Lee Smolin's LQG may reproduce the standard model

  • #51
The concept of V(1)=0 for idempotents is intriging.

The MathWorld page on Idempotent appears to suggest that opeartors such as minus [-] or absolute value [| |] could also seve to satisfy x^2=x
suggesting that -x may be an idempotent or some type of relative?
http://mathworld.wolfram.com/Idempotent.html
 
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  • #52
The structure of idempotents of Clifford algebras is related to the elements that square to unity. Given the set of real functions with multiplication given by product of composition, an element that squares to unity (i.e. f(x)=x) is negation, that is, the function f(x) = - x. From that function I guess the generated idempotents would be f(x) = (x-x)/2 = 0 and f(x) = (x+x)/2 = x. In other words, the Clifford algebraic method of defining idempotents from roots of unity doesn't work so well here. But all this is kind of off topic. I think that there is way too much math that is done for the pleasure of finding unimportant relationships between things of not much importance. I guess I'll continue to the next step in the derivation of the structure of the elementary fermions.

With the above definition of potential energy, it is apparent that a simple solution to it is to just have a complete set of annihilating primitive idempotents. Such a complete set adds to unity, so would have a potential energy of zero. But this sort of solution is not so simple. It is made up of a collection of individual primitive idempotents, and these primitive idempotents cannot stay together becaue they will move in different directions. Such a solution would minimize energy, but only for a moment, it would fly apart. The problem is that the particle has to reverse its direction, and using the spinor probability function P = (1+\cos(\theta))/2, the probability of this is zero.

The simplest wave equation in a Clifford algebra is the "generalized massless Dirac" equation. The Dirac equation includes mass, and this makes it somewhat more complicated than what will be described here. Eliminating mass, as is appropriate for a theory that treats mass as an interaction between particles gives the simple equation:

\nabla \Psi = 0

The left hand side is the usual Dirac operator, generalized to a Clifford algebra. Rather than writing it in Dirac's gamma notation, I will write it in notation that brings out the geometric quality of the equation:

(\hat{x}\partial_x + \hat{y}\partial_y + \hat{z}\partial_z + \hat{s}\partial_s + \hat{t}\partial_t) \Psi = 0

In the above, s is a coordinate corresponding to a hidden dimension. This single hidden dimension (used like Kaluza-Klein in some ways) is needed to get the elementary particles as will be seen later. For now, treat it as just like the other spatial dimensions. Since we're working on a mass theory for point particles (i.e. a finite dimensional system) we don't need to treat s as special in any way. The various hatted objects are the canonical basis vectors for the Clifford algebra. In the Dirac notation, these are \gamma^\mu. They square to the signature, in the order above this is [++++-], and they anticommute with each other.

If \Psi has no space-time dependence on s, then you can eliminate that element and what you have would look suspiciously like the usual Dirac equation. But it would not be so, for two reasons. First, even though Psi has no dependence on the coordinate s, its wave function still carries the extra degrees of freedom associated with the 2x larger Clifford algebra that s implies. Second, Psi is taken to be a member of the Clifford algebra, rather than a spinor. This is similar to the "square spinor" discussed by Lounesto in his classic text on spinors, but without the restriction that Psi be the square of a spinor.

Upgrading Psi to be a Clifford algebra element instead of a spinor means that there are a lot more degrees of freedom available in Psi. In terms of relating the above "massless generalized Dirac" equation to the usual Dirac equation, this means that in a single equation we are simultaneously writing the Dirac equations for a bunch of different spin-1/2 particles. For an example of the literature where this is done (but with spinors instead of the density matrix formalism that I follow) see Trayling and Baylis, and citations: http://arxiv.org/abs/hep-th/0103137
Since Trayling and Baylis model the fermions directly, rather than use a preon model, they require a much larger number of hidden dimensions, and of course they do not get the three generations.

The classic approach to putting the Dirac equation into geometric form is the famouse "Dirac-Hestenes" equation. This formula looks very similar to the above, except that Psi is restricted to an even subalgebra. You can learn more about this by searching for "Dirac-Hestenes" on arXiv. My favorite article on this is Bayls' critque of another paper on the subject: http://www.arxiv.org/abs/quant-ph/0202060 .

Psi is composed of multiple copies of the Dirac equation. If we are given a solution for the massless generalized Dirac equation and we want to split it into a set of Dirac equations, (note that there are an infinite number of ways of doing this), we can use a complete set of primitive idempotents.

In adding one hidden dimension, the number of primitive idempotents in a complete set has doubled, so instead of the four that one would have for the Dirac algebra, we will have eight. I will write these as \rho_{---}, \rho_{--+}, ... \rho_{+++}. To make sure that the notation is familiar to the reader, let me write down the natural primitive idempotents (i.e. the diagonalized PIs) for some particular representation of the Dirac algebra.

A quick google search found gamma matrix definitions at http://www.answers.com/topic/gamma-matrices so I look for two diagonal matrices, \mu_1, \mu_2 that (a) square to unity, and (b) commute, and (c) cannot be written in terms of one another. These are the "commuting roots of unity" that are so important for Clifford algebra primitive idempotents. Since (b) and (c) are trivial for diagonal 4x4 matrices, the solution is:

\mu_1 = i \hat{t} = \gamma^0 = \left(\begin{array}{cccc}<br /> 1&amp;0&amp;0&amp;0\\0&amp;1&amp;0&amp;0\\0&amp;0&amp;-1&amp;0\\0&amp;0&amp;0&amp;-1\end{array}\right)

\mu_2 = i \hat{x} \hat{y} = i\gamma^1\gamma^2 = \left(\begin{array}{cccc}<br /> 1&amp;0&amp;0&amp;0\\0&amp;-1&amp;0&amp;0\\0&amp;0&amp;1&amp;0\\0&amp;0&amp;0&amp;-1\end{array}\right)

In the above, I've also written in the geometric description of the roots of unity in hat (Clifford algebra) form which I prefer to use. We can now write the four primitive idempotents in terms of the above matrices as:

\rho_{--} = (1-\mu_2)(1-\mu_1)/4
\rho_{-+} = (1-\mu_2)(1+\mu_1)/4
\rho_{+-} = (1+\mu_2)(1-\mu_1)/4
\rho_{++} = (1+\mu_2)(1+\mu_1)/4

or
\rho_{\pm\pm} = (1\pm\mu_2)(1\pm\mu_1)/4

Adding the hidden dimension s doubles the number of primitive idempotents (i.e. adds one more commuting root of unity) so we can write them as:

\rho_{\pm\pm\pm} = (1\pm\mu_3)(1\pm\mu_2)(1\pm\mu_1)/8

where \mu_3 is a root of unity that commutes with the other two and isn't in the group they generate. (In the above example, we could have \mu_3 = i\hat{z}\hat{s} or \mu_3 = \hat{z}\hat{s}\hat{t} but not \mu_3 = \hat{x}\hat{y}\hat{t} as this is in the group generated by the other two. )

With all that preparation out of the way, one splits the generalized Dirac equation into Dirac equations by right multiplying by the primitive idempotents. But there are an infinite number of ways of choosing those primitive idempotents.

Plane Wave Solutions and Feynman's Checkerboard

The propagators of our theory have to preserve particle identity. In the usual model, with a propagator devoted to each particle type, this is not a problem, but with a single Dirac equation that handles multiple particls, it is important that they not leak into each other. Accordingly, we now solve for the primitive idempotents that correspond to plane wave solutions to the generalized Dirac equation.

Let Psi be a function of z and t that satisfies the generalized massless Dirac equation as follows:

\Psi(x,y,z,s,t) = \Psi_0\; \sin(z-ct).

where \Psi_0 is a Clifford algebra constant and c is a real constant (to be interpreted as the speed of the wave). Applying this to the massless generalized Dirac equation gives:

(\hat{z} -c\hat{t})\;\Psi_0 = 0.

Multiplying the above equation on the right by \hat{t}, (an operation which is reversible and so does not change the equation's solutions) and rearranging terms by using anticommutation gives:

(-\widehat{zt} +c)\;\Psi_0 = 0.

which has a solution only for c=1:

\Psi_0 = (1 + \widehat{zt})/2.

where the overall sign and the 2 have been chosen to put the answer into idempotent form. To translate this back into the language of the representation of the Dirac algebra linked above, we have:

\Psi_0 = \frac{1}{2}\left(\begin{array}{cccc}<br /> 1&amp;0&amp;-1&amp;0\\<br /> 0&amp;1&amp;0&amp;1\\<br /> -1&amp;0&amp;1&amp;0\\<br /> 0&amp;1&amp;0&amp;1\end{array}\right)

Note that the above matrix is similar to the chirality matrices, (1\pm\gamma^5)/2. If all the off diagonal signs had been +, it would be the projection operator for right handed states, and if all the off diagonal signs had been -, it would be the projection operator for left handed states.

Breaking the above matrix into spinors (i.e. column vectors and ignoring repeats with different arbitrary complex phases), we see that there are two, (1,0,-1,0) and (0,1,0,1), transposed. In this representation of the Dirac algebra, these spinors are the right handed particle and the left handed antiparticle traveling in the +z direction. (I have about a 50% chance of reversing my particle and antiparticle in that last sentence, but it doesn't matter.) The fact that the above projection operator picks out different handed states depending on particles or antiparticles is why I called this quantum number "anti handedness" in post #32 of this thread. In some of my writings, I use "L" and "R" to refer to anti handedness and this can be confusing to people used to dealing with handedness.

When one converts the Dirac equation into an equation appropriate to density matrices, one finds that the density matrix has to be hit on both sides by the operator. I.e. i\partial_t \rho = H \rho -\rho H. For this reason, any density matrix plane wave +z traveling wave solution of the density matrix equivalent to the generalized Dirac equation will have to have the above as an idempotent factor.

We therefore choose \widehat{zt} as one of our three commuting root of unity. In order to match my notes, in which all this was derived sort of backwards, I put:

\mu_3 = \widehat{zt}

For choosing the other two commuting roots of unity, first note that the elements of the Clifford algebra that commute with the above consist of any products of \hat{x},\hat{y},\hat{s},\widehat{zt}.

The above root of unity defines two (non primitive) idempotents, (1\pm \widehat{zt})/2. The + sign gives stuff that is traveling in the +z direction, while the - sign gives stuff traveling in the -z direction. This is reminiscent of the Feynman checkerboard (or chessboard) model of the one-dimensional Dirac propagator: "Feynman, R. P. and A. R. Hibbs. Quantum Mechanics and Path Integrals. New York: McGraw-Hill, 1965". To learn more about this, do a google search for Feynman+checkerboard or Feynman+chess+board or see Tony Smith:
http://www.valdostamuseum.org/hamsmith/Sets2Quarks7.html

Since the Feynman checkerboard model of a (one dimensional!) elementary particle consists of something that alternately goes in two different directions, and since we are looking here at splitting the elementary fermions into right handed and left handed parts (which must go in opposite directions in order to make a particle with spin defined in that direction), our choice of this as a commuting root of unity is very natural. Naively, the spread of the wave function in z is caused by the points at which the particle switches from being left handed to right handed being non deterministic.

But Feynman checkerboard is only a one-dimensional model of a quantum particle. Getting away from the plane wave solutions, actual electrons are 3-dimensional particles (that is, their wave functions spread in all three dimensions). This suggests that in modeling the electron we are going to have to also take into account idempotents for the other two dimensions, that is, (1\pm\hat{xt})/2 and (1\pm\hat{yt})/2. The name that we will use to call the stuff that shares one of these idempotents is "snuark". From this the reader may have realized that snuarks do not obey the Heisenberg uncertainty principle. Instead, only the bound combination of them can do so, and to get uncertainty in all directions requires three snuarks for the left handed particle and three more for the right handed particle. A single pair of snuarks would satisfy the Heisenburg uncertainty principle in one dimension only, and would be classical in the other two. But since the rules we give here allow snuarks to convert from one type to another, such a monstrosity would not be stable.

The necessity of having three snuarks per handed fermion thus comes from the following reasons: (a) to allow the Heisenburg uncertainty principle to apply in all three directions rather than just one, (b) to allow for quarks to be intermediate to the leptons in quantum numbers, that is, to make the quarks and leptons from bound states of three preons, (c) to allow a minimization of the potential energy (to be discussed in next post I guess), and (d) to use up enough degrees of freedom in the Clifford algebra to explain why only two electrons (spin up and down) can fit into a given position (the Pauli exclusion principle for spin-1/2, to be discussed later). In some of this reasoning, there are hints of a sort of classical behavior among the preons.

Carl
 
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  • #53
Hi CarlB

I'm thinking of reviving this thread again soon. What do you think?

:smile:
 
  • #54
I felt kind of bad about hijacking the thread. Do you mean to rejack it back to the original topic? By the way, I put up a new copy of my book, but it's not worth looking at. The major change is that I added the chapter divisions, with poetry.
 
  • #55
I have a question about the original topic.

It basically states that some configurations of pure gravity LQG could behave as particles.

On the other hand we have the work of baratin and Freidel (whose 4-d paper has been realized these days) which is discused in another thread and which states that any "ordinary" point particle feyman diagram can be expresed as an amplitud in a pure LQG spin-foam model.

These two results seem to me very similars in the conclusions, but aparently very diferent in the way they arrive to them. That looks at least I see it so, an invitation to try to search a relation betwen the two aproachs. Anyone is doint it? Or I am missing something and what I wonder makes no sense?
 
  • #56
Sauron said:
...
These two results seem to me very similars in the conclusions, but aparently very diferent in the way they arrive to them. That looks at least I see it so, an invitation to try to search a relation betwen the two aproachs. Anyone is doint it? Or I am missing something and what I wonder makes no sense?

the two approaches differ quite a bit, as you remarked, and they are both unfinished or incomplete. I think it would be difficult to match them up at this point.

Smolin et al's paper IIRC only involves spin NETWORKS, and there remains the problem of specifying how the networks evolve.

The paper by Baratin and Freidel investigates a spinFOAM model, and proves a result about the zero-gravity limit.

In principle the B&F model should have two parameters, h-bar, and Newton G, which one can take to zero and check the behavior.
I believe that they have done half the work: they have shown that if you make G -> 0 you get something recognizable as closed Feynman diagrams. Maybe this result can be strengthened but it is already a positive indication.

But they also now must show that if you do not make G -> 0, but instead make h-bar -> 0, you get something like classical gravity.

You know that Rovelli et al recently put out some work about spinFOAM where they derived gravitons. This is suggestive, but it is no guarantee that B & F, with their spinfoam model, can get classical gravity in the limit of small h-bar.

Speaking not as an expert, and hoping others will correct me if I am mistaken, I would say that B & F paper is very different from Smolin et al in the sense that B & F is closer to having dynamics.

It seems to me that the virtue of the Smolin et al paper is that it gives more or less the right types of particles in a conceptually simple QG scheme. The Smolin picture, I think, is of a spinnetwork evolving by LOCAL MOVES which reconnect nearby vertices in different ways or which insert and remove vertices. To have a structured dynamics, they still must assign amplitudes to these moves, time would presumably be some index of the rate that these local moves are occurring. It is an elegant and evocative picture of the universe which has seeds of ideas for a theory more fundamental than quantum mechanics (see Smolin's most recent preprint) and better adapted to handling cosmology. But I think it is not at a comparable stage of definition so that one could connect it with Freidel et al's work.
 
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  • #57
Kea said:
Hi CarlB

I'm thinking of reviving this thread again soon. What do you think?

:smile:

Bilson updated his article Oct 26, 2006

http://arxiv.org/abs/hep-ph/0503213

A topological model of composite preons
 
  • #58
Kea said:
Hi CarlB

I'm thinking of reviving this thread again soon. What do you think?

:smile:

As Yershov correctly noted in a private email to me,
I personally wrote (or substantially added) this for wikipedia preon
as " 65.26.44.75 " and "216.16.237.110 "

Preon research is motivated by the desire to explain already existing facts (postdiction), which include:

To reduce the large number of particles, many that differ only in charge, to a smaller number of more fundamental particles. For example, the electron and positron are identical except for charge, and preon research is motivated by explaining that electrons and positrons are composed of similar preons with the relevant difference accounting for charge. The hope is to reproduce the reductionist strategy that has worked for the periodic table of elements.
The second and third generation fermions are supposedly fundamental, yet they have have higher masses than those of the first generation, and the quarks are unstable and decay into their first generation counterparts. Historically, the instability and radiactivity of some chemical elements were explained in terms of isotopes. By analogy this suggests a more fundamental structure for at least some fermions. [[1]]
To unify particle physics with gravity, for example, Bilson-Thompson model with loop quantum gravity.
To give prediction for parameters that are otherwise unexplained by the Standard Model, such as particle masses and charges and color, and reduce the number of experimental input parameters required by the standard model.
To provide reasons for the very large differences in energy-masses observed in supposedly fundamental particles, from the electron neutrino to the top quark.
To explain the number of generations of fermions.
To provide alternative explanations for the electro-weak symmetry breaking without invoking a Higgs field, which in turn possibly needs a supersymmetry to correct the theoretical problems involved with the Higgs field. Supersymmetry itself has theoretical problems.
To explain the features of particle physics without the need for higher dimensions, supersymmetry, higgs field, or string theory.
To account for neutrino oscillation and mass.
The desire to make new nontrivial predictions, for example, to provide possible cold dark matter candidates, or to predict that the LHC will not observe a Higgs boson or superpartners.
The desire to reproduce only observed particles, and to prevent prediction within its framework for non-observed particles (which is a theoretical problem with supersymmetry).
The experimental falsification of certain grand unified theories of particle physics as the result of not observing proton decay may suggest that the grand unification scenario, which string theory is predicated on, and supersymmetry, may be false, and different solutions and thinking will be required for the progress of particle physics.
Were string theory successful in its original objectives, preon theory research would not be necessary. String theory was supposed to account for the above issues in terms of string dynamics. The different particles of the standard model were accounted for as different frequencies (tension) of a Planck-scale string, particle dynamics were explained in terms of the worldsheet diagrams, (the string theory equivalent of Feynman diagrams) and the three generations of fermions were explained in terms of strings "wrapping around" specific configuration of higher-dimensional moduli. The continuing failure of string theory to achieve the above objectives as a theory of particle physics Relevant literature include: Peter Woit Not Even Wrong, or Lee Smolin's The Trouble with Physics, or Daniel Friedan's "String theory is a complete scientific failure". Andrew Oh-Willeke states "as string theory develops more doubters, I think [preon theory] will be an obvious direction for non-string theory investigators and theorists."

The vast bulk of recent theoretical research into the particle zoo has been string theory. It was thought string theory has completely supplanted preon research, and that one dimensional supersymmetric strings can reproduce all the particles of the standard model, and their superpartners, the MSSM, their properties, color, charge, parity, chirality, and energy-masses, obviating any need for preon research. To date, string theory has been unable to reproduce the standard model.

A search through Spires and Arxiv, show that approximately over 30, 000 papers in string theory or supersymmetry since 1982, with several hundred new papers being published every month. In comparison, in 2006, since 2003, there have been about a dozen papers in preon theory listed as such in arxiv.

String theories continuing failure to reproduce the particle spectrum of the standard model has given some life for preon theories, and there have been recent papers on preon theory. As of 2006, Yershov, Fredriksson, and Bilson-Thompson have published papers in Preon theory within the past 5 years: a 2003 paper by Fredriksson [4], and a 2005 paper by Bilson-Thompson [5].

When the term "preon" was coined, it was primarily to explain the two families of spin 1/2 fermions: leptons and quarks. More recent preon models also account for spin-1 bosons, and are still called "preons". The term "preon" is the term of choice for Bilson-Thompson, Yershov, and Fredrickson, although they expand the meaning of the term, in addition to accounting for spin 1/2 fermions of leptons and quarks, which the term was used in its early history, the latter theories also accounts for spin-1 bosons.

Yershov's model is patterned after the idea naked singularities in general relativity, and closely resembles geon from John Archibald Wheeler research program into Geometrodynamics. Electron structure in Yershov's theory was further elaborated on in 2006 [6]. 2003 papers by Yershov [7] [8] are notable for being some of the only papers in the field to use the Preon model as a basis for providing specific numerical values from first principles for the masses of the particles described in the Standard Model. Yershov's model does not predict the mass of the Higgs Boson, and does not need the Higgs boson, and predicts it will not be found. Yershov's model deals with the mass paradox by prosposing a huge binding energy for his preons, which acts as a source of mass-energy, as through mass defect. To get around the mass paradox, Yershov's model proposes a new force that is 10^5 stronger than the strong nuclear force, that binds his preons together.

Fredriksson preon theory does not need the Higgs boson, and explains the electro-weak breaking as the rearrangement of preons, rather a Higgs-mediated field. In fact, Fredriksson preon model predicts that the Higgs boson does not exist. In the above cited paper, Fredricksson acknowledges the mass paradox represents a problem in his accounting for neutrino mass, however, he proposes a specific arrangement of preons in his model, which he calls the X-quark, which his theory suggests could be a stable good cold, dark matter candidate.


[edit] Loop quantum gravity and Bilson-Thompson Preon theory
In a 2006 paper [9] Sundance Bilson-Thompson, Fotini Markopolou, and Lee Smolin suggested that in any of a class of quantum gravity theories similar to loop quantum gravity (LQG) in which spacetime comes in discrete chunks, excitations of spacetime itself may play the role of preons, and give rise to the standard model of particle physics as an emergent property of the quantum gravity theory.

Sundance preon model was inspired by the Harari Rishon Model but posits ribbon-like structures that braid in groups of three, rather than point-particles. Proposing extended ribbon-like braided structures helps explains why ordering matters whereas the older point-particle preon model, the Harari Rishon Model, is unable to do so. It has been shown that the properties of Sundance ribbon-like structure can be derived from coherent states of spin foam, which may also give rise to gravity. His ribbon like structures have been described as "pieces of spacetime ribbon-tape", in that the Bilson-Thompson ribbons are made of the same structure that makes up spacetime itself. [10] While Sundance papers do offer braiding and an explanation on how to get fermions and spin-1 bosons, he does not show a braiding that would account for the Higgs boson [11].


Specifically, Bilson-Thompson et al proposed that loop quantum gravity could reproduce the standard model. The first generation of fermions (leptons and quarks) with correct charge and parity properties have been modeled using preons constituted of braids of spacetime as the building blocks[1]. Bilson-Thompson's original paper suggested that the higher-generation fermions could be represented by more complicated braidings, although explicit constructions of these structures were not given. The electric charge, colour, and parity properties of such fermions would arise in the same way as for the first generation. Utilization of quantum computing concepts made it possible to demonstrate that the particles are able to survive quantum fluctuations.[2]

In a 2006 paper [12], L. Freidel, J. Kowalski--Glikman, A. Starodubtsev suggests that elementary particles are Wilson lines of gravitational field, which implies that the properties of elementary particles, such as mass, energy, and spin, can be described by LQG's Wilson loops, and particle dynamics can be modeled on breaks in these Wilson loops, adding theoretical support to Bilson-Thompson's preon proposals.

Bilson-Thompson's ribbon preon scheme is intended to provide a picture diagram to represent coherent phases of spin foam dynamics whose description is quantum mechanical, not classical. For example, Bilson-Thompson's picture diagram of a preon with a twist, representing a U(1) charge equal to 1/9 of an electron charge, is to map to an eigenstate of spin foam. The spin foam formalism allows for the derivation of certain other particles of the standard model, the spin-1 bosons, such as photons and gluons, [[13]] and gravitons [[14]], [[15]] from loop quantum gravity's fundamental principles, and independent of Bilson-Thompson's braiding scheme for fermions. However, as of 2006, there is not a derivation of Bilson-Thompsons from spin foam formalism, including a derivation of 1/9 e- U(1) charge, and dynamics, as described by braiding. Bilson-Thompsons' braiding scheme does not offer a braiding that would account for a Higgs, but does not rule out the possibility of a Higgs boson. Bilson-Thompson himself observes that since the preons that have mass have charge as part of its internal "structure", it is possible it is this internal structure of charge that interacts with an electric field to give rise to inertial mass, or perhaps interacts with the Higgs field to give rise to inertial mass. et al. (The massless photon is untwisted in Bilson's preon scheme). As of 2006, it remains to be seen whether the derivation of the photon from the spin foam formalism in [[16]] can be matched with Bilson-Thompson's braiding of three untwisted ribbons [17], or perhaps, there are multiple ways to derive photons from the spin foam formalism.

When the term "preon" was first coined, it was used to describe pointlike subparticles that describe spin-1/2 fermions that include leptons and quarks. Such sub-quark pointlike particles would suffer from the mass paradox described below. It is observed that Bilson's ribbon structures are not actually "classical" preons, as defined in the introduction to this article as "pointlike structures or objects" of fermions, but Bilson-Thompson chooses to call his extended ribbon like structures of space-time "preons" in his research papers in the second sense of definition of preon as being more fundamental "subparticles" than elementary particles, and to maintain continuity in terminology with the larger physics community. His braiding also accounts for spin-1 bosons. In many respects, Bilson-Thompson's topological "preon" model resemble the geon more strongly than classical preon, and follows more closely a program inspired by Einstein and John Archibald Wheeler, in which particles are reduced to geometry through Wheeler's program Geometrodynamics (which has its roots in Lord Kelvin's knotting theory of atoms, and possibly to Spinoza's belief that reality is geometrical in structure) and its model of geons and continued through loop quantum gravity. The Wheeler's original Geometrodynamics suffers from the fact that it does not take quantum theory into account, whereas loop quantum gravity does.


[edit] Theoretical objections to preon theories: The mass paradox, chirality, and T'Hooft anomaly matching constraints
Heisenberg's uncertainty principle states that xp >= h bar/2 and thus anything confined to a box smaller than x would have a momentum of uncertainty proportionately greater. Some candidate preon models propose particles smaller than the elementary particles they make up, therefore, the momentum of uncertainty p should be greater than the particles themselves.

One preon model started as an internal paper at the Collider Detector at Fermilab (CDF) around 1994. The paper was written after the occurrence of an unexpected and inexplicable excess of jets with energies above 200 GeV were detected in the 1992—1993 running period.

Scattering experiments have shown that quarks and leptons are "pointlike" down to distance scales of less than 10−18 m (or 1/1000 of a proton diameter). The momentum uncertainty of a preon (of whatever mass) confined to a box of this size is about 200 GeV, 50,000 times larger than the rest mass of an up-quark and 400,000 times larger than the rest mass of an electron.

Thus, the preon model represents a mass paradox: How could quarks or electrons be made of smaller particles that would have many orders of magnitude greater mass-energies arising from their enormous momenta? Yershov's model, referenced above, proposes that when both particles and anti-particles of the proposed Y-particles in the theory are present, such as in the model's proposed neutrino composition, the mass of the constituent parts "cancels out", but can appear again when the structure of the Y-particles is changed. Yershov's model also proposes that particle mass arises as a mass defect binding energy among his preons, which helps account for the mass paradox.

Sundance preon model may avoid this by denying that preons are pointlike particles confined in a box less than 10−18 m, and instead positing that preons are extended 2-dimensional ribbon-like structures, not necessarily smaller than the elementary particles they compose, not necessarily confined in a small box as point particles preon models propose, and not necessarily "particle-like", but more like glitches and topological folds of spacetime that exist in three-fold bound states that interact as though they were point particles when braided in groups of three as a bound state with other particle properties such as mass and pointlike interatcion arising as an emergent property so that their momentum uncertainty would be on the same order as the elementary particles themselves.

String theory posits one-dimensional strings on the order of the Planck scale as giving rise to all the particles of the Standard Model, which would appear to also have the mass paradox problem. String theorist Lubos Motl has offered explanations as to how string theory gets around the mass paradox [18].

Any candidate preon theory must address particle chirality and T'Hooft anomaly matching constraints, and ideally be more parsimonious in theoretical structure than the Standard Model itself. Often, preon models propose additional unobserved forces or dynamics to account for their proposed preons compose the particle zoo, which may make the theory even more complicated than the Standard Model, or have implications in conflict with observation. One specific example: should the LHC observe a Higgs boson, or superpartners, or both, the observation would be in conflict with the predictions of many preon models, which predict the Higgs boson does not exist, or are unable to derive a combination of preons which would give rise to a Higgs Boson.


[edit] String theory and preon theory
String theory proposes that a one dimensional string on the order of a Planck scale has a tension, and differences in tension give rise directly to all the particles of the standard model and their super partners, in interaction with the proper compactified 6 or 7 dimensional Yau-Calabi mainfold and SUSY breaking. To date, string theory has been no more successful than preon theory in achieving this goal. John Baez and Lubos Motl have discussed the possibility that [19] that should preon theory prove successful, it may be possible to formulate a version of string theory that gives rise to a successful model of preons.

There have been recent research papers that have proposed preon models that are made of superstrings in Arxiv [[20]], [[21]] or supersymmetry [[22]]
 
  • #59
CarlB said:
I felt kind of bad about hijacking the thread. Do you mean to rejack it back to the original topic? By the way, I put up a new copy of my book, but it's not worth looking at. The major change is that I added the chapter divisions, with poetry.

You shouldnt' feel bad, you can talk about whatever you wish :)
 
  • #60
Is there a spin network/spin foam state that maps to a "twist" in Bilson's ribbon which creates a 1/9 electron U(1) charge, and an explanation why they "braid" (presumably state-sum) in groups of 3, as opposed to 2 or 4?




marcus said:
the two approaches differ quite a bit, as you remarked, and they are both unfinished or incomplete. I think it would be difficult to match them up at this point.

Smolin et al's paper IIRC only involves spin NETWORKS, and there remains the problem of specifying how the networks evolve.

The paper by Baratin and Freidel investigates a spinFOAM model, and proves a result about the zero-gravity limit.

In principle the B&F model should have two parameters, h-bar, and Newton G, which one can take to zero and check the behavior.
I believe that they have done half the work: they have shown that if you make G -> 0 you get something recognizable as closed Feynman diagrams. Maybe this result can be strengthened but it is already a positive indication.

But they also now must show that if you do not make G -> 0, but instead make h-bar -> 0, you get something like classical gravity.

You know that Rovelli et al recently put out some work about spinFOAM where they derived gravitons. This is suggestive, but it is no guarantee that B & F, with their spinfoam model, can get classical gravity in the limit of small h-bar.

Speaking not as an expert, and hoping others will correct me if I am mistaken, I would say that B & F paper is very different from Smolin et al in the sense that B & F is closer to having dynamics.

It seems to me that the virtue of the Smolin et al paper is that it gives more or less the right types of particles in a conceptually simple QG scheme. The Smolin picture, I think, is of a spinnetwork evolving by LOCAL MOVES which reconnect nearby vertices in different ways or which insert and remove vertices. To have a structured dynamics, they still must assign amplitudes to these moves, time would presumably be some index of the rate that these local moves are occurring. It is an elegant and evocative picture of the universe which has seeds of ideas for a theory more fundamental than quantum mechanics (see Smolin's most recent preprint) and better adapted to handling cosmology. But I think it is not at a comparable stage of definition so that one could connect it with Freidel et al's work.
 
  • #61
bananan said:
Bilson updated his article Oct 26, 2006

http://arxiv.org/abs/hep-ph/0503213

A topological model of composite preons

Thanks for flagging that!

The paper has been substantially rewritten at least in the introduction and the conclusion sections. Also a new section was added called
"Unresolved Issues"

It seemed sufficiently different to print out the new version.

Maybe we should have a thread about the new version, just to call attention to it.
 
  • #62
bananan said:
Any candidate preon theory must address particle chirality and T'Hooft anomaly matching constraints...

Only too true.. that's why the Rishon model of Harari took a sudden nose dive, namely when it was realized by his student Nati Seiberg that the anomalies do not match. It simply disappered since then.

This is what I thought til today. However, in the paper 0503213 mentioned above it made a surprise reapperance:

"The rishon model explained the number
of leptons and quarks, the precise ratios of their elec-
tric charges, and the origin and nature of colour charge.
The helon model does all this, but in additionin the framework of Loop Quantum Gravity [11]...
"

Christ... but well, it kind of makes sense. Since LQG people do not seem to care about anomalies, why bother and not re-introduce an inconsistent preon theory?
 
  • #63
R.X. said:
Only too true.. that's why the Rishon model of Harari took a sudden nose dive, namely when it was realized by his student Nati Seiberg that the anomalies do not match. It simply disappered since then.

This is what I thought til today. However, in the paper 0503213 mentioned above it made a surprise reapperance:

"The rishon model explained the number
of leptons and quarks, the precise ratios of their elec-
tric charges, and the origin and nature of colour charge.
The helon model does all this, but in additionin the framework of Loop Quantum Gravity [11]...
"

Christ... but well, it kind of makes sense. Since LQG people do not seem to care about anomalies, why bother and not re-introduce an inconsistent preon theory?

I recentally added this to wiki.

Bilson-Thompson has recently updated his paper dated October 27, 2006, [[18]] and acknowledges that his model, while not preon in the strict sense of the term, nevertheless is preon-inspired model, and is open to the possibility other more fundamental theories, such as M-Theory, may account for his topological diagrams, as well as the Higgs boson and gravity. The theoretical objections that apply to classic preon models do not necessarily apply to his preon inspired model, as it is not the particles themselves, but the relations between his preons (braiding) that give rise to the properties of particles. In this newer version of his paper, he has added a new section, section IV, called "unresolved issues" and acknowledges that open issues include mass, spin, cabbibo mixing, and grounding in a more fundamental theory. He states that grounding preons in M-theory is a possibility, as well as loop quantum gravity.
 
  • #64
R.X. said:
Only too true.. that's why the Rishon model of Harari took a sudden nose dive, namely when it was realized by his student Nati Seiberg that the anomalies do not match. It simply disappered since then.

This is what I thought til today. However, in the paper 0503213 mentioned above it made a surprise reapperance:

"The rishon model explained the number
of leptons and quarks, the precise ratios of their elec-
tric charges, and the origin and nature of colour charge.
The helon model does all this, but in additionin the framework of Loop Quantum Gravity [11]...
"

Christ... but well, it kind of makes sense. Since LQG people do not seem to care about anomalies, why bother and not re-introduce an inconsistent preon theory?

What sort of anomalies do you have in mind, in LQG?
 
  • #65
bananan said:
What sort of anomalies do you have in mind, in LQG?

Anomaly matching refers to chiral anomalies.

But yours is a tricky question, because it has been suggested (from what I gather from Thiemann's and other's papers), that anomalies simply do not exist in LQG, due to the kind of quantization procedure applied there.

One can only wonder how a standard quantum field theory that suffers from chiral anomalies and thus is inconsistent (gauge invariance broken, longitudinal modes do not decouple, path integral and thus correlation functions ill defined) should suddenly become consistent when treated with those methoids ...well, frankly they do not make much sense, see comments in Distlers' and Helling's blogs.

I think the least what one would require from any extension of ordinary QFT that it should reproduce the known features of QFT, and not plainly contradict them.
 
  • #66
R.X. said:
think the least what one would require from any extension of ordinary QFT that it should reproduce the known features of QFT, and not plainly contradict them.

Well, reproduced or better the RESULTS but there's no requirement to reproduce the details of the calculations. Particle physicists have over the decades taught themselves to believe six impossible things before breakfast, like Popov ghosts for example.

And this may be off base, but isn't the problem with QCD that it theoretically should have a chiral anomaly but phenomenologically doesn't, so they have to speculate on fine tuning schemes (like axions) to carefully cancel out the anomaly by two counterterms?
 
  • #67
selfAdjoint said:
Well, reproduced or better the RESULTS but there's no requirement to reproduce the details of the calculations. Particle physicists have over the decades taught themselves to believe six impossible things before breakfast, like Popov ghosts for example.

What's wrong with this neat computational trick? It is simply a clever way to deal with gauge fixing. No one ever has claimed that FP ghosts would be more than ficticious degrees of freedom and be at the same level es eg electrons. The rules of QFT work so well so that one can call it the most accurate theory of all of natural sciences. And giving up proven fundamental principles, like requiring the path integral be well defined, without very very strong reasons does not hold a lot of promise.

selfAdjoint said:
And this may be off base, but isn't the problem with QCD that it theoretically should have a chiral anomaly but phenomenologically doesn't, so they have to speculate on fine tuning schemes (like axions) to carefully cancel out the anomaly by two counterterms?

I don't know what you mean. Perhaps there is a confusion between global and local anomalies? Perturbative QCD at high energies is a very well established and experimentally proven theory, it is pointless to argue against its validity.

Frankly, in order to understand these things and hopefully proceed with one's own research in the future, there is no way other than really learning this stuff from the ground, and this takes many years of hard work. I understand the temptation to avoid this by simply declaring the results of many thousand hard working people as misguided, failed and not even wrong, in order to cook up "alternative" theories that are in contradiction with those results.

Well, science just works in a different way, and those who don't recognize this won't get anywhere.
 
  • #68
R.X. said:
The rules of QFT work so well so that one can call it the most accurate theory of all of natural sciences. And giving up proven fundamental principles, like requiring the path integral be well defined, without very very strong reasons does not hold a lot of promise.

I always love this argument, especially when it is known that all QED results such as Lamb shift, g factor, Casimir effect ... can be derived by treating the EM field classically while obtaining similar precision. Nobody really argues that the results of QED and QCD don't come out well perturbatively, but another thing is to appreciate this fact for the right reasons ! The latter might very well shake up some fundamental assumptions seriously (actually I am sure of this). But I agree with you, on the other hand, that in doing so you must always keep QED in mind and progress comes in small steps. I moreover concur that ``background independence'' is not going to solve the problems at hand. On the other hand, there are very good reasons from the theoretical side to protest against QED : sometimes it is good to go against something in order to learn to appreciate it for the right reasons, progress often comes from that direction.

Careful
 
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  • #69
R.X. said:
And giving up proven fundamental principles, like requiring the path integral be well defined, without very very strong reasons does not hold a lot of promise.

Indeed.

o:)
 
  • #70
I'm not willing to surrender SA's point without resistance. Careful is very bright but a bit reckless, IMO. Going against things is all about science, going through the motions is another matter.
 
  • #71
Chronos said:
I'm not willing to surrender SA's point without resistance. Careful is very bright but a bit reckless, IMO. Going against things is all about science, going through the motions is another matter.
A bit reckless ?? Oh yes, I forgot that those who point out that we need to get a better understanding of the calculations we know to work and point out that some fundamentals behind it might be wrong are always guilty. It is indeed much more rewarding to say that everything is more or less correct, work with self contradictory principles and do something which only adds an esthetic argument to the discussion : ``background independent´´ cutoff, instead of a ``naive'' cutoff in some Lorentz frame. :biggrin:
 
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  • #72
R.X. said:
No one ever has claimed that FP ghosts would be more than ficticious degrees of freedom and be at the same level es eg electrons.

Err, actually, someone did claim that.
 
  • #73
R.X. said:
selfAdjoint said:
And this may be off base, but isn't the problem with QCD that it theoretically should have a chiral anomaly but phenomenologically doesn't, so they have to speculate on fine tuning schemes (like axions) to carefully cancel out the anomaly by two counterterms?

I don't know what you mean. Perhaps there is a confusion between global and local anomalies? Perturbative QCD at high energies is a very well established and experimentally proven theory, it is pointless to argue against its validity.

This is what I meant:

http://adsabs.harvard.edu/abs/2003APS..SES.DC001G
 
  • #74
selfAdjoint said:

Hm.. I am not able to get hold a copy of that one... it appears not to have been submitted to arXiv, which is suspicious.. But at any rate, there is definitely no problem that QCD would be inconsistent due to local (gauge) anomalies. The whole particle physicist's world would be in turmoil...

As far as global anomalies are concerned, they are not important for consistency per se, but they serve as a device to check whether a preon model is consistent: the global anomalies of the constituents must match those of the bound states.

Actually, I was perhaps a bit too harsh, in that the author of that paper didn't claim to consider a real preon model any more. So the rules of the game with regard to anomalies are unclear; in particular since the issue of anomalies in LQG is (IMHO) unclear. Thus no conclusions can be drawn at this point. One just should be wary that "new" approaches should not be in contradiction of known facts, rather they should complement them.
 
  • #75
R.X. said:
Hm.. I am not able to get hold a copy of that one... it appears not to have been submitted to arXiv, which is suspicious.. But at any rate, there is definitely no problem that QCD would be inconsistent due to local (gauge) anomalies. The whole particle physicist's world would be in turmoil...

R.X., This is not some marginal crank theory. See this wiki entry on axions, for example. Nobody says QCD is in turmoil, but there is this long-standing, well-known uncertainty within it. http://en.wikipedia.org/wiki/Axion
 
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