[Phys-l] The Helon Model and Possible connections to the Fitzpatrick two space mo...

[Spinoza321@aol.com]

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 requirement  
q_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)