Lab Notes for a Scientific Revolution (Physics)

April 22, 2012

Back to Blogging, Uploaded a paper I wrote in 1986 about Preonic Grand Unification

It has been almost 3 years since my last Blog post.  Much of my time has been diverted into a condo hotel project in Longboat Key Florida, and the focus I need to do good physics has been impossible to come by.  Then, the other day, Ken Tucker, a frequent participant at sci.physics.foundations, emailed me about some new research showing that electrons have constituent substructure.  That brought me back immediately to the half a year I spent back in 1986 developing a 200-page paper about a preonic substructure for quarks and leptons, which culminated six years of study from 1980 to 1986.  I finished that paper in August 1986, and then took an 18 year hiatus from physics, resuming again in late-2004.

Ken’s email motivated me to dig out this 1986 paper which I manually typed out on an old-fashioned typewriter, scan it into electronic form, and post it here.  Links to the various sections of this paper are below.  This is the first time I have ever posted this.

Keep in mind that I wrote this in 1986.  I tend to study best by writing while I study, and in this case, what I wrote below was my “study document” for Halzen and Martin’s book “Quarks and Leptons” which had just come out in 1984 and was the first book to pull together what we now think of as modern particle physics and the (then, still fairly new) electroweak unification of Weinberg-Salam.

What is in this paper that I still to this day believe is fundamentally important, and has not been given the attention it warrants, is the isospin redundancy between (left-chiral) quarks and leptons.  This to me is an absolute indication that these particles have a substructure, so that a neutrino and an up quark both have contain the same “isospin up” preon, and an electron and a down quark both contain the same “isospin down” preon.  Section 2.11 below is the key section, if you want to cut to the chase with what I was studying some 26 years ago.  I did post about this in February 2008 at, though that post merely showed a 1988 summary I had assembled based on my work in 1986, at the behest of the late Nimay Mukhopadhyay, who at the time was teaching at RPI and had become a good friend and one of my early sources of encouragement.  This is the first time I am posting all of that early up-to-1986 work, in complete detail.

Lest you think me crazy, note that seventeen years later, G. Volovik, in his 2003 book “The Universe in a Helium Droplet,” took a very similar tack, see Figure 12.2 in this excerpt: Volovik Excerpt on Quark and Lepton Preonic Structure.

The other aspect of this 1986 paper that I still feel very strongly about, is taking the Dirac gamma-5 as a fifth-dimension indicator.  I know I have been critiqued by technical arguments as to why this should not be taken as a sign of a fifth dimension, but this fits seamlessly with Kaluza Klein which geometrizes the entirely of Maxwell’s theory and is still the best formal unification of classical electromagnetism and gravitation ever developed.  For those who maintain skepticism of Kaluza-Klein and ask “show me the fifth dimension,” just look to chirality which is well-established experimentally.  Why do we have to assume that this fifth dimension will directly manifest in the same way as space and time, if its effects are definitively observable in the chiral structure of fermions?  Beyond this, I remain a very strong proponent of the 5-D Space-Time-Matter Consortium, see, which regards matter itself as the most direct manifestation of a fifth physical dimension.  Right now, most folks think about 4-D spacetime plus matter.  These folks correctly think about 5-D space-time-matter, no separation.  And Kaluza-Klein, which historically predated Dirac’s gamma-5, is the underpinning of this.

After my hiatus of the past couple of years, I am going to try in the coming months to write some big-picture materials about physics, which will pull together all I have studied so far in my life.  I am thinking of doing a “Physics Time Capsule for 2100” which will try to explore in broad strokes, how I believe physics will be understood at the end of this century, about 88 years from now.

Anyway, here is my entire 1986 paper:

Preonic Grand Unification and Quantum Gravitation: Capsule Outline and Summary

Abstract and Contents

Section 1.1: Introduction

Section 1.2: Outline and Summary

Section 2.1: A Classical Spacetime Introduction to the Dirac Equation, and the Structure of Five-Dimensional Spacetime with a Chiral Dimension

Section 2.2: Particle/Antiparticle and Spin-Up/Spin-Down Degrees of Quantum Mechanical Freedom in Spacetime and Chirality, Gauge Invariance and the Dirac Wavefunction

Section 2.3: Determination and Labeling of the Spinor Eigensolutions to the Five-Dimensional Dirac Equation, and the High and Low Energy Approximations

Section 2.4: The Fifth-Dimensional Origin of Left and Right Handed Chiral Projections and the Continuity equation in Five Dimensions: Hermitian Conjugacy, Adjoint Spinors, and the Finite Operators Parity (P) and Axiality (A)

Section 2.5: Conjugate and Transposition Symmetries of the Dirac Equation in Five Dimensions, the Finite Operators for Conjugation (C) and Time Reversal (T), and Abelian Relationships Among C, P, T and A

Section 2.6: Charge Conjugation, and the Definitions and Feynman Diagrams for “Electron” and “Positron” Spinors

Section 2.7: Simple Unpolarized s,t,u Scattering Channels with a Covariant Propagator, and the Covariant (Real and Virtual) Polarization States of Massive and Massless Vector Bosons

Section 2.8: Prelude to Preons: The Spinor Decomposition of Four Real Spacetime Dimensions ct,x,y,z into Two Complex Spinor Dimensions Using the Covariant Polarization States of Vector Bosons

Section 2.9: Introduction to Isospin Preons in Electroweak Theory: The Preonic Decomposition of Four Real Electroweak Bosons A, W+, W-, Z into Two Complex Preons Denoting “Isospin Up” and “Isospin Down”

Section 2.10: Summarization of Prior Discussion, and on the Fundamental Importance of Preons in Particle Physics

Section 2.11: The Four-Preon Flavor SU(4) Unification of the Electromagnetic, Weak and Colorless Strong Interactions Excluding Quantum Gravitation; and the Colorless Flavor Classification of Left Handed Real Fermion and Boson Chiral Projections, for a Single Fermion Generation

Section 2.12: The Four-Preon Flavor SU(4)xU(1) Unification of Electromagnetic, Weak, Colorless Strong and Quantum Gravitational Interactions; and the Colorless Flavor Classification of Left and Right Handed Real Fermion and Boson Chiral Projections, for a Single Fermion Generation

Addendum to Section 2.12

Section 2.13: The Six-Preon Unification of Flavor SU(4)xU(1) with High Energy Color SU(4)xU(1) and Two Overlapping Degrees of Freedom; the Flavor and Color Classification of Real Fermions and Vector Bosons for a Single Generation; and the Derivation of Electroweak and Strong/Hyperweak Massless and Massive Neutral Current Vector Bosons

Section 2.14: On the Replication of Fermion Generations: Four Generational Grand Unification with Eighteen Preons and Nine Independent Flavor/Color/Generation Degrees of Freedom, and a Preonic Discussion of Mesons and Meson Decay

References and Bibliography

March 30, 2008

Revised Paper on Kaluza-Klein and Intrinsic Spin, Based on Spatial Isotropy

I have now prepared an updated revision of a paper demonstrating how the compact fifth dimension of Kaluza-Klein is responsible for the observed intrinsic spin of the charged leptons and their antiparticles.  The more global, underlying view, is that all intrinsic spins originate from motion through the curled up, compact x^5 dimension.  This latest draft is linked at:

Intrinsic Spin and the Kaluza-Klein Fifth Dimension, Rev 3.0

Thanks to some very helpful critique from Daryl M. on a thread at sci.physics.relativity, particularly post #2, I have entirely revamped section 5, which is the heart of the paper wherein we establish the existence of intrinsic spin in x^5 , on the basis of “fitting” oscillations around a 4\pi loop of the compact fifth dimension (this is to maintain not only orientation but entanglement version).  From this approach, quantization of angular momentum in x^5 naturally emerges, it also emerges that the intrinsic x^5 angular momentum in the ground state is given by (1/2) \hbar .

In contrast to my earlier papers where I conjectured that the intrinsic spin in x^5 projects out into the three ordinary space dimensions by virtue of its orthogonal orientation relative to the x^5 plane, which was critiqued in several Usenet posts, I now have a much more direct explanation of how the intrinsic spin projects out of x^5  to where we observe it.

In particular, we recognize that one of the objections sometimes voiced with regards to a compactified fifth dimension is the question: how does one “bias” the vacuum toward one of four space dimensions, over the other three, by making that dimension compact?  This was at the root of some Usenet objections also raised earlier by DRL.

In this draft — and I think this will overcome many issues — we require that at least as regards intrinsic angular momentum, the square of the J^5 = (1/2) \hbar obtained for the intrinsic angular momentum in x^5 , must be isotropically shared by all four space dimensions.  That is, we require that there is to be no “bias” toward any of the four space dimensions insofar as squared intrinsic spin is concerned.  Because J^5 = (1/2) \hbar emanates naturally from the five dimensional geometry, we know immediately that \left(J^{5} \right)^{2} ={\textstyle\frac{1}{4}} \hbar ^{2} , and then, by the isotropic requirement, that \left(J^{1} \right)^{2} =\left(J^{2} \right)^{2} =\left(J^{3} \right)^{2} ={\textstyle\frac{1}{4}} \hbar ^{2} as well.  We then arrive directly at the Casimir operator J^{2} =\left(J^{1} \right)^{2} +\left(J^{2} \right)^{2} +\left(J^{3} \right)^{2} ={\textstyle\frac{3}{4}} \hbar ^{2} in the usual three space dimensions, and from there, continue forward deductively.

For those who have followed this development right along, this means in the simplest terms, that rather than use “orthogonality” to get the intrinsic spin out of x^5 and into ordinary space, I am instead using “isotropy.”

There is also a new section 8 on positrons and Dirac’s equations which has not been posted before, and I have made other editorial changes throughout the rest of the paper.

March 3, 2008

Intrinsic Spin and the Kaluza-Klein Fifth Dimension: Journal Submission

   I mentioned several days ago that I had submitted a Kaluza Klein paper to one of the leading journals.  That lengthy paper was not accepted, and you can read the referee report and some of my comments here at sci.physics.foundations or here, with some other folks’ comments, at sci.physics.relativity.  The report actually was not too bad, concluding that “the author must have worked a considerable amount to learn quite a few thing in gravitation theory, and a number of the equations are correctly written and they do make sense, however those eqs. do not contain anything original.”  I would much rather hear this sort of objection, than be told — as I have been in the past — that I don’t know anything about the subject I am writing about.

   In fact, there is one finding in the above-linked paper which, as I thought about it more and more, is quite original, yet I believe it was lost in the mass of this larger paper.  And, frankly, it took me a few days to catch on to the full import of this finding, and so I downplayed it in the earlier paper.  Namely:  that the compactified fifth dimension of Kaluza-Klein theories is the mainspring of the intrinsic spins which permeate particle physics.

   I have now written and submitted for publication, a new paper which only includes that Kaluza-Klein material which is necessary to fully support this particular original finding.  You may read the submitted paper at Intrinsic Spin and the Kaluza-Klein Fifth Dimension.  I will, of course, let you know what comes from the review of this paper.

   I welcome your comments and feedback.


February 29, 2008

Lab Note 2: Why the Compactified, Cylindrical Fifth Dimension in Kaluza Klein Theory may be the “Intrinsic Spin” Dimension


I am posting here a further excerpt from my paper at Kaluza-Klein Theory, Lorentz Force Geodesics and the Maxwell Tensor with QED. Notwithstanding some good discussion at sci.physics.relativity, I am coming to believe that the intrinsic spin interpreation of the compacified, hypercylindrical fifth dimension presented in section 4 of this paper may be compelling. The math isn’t too hard, and you can follow it below: The starting point for discussion equation is (3.2) below,

frac{dx^{5} }{dtau } equiv -frac{1}{b} frac{sqrt{hbar calpha } }{sqrt{G} m} =-frac{1}{b} frac{1}{sqrt{4pi G} } frac{q}{m} . (3.2)

which is used to connect the q/m ratio from the Lorentz law to geodesic motion in five dimensions, and b is a numeric constant of proportionality. Section 4 below picks up from this.

Excerpt from Section 4:

Transforming into an “at rest” frame, dx^{1} =dx^{2} =dx^{3} =0, the spacetime metric equation d/tau ^{2} =g_{/mu /nu } dx^{/mu } dx^{/nu } reduces to dtau =pm sqrt{g_{00} } dx^{0} , and (3.2) becomes:

frac{dx^{5} }{dx^{0} } =pm frac{1}{b} sqrt{frac{g_{00} }{4pi G} } frac{q}{m} . (4.1)

For a timelike fifth dimension, x^{5} may be drawn as a second axis orthogonal to x^{0} , and the physics ratio q/m (which, by the way, results in the q/m material body in an electromagnetic field actually “feeling” a Newtonian force in the sense of F=ma due to the inequivalence of electrical and inertial mass) measures the “angle” at which the material body moves through the x^{5} ,x^{0} “time plane.”

For a spacelikefifth dimension, where one may wish to employ a compactified, hyper-cylindrical x^{5} equiv Rphi (see [Sundrum, R., TASI 2004 Lectures: To the Fifth Dimension and Back, (2005).], Figure 1) and R is a constant radius (distinguish from the Ricci scalar by context), dx^{5} equiv Rdphi . Substituting this into (3.2), leaving in the pm ratio obtained in (4.1), and inserting c into the first term to maintain a dimensionless equation, then yields:

frac{Rdphi }{cdtau } =pm frac{1}{b} frac{sqrt{hbar calpha } }{sqrt{G} m} =pm frac{1}{b} frac{1}{sqrt{4pi G} } frac{q}{m} . (4.2)

We see that here, the physics ratio q/m measures an “angular frequency” of fifth-dimensional rotation. Interestingly, this frequency runs inversely to the mass, and by classical principles, this means that the angular momentum with fixed radius is independent of the mass, i.e., constant. If one doubles the mass, one halves the tangential velocity, and if the radius stays constant, then so too does the angular momentum. Together with the pm factor, one might suspect that this constant angular momentum is, by virtue of its constancy independently of mass, related to intrinsic spin. In fact, following this line of thought, one can arrive at an exact expression for the compactification radius R, in the following manner:

Assume that x^{5} is spacelike, casting one’s lot with the preponderance of those who study Kaluza-Klein theory. In (4.2), move the c away from the first term and move the m over to the first term. Then, multiply all terms by another R. Everything is now dimensioned as an angular momentum mcdot vcdot R, which we have just ascertained is constant irrespective of mass. So, set this all to pm {textstylefrac{1}{2}} nhbar , which for n=1, represents intrinsic spin. The result is as follows:

mfrac{Rdphi }{dtau } R=pm frac{1}{b} frac{sqrt{hbar c^{3} alpha } }{sqrt{G} } R=pm frac{1}{b} frac{c}{sqrt{4pi G} } qR=pm frac{1}{2} nhbar . (4.3)

Now, take the second and fourth terms, and solve for R with n=1, to yield:

R=frac{b}{2sqrt{alpha } } sqrt{frac{Ghbar }{c^{3} } } =frac{b}{2sqrt{alpha } } L_{P} , (4.4)

where L_{P} =sqrt{Ghbar /c^{3} } is the Planck length. This gives a definitive size for the compactification radius, and it is very close to the Planck length. (more…)

February 16, 2008

Lab Note 2 Intermezzo: Change of View to a Spacelike Fifth Dimension, as the Geometric Foundation of Intrinsic Spin

(A PDF version of this Lab Note may be downloaded from Lab Note 2 Intermezzo.) 

 Those who have followed the development of this lab note know that I have been working with a Kaluza-Klein theory which regards the fifth dimension as timelike, rather than spacelike.  After reviewing some key literature in the field including a Sundrum Lecture recommended by Martin Bauer and several articles by Paul Wesson linked over at The 5-D Space-Time-Matter Consortium, I have undergone a conversion to the view that the fifth dimension needs to be spacelike – not timelike – and specifically, that it needs to be a compact, spacelike hypercylinder.  In this conversion, I am motivated by the following reasoning, which gives a geometric foundation to intrinsic spin: 

February 7, 2008

Lab Note 3, Part 2: Unification of Particle, Nuclear and Atomic Phenomonology

This lab note will be brief.

On April 28, 2007, I posted a paper which went from baryons and confinement to strings to particle phenomenology to atomic physics and deuterons and a whole range of phenomenology including fermion generation replication which appeared to lend itself to a common, underlying explanation based on the work I have previously discussed with respect to baryons and confinement in particular.  The underlying thread throughout, is to connect spacetime symmetry to internal symmetry using the Pauli fermionic exclusion principle.   I am afraid, however, that this paper may have been buried amidst all of the other postings, so I want to specifically call it to your attention, at the link below:

On The Natural Origin of Baryons, Short-Range Mesons, and QCD Confinement, from Maxwell’s Magnetic Equations for a Yang-Mills Field

In the spirit of “Lab Notes” which are a scientific diary of theoretical explorations, I ask you in particular to look at the second half of this paper, starting at section 6.  In football, there is something known as a “Hail Mary” pass where the quarterback throws the ball all the way down the field hoping for a touchdown.  The second half of the above paper is just that.  While certainly speculative, it seems to me that this ties together a very diverse range of observable phenomenology which has not previously been tied together.   It is probably the most audacious piece of physics writing I have done, and I don’t want it to get lost in the shuffle.

So, if nothing comes of it, so be it.  But, it may well be that someone in the end zone will catch this long pass, and physics will come to rest in a different place from where it rests today.  That is why it is so important to take good lab notes!

February 2, 2008

Lab Note 4: An Interesting Left-Chiral Muliplet Perhaps Indicative of Preonic Structure for Fermions

I return in this brief Lab Note to the underlying spirit of one of the basic premises of this Weblog, which is that these are a series of “Lab Notes.”  We often tend these days to think and speak about “theories,” rather than “notes,” and certainly, many of the “Lab Notes” which I am presenting here are intended to be thought of as “theories,” or “theories-under-development,” as much as “lab notes.”

But when one talks about “Lab Notes,” what should be the prevailing thought is that sometimes, in the course of research, one uncovers an interesting “data point.”   Perhaps that data point goes nowhere; perhaps, when one looks hard at that data point and follows it up carefully, it leads in a whole new direction and changes many things in physics.

It is in this spirit that I present Lab Note 4, “An Interesting Left-Chiral Muliplet Perhaps Indicative of Preonic Structure for Fermions,” which I offer in the spirit of an interesting theoretical “data point” I uncovered back in 1988.  No more, no less.

For some history, I had been auditing some physics courses at nearby Rensselaer Polytechnic Institute (which my daughter Paula is now attending as a Freshman Chemical Engineer), and in the course of my studies there began a dialogue and I later became friends with the tragically-late Professor Nimai Mukhopadhyay, who was a particle physicist. 

At the time, particularly because of the “isospin redundancy” between quarks and leptons — which is my way of saying that both quarks and leptons can exist in both an “isospin up” and an “isospin down” state — I began to realize that there are really two distinct “attributes” which specify the “flavor” of an “elementary” fermion, within each generation.   First: is it a “quark” or a “lepton”?  Second, is its isospin “up” or “down.”  And, this, I began to suspect, was indicative of a preon substructure for the fermions — part of which provided the quark versus lepton aspect of flavor, the other part of which provided the up versus down isospin aspect of flavor. 

Following this thinking, I found that if one were to consider the flavor quantum numbers for only the left-chiral fermions, it turned out that the simple gauge group SU(4) could be used to represent the flavor symmetry of these left-chiral fermions, and that four preons, simply, A, B, C, D so as to avoid any preconceptions at all, could be used in pairs so as to construct the left-chiral fermion flavors.  I wrote this up for the 1988 “Excited Baryons” conference at RPI, and Dr. Mukhopadhyay included the writeup with the conference program.  For your consideration as a “lab note,” i.e., as an interesting piece of research data to keep in one’s mind, I link to a copy of that 1988 writeup below:

Left-Chiral Flavor Muliplet 

At this point in time, 20 years later, it is clear to me that I am not the only person to have thought in this way.  For example, G. Volovik, in his 2003 book “The Universe in a Helium Droplet,” includes an excellent discussion in section 12.2, which I have uploaded to the following link:  

Volovik Excerpt on Quark and Lepton Preonic Structure

Volovik makes a separation very similar to what I was going after in 1988, does so very clearly, and also, nicely handles the right-chiral states which drove me to fits back in 1988.  In fact, this excerpt from Volovik is another very important “lab note,” in and of itself, and I commend it to the reader.   The main problem which I perceive with this excerpt from Volovik, however, is his handling of the spins, which motivates the use of “holons” (spin 0) and “spinons” (spin 1/2) to construct a spin 1/2 fermion out of two preons.  In my view, it would be preferred for each of these preons to have spin 1/2, and when combined, for the resulting particle to also have spin 1/2.  That is, we need to find a way to have 1/2 = 1/2 + 1/2.

How we do this is another story which utilizes the fact that a fermion is a four-component Dirac spinor, and that left- and right-chirality each occupy two of the four components.  Thus, for the left- and right-chiral components of a fermion f, each of which has spin 1/2, one can combine those into the whole four-component fermion — which still has spin 1/2.  That is, f=f_{L}+f_{R} may be a way to implement 1/2 = 1/2 + 1/2 within the context of Volovik, thereby avoiding the seemingly-artificial (to me) holons and spinons.  But, that is a topic for another lab note, and this f=f_{L}+f_{R} approach clearly exploits pre-existing chiral properties of fermions. 

In any event, please take a look at my 1988 publication linked above, look also at the linked Volovik excerpt, think about his and my separation of the fermion flavor attributes into quark/lepton and isospin up/down, think about the inelegance of using holons and spinons (at least if you and I have the same sense of elegance), and think about the chiral properties of fermions.  I do continue to believe the believe that the clearly-established “isospin redundancy” between quarks and leptons is the best evidence we have, of a preonic substructure for fermions which is waiting to be better understood, and cast into a suitable formal pedagogical structure.

That concludes this lab note.

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