- It is the information in the quantum states. I saw it was useful for quantum computers to translate a quantum state into 'bits'.

- a method to translate a given quantum state into a tensor network, and how this places a nice handle on a few things and extends the state of the art in tensor network theory.

- and also current existing graphical methods in quantum many-body physics - (as the 3 generations of fermions?) This is classic physic, so it is then the oscillation matter - antimatter too, as your matrix shows.

- “Modelling tensor interchange phenomena by homotopies in 2 dimensions” is just a super-groovy way to say that you can wiggle string diagrams around without changing their meaning, (this I cannot understand, it says it is because the changing agent is a function)

- the antimatter is then also bosons, forces? Quantum states are bosons (non-local) too. So here you have the trinity present, boson, anyon, fermion. The anyonic zone is the interesting one, the one that react and oscillate?

- outcome is stable configurations, as Lie-groups, qutrit tetractys etc. Pythagoras triangulars?

- the hierarchy of weak n-categories and their generalisations. - how is the strong and weak forces distinguished?

Can you please write a summary post, so I would understand too, although I am no math-freak.

Lawrence re- "the physical interpretation is..." rather than comparable the eight colour charged gluon fields represent more than >95% the mass energy of the 3 quarks. The antishielding effect increases the mass energy as the quarks are "stretched". For the leptons the electric charge is shielded and the classic electron radius, which is modelled on the radius of a spherical shell, were all the electric charge a consequence of electron mass. At higher energy the electron charge does run and charge increases but the planck charge^2 =137.036*e^2 remains constant. Were e 3 fold higher the atom is no longer stable and everyting would be neutrons. However, were e 3 fold lower alpha 137 runs up by 9 fold. Real atomic properties change and the Bohr radius increases by the square of charge, 9 fold in this instance, electron mass drops, the Rydberg energy drops by 3^5 etc.

ReplyDeleteThe neutrino isn't shielded nor antishielded etc and like the electron there's no experimental evidence for structure down to 10^-18m.

Carl and Marni's first post on the Minos mass differences came at a time when many gurus were predicting catastrophe were the results correct.

The fascinating thing about the neutrino masses were those first masses of 0.000383ev electron neutrino and 0.00117eV electron antineutrino. The L antineutrino is maximally specific in its handedness in the standard model. Whether or not the SM is incomplete is by the way because electron neutrino has a different mass charge but is still no more incomplete SM as the other. Those mass charges and other charge are empirically measured. These two pairs are not antiparticles of each other, but they would be true antiparticles if there were two chiral forms of each, thus L and R antineutrino for instance. These would annihilate. The antineutrino mass is fascinating re- its temperature appearance threshold from vacuum energy and the annihilation black body radiation was astonishing, t lamda max 2.73 Kelvin!In SUSY a spin change is associated with new particles with higher mass charge. These neutrinos predict no spin change but lower mass generations! What do you do with an R neutrino in a SM; it has to be associated with its lepton and quark partners. This light neutrino could be associated with an allo electron of ca 1/3 electric charge etc. These would produce allo atoms with 1/243 the ionisation 13.6ev energy of the H atom.

Whatever inner complex space dimensional structure you compartmentalise this energy it's just as valid for these alloforms.

These four electron neutrinos may cross hybridise or couple L with R to form a mass charge dipole, to give LR and RL forms or perhaps a tetrahedral tetramer where the chiral forms might form a 3D form in real space. There's no need to suddenly jump down to 14 orders of magnitude to the Planck scale scale.

Unfortunately, I'm wholly ignorant of the mathematical nomenclature lol.

The holographic principle is an aspect of quantum gravity. It is where there isometries on the boundary or horizon of spacetime or AdS are equivalent to the conformal symmetries of gauge fields.

ReplyDeleteUlla, the use of such diagrams is now a huge field ... in mathematics, physics, computer science etc ... and all based on the categorical interpretation of such diagrams. I'm afraid there is no short cut to studying a little of the mathematics. On the other hand, the physics that we discuss is utterly different to most of this work, as you well appreciate. So it might be less confusing if you stuck to simple mathematics texts/papers and avoided the garbage physics that is often discussed. Sorry to be no more helpful at this point, but I have provided several lifetimes worth of links to read!

ReplyDeleteLawrence, our holographic principle does not HAVE to resemble the usual one! Please at least take a look at some of these numbers ...

ReplyDeleteTo my humble opinion one should be very careful in distinguishing between topology and geometry. Braids belong to the realm of topological physics. The basic aspects of elementary particle is its mass and belongs to geometry.

ReplyDeleteI have no doubt that braids are an essential element of fundamental physics and they are emerge quite concretely in quantum TGD. They do not have however anything to do with the known elementary particle numbers unless one refuses to accept what is known about the notion of four-momentum and mass. Many particle physics is the natural place for braids and topological quantum computation and its analog even at fundamental parton level would be the concrete application for braids. Lubos has expressed this view using more colorful language when he as stated his opinion about attempts in this direction.

The objections against the reduction of elementary particle numbers to topological characteristics of braids are quite strong. What matters are the gauge symmetries of the standard model and they belong to the realm of geometry, not topology. The recipes for the identification of standard model quantum numbers in terms of braid characteristics is therefore not enough: one should also how the gauge symmetries emerge. Otherwise there is infinitely long way to expressions for scattering amplitudes testable at LHC.

I do not understand why you are speaking about neutrino masses as something known with many digits. To my best knowledge neutrino masses are very badly known. The data is only bounds to mass squared differences and experiments suggests that these differences can appear in several scales. In TGD framework this comes as a prediction of p-adic length scale hypothesis - also in the case of quarks. The mass difference between neutrino and antineutrino could be understood without actual CPT breaking as a p-adic mass scale difference induced by different measurement arrangements for antineutrino and neutrino mixing.

To summarize with something which I regard as realism. A new successful theory cannot be created from vacuum. It cannot throw those parts of existing theories which work excellently into a paper basket. A successful new theory must generalize and unify, provide a deeper understanding and new interpretations. It can predict entirely new worlds but it must have precise connection with existing theories and be able to reproduce what is good in them.

Matti, if you ever actually bothered to read anything here you would know that Graham is referring to the Koide matrix PREDICTIONS for the neutrino masses. And I have heard of gauge theories.

ReplyDeleteFor those who simply can't think about emergent gauge theories without using the tools of gauge theory, one nice place to begin is with Xiao-Gang Wen's string pictures.

ReplyDeleteTo Kea: this is just what I meant. You are talking as if the Koide predictions had been verified. Koide mass formula is just an ad hoc numerological proposal for neutrino masses without any physical argument supporting it and one can invent endless variety of similar proposals in absence of empirical data.

ReplyDeleteMy purpose is not discourage but the emergence of metric concepts from purely topological ones is a Muenchausen effect and belongs to the same category of wishful romantic thinking as the emergence of continuum theory like GRT from a discrete theory.

The effective field theory wisdom giving hopes about connection of super string theory with experimental physics represents a very refined form of this "put it in by hand when no one is looking" theorizing. Very natural when string models as such tell nothing about our physical world.

I am not free of this sin. For first five years of TGD I constructed quasi-classical path integral arguments based on guesses for effective actions showing this and that until I was mature to accept the fact that neither path integral approach nor effective action approach makes sense in TGD framework. After this it took only few years to find the formulation of the geometry of world of classical worlds which I believe to capture the essentials. The lesson I learned is that we have extremely strong tendency to project to our theories something which we want to be there.

Graham D.: I am presuming you propose here that the neutrino is composed of preons with a charge, but where the net charge is zero. That would seem to suggest something like a magnetic moment is associated with the neutrino. I will have to ponder this a little bit, for I am not sure what is meant by “electric shielding” in what you wrote.

ReplyDeleteMatti, before you assume that I have not learned a few lessons myself, you should better understand the arguments for the Koide quantum numbers.

ReplyDeleteLawrence: No I'm not presuming a preon model although that comes from the prediction by Carl for lepton masses. As an analogue, like the neutron, where the the net electric charge is zero the nuclear g factors for proton and neutron are very different and measurable. The predicted neutrino masses display different mass charges within each generation! Quark colour charge is not electric charge but I presume they are modelled as a coulombic interaction.

ReplyDeleteBy shielding I mean the concept of screening in superconductivity theory whereby the full strength of the charge is reduced by the presence of virtual particle charge as per Wilczek's explanation.

Conceptually, my interest arose from attempting to predict what dark matter is. Were you to discover a new stable form of matter with reduced electric charge, some other attributes would scale accordingly. Thus, our H atom would have allo analogue(s). It would however have different atomic properties eg. Bohr radius and different electromagnetic emission and absortion frequencies and chemical properties. However, at least one frequency, the socalled Hydrogen 21cm or 1420.4 MHz frequency would remain invariant, if the allo gI ratio for the alloproton is conserved . In the rotation profiles of the local galactic group of individual galaxies there's a huge abundance of H atoms beyond the star envelopes in a position where gravitationally it wouldn't be expected. Yet an allo form of matter, that is allo hydrogen, would qualitatively fit the rotation curve profile, and quantitatively were the alloH to comprise an electron with -1/3 charge and alloproton with +1/3 electric charge.

Well, I am apparently the fifth wheel under the vagoon here, but some reflections nevertheless. Take it or leave it.

ReplyDeleteWhen we talk of the lightcone it is the topological part and the geometrical part. In my mind geometry IS topological, because the same parts are repeated again and again. A trinity is a good beginning, and Keas figures are geometrical too. Cones within cones still follows this border? Entropy is not changed, only density and information? Topology is never complete. Change is needed.

Outside the lightcone is the Sea of possibilities/potentials, what I would call the quantum chaos, which Goldfine is so fond of. Also chaos has braidings, but randomly, entropically, giving rise to very little, but sometimes it happen (Wolfram).

If we take the analogy with the bicycle parts that God is scrambling when he creates the bicycle/Universe, we know that it isn't the scrambling force that is the important thing because the entropy grows more by more force. Instead the force must be directed, working against the entropy. So chaos cannot be pure chaos. No mexican hat with chaos.

Or look at graphene and its energy gap, clearly 3 phases. Kea had a figure that could be a gap.

The rotation? 2 pi or 4 pi? What happens with 4 pi?

I have looked at Wen's pictures, and in my mind they can be compared to the skyrmion model. Maybe it would be a possibility here? It suits also TGD?

I have big confidence in Mattis thinking, but also he can be wrong/blind sometimes. Matti, I just asked you to look at this and scramble the pieces a little to see what would be created :).