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*From*: Spinoza321@aol.com*Date*: Tue, 5 Sep 2006 04:27:40 EDT

This might be of interest.

INTRODUCTION

Here is a summary of the new particle model by Sundance O. Bilson-Thompson

of the University of Adelaide, Australia. This work represents an interesting

evolution of proposals forwarded by Haim Harari of the Weizmann Institute in

Israel and independently, Michael A Shupe of the University of Illinois.

This idea has been embraced by Lee Smolin and other Loop Quantum gravity

theorists because it shows promise of providing a particle theory which

satisfies diffeomorphism constrains something which string theory fails to do.

However these particle structures may well manifest as string physics at the

string scale and correspondence may be possible with the proposed topological

charge structure and the momentum states of the compactified Calabi-Yau space of

string theory.

Since this model describes a topological structure at the Planck scale, the

problems of how any structure can exist at what is predicted to be a chaotic

realm by standard Quantum theory becomes central. This gets us in deep water

because at this scale physical reality loses all it macro attributes.

However, like LQG this theory presumes a pre geometric causal structure not too

dissimilar from causal set theory or causal dynamical triangulations.

This pre geometric causal structure may also be related to the ideas

proposed by H.B. Nielsen, D.L. Bennett and N Brene in their landmark “Developments

in Quantum Field Theory” which involved proposals which attempted to explain

how the standard model symmetries were emergent properties of an underlying

Planck scale physics.

This model is also very much in the spirit of the particle ontology

advocated by Feynman, Sorkin, Stenger and others. Here however, it can be no surprise

that the model of point particles is merely a low energy approximation. A

more complete theory requires a real structure for the fundamental building

blocks of nature. However, it can not be avoided that the truly fundamental

structure that forms the building blocks for particles are the quantized causal

structure which at low energy emerges as space time. So in this model we see a

unification of atom and void as emergent properties of a more fundamental

underlying structure.

Of course part of my interest here is to explore any possible connections

between the Fitzpatrick two space model and the helon model. The Two Space

model postulates the existence of topological constrains in Neutrino mixing,

predicting bimaximal or near bimaximal equilibrium mixing ratios for neutrinos,

which has been confirmed by the observation of solar, reactor and cosmic

neutrinos. However, what is lacking is a more fundamental explanation for these

topological constrains. As will be obvious such a structure would seem to be a

logical extension of the Helon model.

THE ORIGINAL PRE QUARK THEORY

The idea that there exist yet another layer of structure for fermions was

very much part of mainstream physics in the 70’s. The success of QCD seemed to

open the possibility of a unification model based on a more fundamental

particle structure for all the fermions.

The pre quark theory which serves as a precursor for the Helon model is the

Rishon (Hebrew for primary) model of Haim Harari and Michael Shupe. I will

briefly describe this model because it forms the basis for the Helon model.

The failings of this model relate to its failure to account for the existence

of fermion generations and the difficulty of any formulation of composite

structure in the low mass lepton sector. These issues were clearly stated by

Harari and Shupe in their original proposal.

Harari and Shupe postulated that there are only two fundamental particles

in nature. All other particles in the Universe are composite structures made

up of these particles. This of course required a confinement scheme and

Harari and Shupe propose a new SU (3) color force, which Harari calls hyper color,

to account for the needed confinement for this new layer of structure. (I

will use the better known Harari terminology henceforth here.)

These particles are

Tohu ( Formless)

Electric charge +1/3

Hyper color

Color charge

Vavohu ( void)

Electric charge 0

Hyper color

Anti Color charge

So just looking at the first generation we get (Anti particles

Rishons lower case letters)

U= TTV Ubar= ttv

d= vvt dbar=VVT

e = ttt ebar= TTT

v_e=VVV v_ebar= vvv

Of particular interest here is the relationship between electric charge and

particle anti particle identity. In formulating the mathematical model for

absorber and emitter amplitudes in the interaction theory to incorporate the

supplemental states the particle anti particle structure is very apparent for

the strong force. However, in the electroweak sector the amplitude divides

along charge polarity. This was puzzling until you realize that this particle

anti particle structure for the electroweak interaction emerges at a more

fundamental level.

MAGENETIC CONFINMENT OF PRE QUARKS

The problem of the very low mass of fermions in the lepton sector makes any

confinement scheme involving Noether charges such as the proposed hyper color

force, very difficult to make workable. Also the addition of a new and

unobserverable force seemed uneconomic.

This led Clemons Heuson to propose that the confinement mechanism for the

Pre quarks proposed by Harari and Shupe might be based on magnetic monopole

charges. Monopoles are predicted to exist by grand unification theory but so far

none have been detected. Heuson proposal has these magnetic monopole charges

existing at the most fundamental level, but that nature doesn't allow bare

magnetic monopole charge to be observed. Just as naked color or fractional

charge is never seen.

In this model the T particle becomes a dyon and the V particle a monopole.

From the Magnetic electric duality charge requirementq_1*g_2-q_2*g_1 = (hbar*c/2)*N

which gives as the most parsimonious magnetic charge structure as

( 1,2,-3)

So that we get (using the same notation for particle anti particle

notation).

e= t(-1)t(3)t(-20

v_e=V(1)V(-3)V(2)

u_r=V(1)T_(-3)T(2)

u_b=T(1)V(-3)T(2)

u_g=T(1)T(-3)V(2)

d_r=t(-1)v(-3)v(-2)

d_b=v(-3)t(3)v(-2)

d_g=v(-1)v(-3)v(2)

This model also goes on to predict specific structure for bosons including

the graviton. However, the most important part of this proposal involves the

concept that particle structure is topological in origin. This concept meshes

well with Loop Quantum gravity providing a possible connection between the

underlying causal discrete structure of the “atoms” of space time and

fundamental particles. This idea also provides a deeper more fundamental conceptual

basis for particle ontology. And finally it may provide an identified

physical basis for the topological predictions of the two space model.

THE HELON MODEL

The Helon model of Sundance O Bilson-Thompson requires abandoning the idea

that particles are point like objects. In his proposal Thompson models the

fundamental particles as topological structure of space time itself. (Though

at the Planck scale it might be more accurate to say these are topological

structures of the relational order between the causal structures which makes up

space-time.)

Therefore, while these structures are presented as ribbon like entities

which can braid and twist it must be remembered that these structures exist at

the pre geometry Planck scale. So while this simple depiction is useful, the

actual entities might more accurately be modeled as a sum over topologies

involving the twist and braid charges of this model.

.

Z= Integral D[T] D[theta] exp{ -Integral d^4x Sqrt[g] ( R-L_matter)

Unfortunately such a Mathematical structure is not well defined but work

progresses to make this proposal more rigorous. More on this point later.

The fundamental building block is the Helon, which is analogous to the

Rishon in the original Harari- Shupe model.

As mentioned , the Helon can be modeled as a ribbon structure. This ribbon

can be topological charged, represented as a twist of the ribbon. These

charges are called Tweedles. They come in two polarities tweedle-dee and

tweedle-dum. (Don’t blame me for this terminology) Mercifully Thompson also equates a

dum with U and Dee with E. Charges come in pairs of +-pi twists. So that

each charge pair results in either a 0 or +-2*pi twist.

So since U= +pi and E=-pi we get

UU=+2*pi EE=-2*pi UE=EU=0

These topological charges equate with 0 or +- 1/3 electric charge.

The Helons always form triplet structures which allow an additional

topological charge called braiding. This can be depicted as the ribbons twisting

around each other. This can be mathematically represented as a crossing of

beginning and end point positions for the ribbons. This braiding relates to the

helicity of the particle. So we get

Left = {B_13 B_21 B_32} Right = {B_12 B_23 B_31}

It can be seen here that

P {B_13 B_21 B_32} = {B_12 B_23 B_31}

The twisting Charge can be seen to be related to the SU (3) color symmetry

while the braiding charge relates to the SU (2) _w symmetry. Therefore these

are emergent symmetries based on the extended helon structure.

Based on this we get

e(+)= H(+) H(+) H(+)

V_e= H(0) H(0) H(0)

e(-) = H( -) H(-) H(-)

u_b= H(+) H(+) H(0)

u_g= H(+) H(0) H(+)

u_r=H(0) H(+) H(+)

d_b= H(0) H(0) H(-)

d_g=H(0) H(-) H(0)

d_r= H(-) H(0) H(0)

Therefore we get

Q_SU(3)_c =

½ { b-r r-g g-b}= ½{ T_1-T_3 T_2_T_1 T_3-T_2 }

Here we can see that the neutrino is its own antiparticle. We get the

following multiplet structure based on helicity and electric charge.

{e (+) U(+) d(+) } _L { v_R d(+) U(+) e(+)}_R

{ e(-) U(-) d(-)}_R { v_L d(-) U(-) e(_) }_L

In this model particles with braid charge (crossed ribbons) are spinors.

All the electroweak bosons carry zero braid charge. ( no crossed ribbons) This

structure accounts for the restricted weak coupling we see in weak

interactions which is only between same family generations. Of course this is a broken

symmetry in the quark sector, but this symmetry is expected to exist at high

energy even in the quark sector as illustrated by the proposed quark lepton

complementarity proposal.

Interestingly this model provides no fundamental structure for gravitons or

scalar particles. This may be a flaw or it may be indicating something

fundamental about which fields are fundamental quantum fields. It may well be that

scalar particles and gravitons are a next layer up of collective excitations

of the more fundamental matter fields , an idea suggested by Afsar Abbas and

others as well as Sakharov for gravity.

THE FAMILY PROBLEM

In the Fitzpatrick model it is proposed that the reason we observe bimaximal

equilibrium mixing ratios , in other words the reason the parameters of

the MNS mixing matrix have the values it does, is because the upper family

fermions have a different topology than the first family fermions. This is

illustrated by the application of the F(V) operator to the Fermion charge

vectors which produces different results between the first and second/third family.

Therefore any model which describes Fermions as composite topological

structure would certainly be of interest.

This fermion generation explanation of the Helon model has not been worked

out in detail yet so I am limited in what I can say. However, it is perfectly

conceivable that a three valued topology will emerge. There is of course

strong experimental support for the existence of only three Fermion families.

In the Fitzpatrick model the global U square charge related directly to this

model given by

Usqr=g_ij*u_iu)j

Where g_ij is the 2 space metric and u are charge values of the 2 space

vector.

So that we get

Usqr( 1)=0 Usqr(2)=+1 Usqr(3)=-1`

The quarks must also carry the same topological charges related to family

number. But we do not see the same mixing ratios in the quark sector. In fact

the ckm matrix is nearly diagonal. So if there are topological charges which

are responsible for the observed mixing we see in the lepton sector this

effect must be suppressed for quarks.

However, it is believed that in fact that the parameters of the mixing

matrix might be energy related. At high energies, based on Quark lepton

complementarity considerations, we might expect a common mixing matrix given by

W= U_mns*V_ckm

This would give us

Theta_12 =42.3 +- 6.8 degrees Theta_13= 9.3 +- 14.3 degrees

Theta_23=47.4+-12.7 degrees.

Which indicate near bimaximal mixing.

The details of the helon model require family structure be a result of some

yet to be identified topological structure. If further work reveals a the

basic kind of topological structure predicted by the two space model this

would be a confirming data point for the 2 space model , increasing the

credibility of the connection of these predications and fundamental particle

structure. More than this can not be said at this time.

DEEP WATERS

Helon structures are believed to exist at the Planck scale. But obviously

notion of space, time and casualty are questionable

descriptives at this scale. The fundamental translation symmetries of time

and space are clearly emergent properties. Therefore in what sense are

descriptives like locality and causality meaningful for this model? Causality can

be seen to be emergent from the suppositions of topologies existing at this

scale. This invokes a measurement process as an essential element of the

descriptive of causality.

Locality is even more problematic. In LQG locality is defined as when

neighboring structure are connected by a link. This is called micro locality. But

without any possible notion of space or time it seems impossible to connect

this with macro locality.

The actual causal relationships at this scale are abstract. We can only

represent this energy regime by evolution algebra, an abstract description of the

causal structure.

We can describe the space of these braiding and twisting topological charges

as

H=H^T X H^B

But in reality is it misleading to describe H as any kind of space at all.

At this scale all descriptives are pre geometric. We are forced to view this

algebra as nothing more than a quantum information processing system. Here

each parameter is not a defined bit but a qubit , a superposition quantum

state of information. Any observable descriptive is emergent and measurement

dependent.

An important requirement is that these superposition states are the robust

states defined by noiseless subsystem formalism. These are protected from

decoherence because they transform under symmetries that commute with their

evolution.

[H, A_evol]=0

Where H are the robust superposition states and A_evol is the evolution

function. Here a quote may be useful.

“ From the NS perspective these translation symmetries should emerge as

additional symmetries which protect the degrees of freedom we have identified as

elementary particles. This will guarantee that the interactions among the

particles conserve the EMERGENT NOTIONS OF ENERGY AND MOMENTUM. It is this that

allows us to use topological conservation numbers to represent matter. “

The striking point here is that all of observables in physics are emergent

properties of matter. In essence this is the ultimate relational perspective

on reality.

What we call reality, the reality that kicks back, is the product of an

underlying unobserverable abstract structure. We should not be surprised that our

normal categories of perception which evolved to be useful at the macro

scale fail us completely at the micro scale. What perhaps we should find

surprising is that our mathematical tool box still allows us to explore physical

reality at this scale. See Links.

Bob Zannelli

(http://arxiv.org/ftp/hep-ph/papers/9904/9904493.pdf)

_http://arxiv.org/PS_cache/hep-ph/pdf/0503/0503213.pdf_

(http://arxiv.org/PS_cache/hep-ph/pdf/0503/0503213.pdf)

_http://arxiv.org/ftp/hep-ph/papers/9904/9904493.pdf_

(http://arxiv.org/ftp/hep-ph/papers/9904/9904493.pdf)

_http://arxiv.org/ftp/hep-th/papers/0603/0603022.pdf_

(http://arxiv.org/ftp/hep-th/papers/0603/0603022.pdf)

_http://arxiv.org/PS_cache/quant-ph/pdf/9807/9807004.pdf_

(http://arxiv.org/PS_cache/quant-ph/pdf/9807/9807004.pdf)

_http://xxx.lanl.gov/PS_cache/physics/pdf/0108/0108009.pdf_

(http://xxx.lanl.gov/PS_cache/physics/pdf/0108/0108009.pdf)

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