Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

On Vortex Particles

David Saint John

"In short, we can reach the final unified theory -- which we symbolically place at the top of Motion Mountain --

only if we are not burdened with ideological or emotional baggage. The goal we have set requires extreme thinking,

i.e., thinking up to the limits. After all, unification is the precise description of all motion. Therefore, unification is a

riddle. The search is a pastime. Any riddle is best approached with the lightness that is intrinsic to playing. Life is

short: we should play whenever we can." -Christoph Schiller, Motion Mountain, Volume 6

The following text is an attempt to reconsider the Victorian-era vortex model of the atom in a

modern context, with an emphasis on the phenomenology of particles as experienced

experimentally. This involves a departure from certain currently accepted traditional constructs

of physics, but remains a synthesis of several ideas which have been floating around in some

form or another for many years. It should be considered a remix of what has already been

developed previously by various scientists and natural philosophers, with a view toward our

current state of scientific endeavours at the level of subatomic phenomena.

The initial stimulus for this work lies in the relative mystery of isotopic stability as a

function of protons and neurons, along with the haunting staircase structure of this stability -

often described over-simply as being due to ‘magic numbers’. Figure 1 illustrates this stability

staircase, wherein the shallow steps of the lighter nuclei eventually give way to a more regular

staircase (from Oxygen16 to Argon36), with a more complex set of stairs and stable isotope

‘islands’ up until one reaches the ‘island of stability’. The standard model is silent in regard to

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

this behavior of isotopic stability - having applicability to primarily sub-nuclear phenomena, it

gives little insight into the distinctions between protons and neutrons. But before treating this

isotope issue, we will first explore the idea of knots as particles, and see if we can work our way

back to isotopes.

One form of an isotope stability table showing the ‘staircase of stability’, from Wikipedia. Notice the step like patterns which stable isotopes trace out - perhaps suggesting an underlying mechanism for nuclear stability. A more

useful chart for the isotopic explorer can be found here: http://ie.lbl.gov/toi/pdf/chart.pdf

Before our attempt at re-contextualizing this vortex knot model (VKM), it is worth

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

tracing back its recent incarnations in brief. A thorough historical account has been made by

others, in particular by Helge Kraigh, and so the descriptions here should by no means be

considered authoritative. Most scholarly discussions of vortex atom models trace the idea to

William Thompson (Lord Kelvin), who developed his VKM after being inspired by the work of

Hermann von Helmholtz, who first developed the mathematics of vortex motion in an

incompressible fluid. Thompson found the model of “Lucretius’ atoms” - their individual atomic

properties being extant for their own sake without recourse to any mechanism - as ontologically

repulsive, while the idea of knotted vortex atoms satisfied his urge for some descriptive

mechanism which seemed powerfully evident to Kelvin when observing the interactions of

vortex rings moving through the air.

This idea of Kelvin’s, that atoms were composed of some sort of ethereal knots, had

many proponents in a time when the very existence of atoms was questioned by those with a

panache for the continuous and/or a distaste for the discrete. One of Kelvin’s contemporaries,

Peter Guthrie Tait, went on to classify knots of up to 9 crossings, developing what would come to

be known as the Prime Knots. Prime knots are analogous to prime numbers, in that they

represent irreducible topological structures while prime numbers are irreducible in terms of their

lack of divisors. As such, prime knots cannot be represented as a knot sum of other knots but are

fundamental to modern knot theory as prime numbers are in number theory.

What really seems to have killed Kelvin’s vortex knot model of the atom was the

profound success of the periodic table, along with the total inability to massage any sort of 8-fold

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

periodicity from the prime knots. With the success of the periodic table, predicting elements

previously undiscovered and unexpected, the vortex knot model languished. Kelvin himself is

said to have discarded it late in his life, but one of his primary assumptions can now, through the

lens of a nuclear era, be considered to have new legs: Kelvin believed atoms to be fundamental -

as small a particle as one needed to consider. We now know this to be false; atomic systems

contain protons and neutrons in the nucleus, electrons occupying energetic states around these

nuclei and their neighbors with photons participating in the transitions between energy states (to

say nothing of the massive zoo of unstable particles discovered as the “Big Machines” of particle

accelerator technologies developed and evolved). If one suspects some value in Kelvin’s

intuitions and reapply them in light of this different understanding, one might find that the vortex

knot model might be applied to something more fundamental in physical space than the atom,

which now appears as a collective of sub-atomic particles, rather than a fundamental construct.

It is worth noting that this desire to connect knots to physical phenomena has not

abated with the passing of Kelvin’s work. Knots have been found useful in the context of light

(as in the work of Mark Dennis, at the University of Bristol), DNA and chemistry writ large

(http://www.math.vt.edu/people/linnell/4994/knot.pdf), magnetohydrodynamic plasmas, and __.

The series of books entitled “Knots and Everything”, currently at 45 volumes, regularly contains

works which relate knots to extant scientific phenomena, including volume one; “Knots and

Physics”.

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

5

http://commons.wikimedia.org/wiki/File:Giant_smoke_ring.jpg

Here we should take a moment to rehearse Kelvin’s experience of observing smoke rings

travel and bounce off of each other in Tait’s lecture room, as this was part of the imaginative

channel through which this idea became embodied in his case*. In Kelvin’s mind, this

magnificent display is made of a collection of smoke particles and gaseous atomic species

exhibiting similar vortical forms as those that the atoms themselves might be dancing in - as

above in the air, so below in the atoms. Kelvin begins his paper “On Vortex Atoms” in the

proceedings of the Royal Society of Edinburgh (available here):

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

6

“After noticing Helmholtz’s admirable discovery of the law of vortex motion in a perfect liquid—that is, in a fluid

perfectly destitute of viscosity (or fluid friction)—the author said that this discovery inevitably suggests the idea that

Helmholtz’s rings are the only true atoms. For the only pretext seeming to justify the monstrous assumption of

infinitely strong and infinitely rigid pieces of matter, the existence of which is asserted as a probable hypothesis by

some of the greatest modern chemists in their rashly-worded introductory statements, is that urged by Lucretius and

adopted by Newton—that it seems necessary to account for the unalterable distinguishing qualities of different kinds

of matter. But Helmholtz has provided an absolutely unalterable quality in the motion of any portion of a perfect

liquid in which the peculiar motion which he calls “Wirbelbewegung” has been once created. Thus any portion of a

perfect liquid which has “Wirbelbewegung” has one recommendation of Lucretius’s atoms—infinitely perennial

specific quality. To generate or to destroy “Wirbelbewegung” in a perfect fluid can only be an act of creative power.

Lucretius’s atom does not explain any of the properties of matter without attributing them to the atom itself.”

The air was an imperfect fluid (having viscosity and fluid friction) while the ether was the

prefect fluid lying underneath, alongside (or as) the electromagnetic fields themselves. These

thoughts require subtle modification in light of our current knowledge. Atoms are no longer the

simplest stable observable particles, that position being taken by photons, electrons, protons,

neutrons, and neutrinos in addition to many inferred particles (quarks, gluons, etc.) In addition

to new distinctions about particle character, there must be some alterations to the ‘ether’ in which

Kelvin placed his knots.

When considering what a vacuum really represents, this historically often involves a

specialized chamber along with various types of apparatus which are employed to remove

atmospheric atoms and molecules from the interior of the vacuum chamber. While there are

inevitably some species remaining in an evacuated chamber, what is obtained through these

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

7

pumping processes is a rough approximation of empty space. The ability of photons to travel

through vacuum led some to believe (especially when thinking of light as a wave) that some sort

of elastic medium was required for these light waves to propagate. The name commonly

ascribed to this medium is ‘ether’ and while this term as fallen out of favor (see Michelson and

Morley), the original descriptive paradigm of the ether has been maintained in a sense through

the concept of the electromagnetic field, which is considered to pass through all space while

bearing some responsibility for photon propagation in vacuum. It is within this context of

electromagnetic ether in which we place ourselves, for the time being.

The idea of knots in the electromagnetic ether was appealing enough to drive many to

find a way to merge these ideas with scientific consensus, especially in the work of Tait, who

classified prime knots for the sake of the periodic table. If one were to proceed like Tait, and

attempt to find a link between this vortex knot model and real physical science, one must

determine then at which level of particle identity the VKM should be applied. For reasons that

should become evident later, it seems prudent to stick to observable particles rather than inferred

ones.

An issue arises when one considers the details of current knot theory with an eye

toward physical application. Most study of knot topology can be done, or at any rate has been

done, often by using simple string or yarn. This allows one to create simple and useful models

while keeping research overhead low. While most of these rope-knots share some characteristics

with our electromagnetic vortex knots, research into knots in the context of plasma physics

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

8

seems to suggest that certain types of helicity are not conserved under a classic knot theory

operation known as the first Reidemeister move. When modified slightly, the modified

Reidemeister I captures an intricacy previously missing from topological knot theory, suggesting

a minor revision to what might constitute an electromagnetic prime knot. There is some

literature to support this line of reasoning (see Yongnian, H. & Weidong, S. Topological

structures of vortex and helicity analysis. Acta Mechanica Sinica 14, 208-214(1998)., and

Bouzarth, E.L. & Pfister, H. Helicity conservation under Reidemeister moves. Am. J. Phys. 74,

141-144(2006). ) Currently, a standard table of prime knots begins with the following:

These symbols illustrate the Unknot, Trefoil knot, and Figure 8 knot, with 0, 3 and 4

crossings respectively - no 1 or 2 crossing knots exist in this scheme. With a modified take on

Reidemeister I, an additional construct appears, with characteristics that suggest it be described

as a sort of ‘mobius knot’, with only one crossing.

We will return to this mobius knot and the other prime knot constructs after

considering the advances in knowledge which precipitated abandonment of vortex knot theories

in the 1900s. The state of scientific understanding at that time was complicated by re-

representation of certain particles in different contexts. Gamma rays, X-rays and other photons

were classified differently, probably due to the differences in their sources and interactions with

matter. By the late 1940s, the cast of characters on the atomic stage had shifted from nuclear

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

9

radiation (alpha, beta, gamma), X-rays, atomic elements and wave-like light into photons,

electrons, protons, neutrons and neutrinos, along with an assortment of other unstable particles.

At that point, the ‘actors’ were limited by the energies obtainable by the particle accelerators in

use, and these simplified characters remain fundamental to nuclei composition to this day.**

A model having protons and neutrons as billiard balls in an nucleic bag, surrounded by

the electron orbitals, is an understanding of the atom that has been dynamic enough to afford

ongoing advances in technological development over the last 70 years - be it nuclear, molecular,

biological or otherwise. A similar “Ball in the bag” paradigm was ultimately applied to the inner

structure of the protons and neutrons as well as the classification of the less stable zoo particles.

The standard model may be crudely approximated by this ‘balls in a bag’ description, where

quarks are the ‘balls’ of various flavour, held in a metaphorical bag by the gluons (Perhaps even

a gluonic bag?). It is useful to consider the experimental phenomenology that helped legitimize

this model. In collision experiments wherein protons were smashed together, an inner structure

began to become apparent. Prior to the use of ‘quark’, the word ‘parton’ was proposed to

describe these inner structures seemingly within protons and other particle species. The

excruciating paradox was that if enough energy was applied to extract a parton/quark, new

particles were generated in the process, without observation of any internal structure in isolation.

Thus the often repeated assertion that no quark has been observed in isolation, but that they

nonetheless constitute an internal mechanism which distinguishes protons, neutrons, and other

(non-leptonic) zoo particles.

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

10

If one considers all particle collision experiments, there is an element of projection to

them, whereby a three dimensional construct is reduced to a two dimensional one. While prior

collision experiments often focus on small numbers of participants, this phenomena is observed

with an ensemble of particle collisions in transmission electron microscopy (TEM), whereby

accelerated electrons interact with a thin sample to produce an image. When tomographic

techniques are not applied, analysis of TEM images requires some care due to this very problem

of projection - the 3D sample is often only captured through a 2D image. A similar problem

likely applies when colliding protons and nuclei, while the collisions are often concieved of as

between seemingly point like particles, their inner structure must have some 3D character to it

which is sampled in a particular way through the relative orientation of the participants of the

collision interaction.

The study of knots has also dealt with the ‘projection issue’, as 3D loops and knots of

string are often drawn or laid out such that special attention is given to the places where two

strands cross. Instead of simply making an ‘X’, which makes the intended structure ambiguious,

a natural convention has been established, perhaps by cavemen or doodling students, wherein a

certain kind of ternary logic manifests:

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

11

These symbols, marked + and -, are often described as ‘crossings’ and illustrate some

of the most simple features of any knot. Any illustration of a knot maintains its information about

the knot through the use of these crossings. Prime knots, like the few shown above, are often

ordered or classified in terms of the fewest crossings required to create a projection of some knot

which maintains its basic topological information. In some very real sense, crossings and quarks

are very analogous in behavior. As quarks cannot be removed without ‘breaking’ the particle and

spawning new ones using available energy, a crossing cannot be removed from a prime knot

without cutting the thread and destroying the knot construct. All prime knots are in some sense,

Gordian.

As quarks are to ‘non-leptonic’ particles, so are crossings to knots in a sense (as we

return to the goal of attempting to relate the two as Kelvin might). If one assumes that the mass

of a particle is somehow related to its ‘tangled-ness’, or the number of crossings, we still seek to

account for particle charge. To this end, knots have properties other than their crossing number,

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

12

particularly their writhe. Some knots, like the unknot and figure 8 knot, have no writhe. Other

knots, like the trefoil knot, have some writhe which has an associated sign. If one is willing to

associate charge with writhe, then we obtain a mechanism for positive, negative and neutral

charges associated with knot constructs, along with a viable route toward a description of

antimatter. Here is a loose outline of how one might attempt this series of analogies:

Photons ~ Unknots/loops. Chargeless / Writhe-less. No mass / no self crossings.

Polarization already seems to exhibit behavior which could be mapped from electromagnetic

ripples persisting on a ring-like topology.

Electrons ~ Mobius knots. Charged / writhe dependant on sign. Gives some insight

into the possibility of electron spin. This sort of idea was proposed before, see "Is the Electron a

photon with toroidal topology?" by J.G. Williamson and M.B. van der Mark (1997) Annals of the

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

13

Louis de Broglie Foundation 22 (2) 133.

Protons ~ Trefoil knots. With three crossings (3 quarks), greater mass than electrons,

and charge / writhe, the quark/crossing interrelationship seems most clear in this example, when

considering the similarity of the phenomenology of each.

Neutrons ~ Figure 8 knots. Without charge/writhe, but with more mass/crossings than

a proton/trefoil, these constructs are their own mirror image, suggesting that it does not have an

anti-particle (with apologies to Bruce Cork). As neutrons are unstable outside of the nucleus,

one would expect that more complex knots would also be of limited stability in comparison to

electrons and protons.

Neutrinos* ~ linked photons might be an explanation for neutrino phenomena, being

chargeless and of very low, but not quite zero, mass. There is much variety in linked loop

configurations, which may be ascribed to different types of neutrinos - should they be

distinguished conclusively from one another.

Consider the mechanism of beta decay, in which a neutron decays into a proton,

electron and (anti-?)neutrino. Or: n → p + e + ν Visualized through vortex knots, the process

might be conceived as:

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

14

All of this is oversimplified - it gives little consideration to the underlying

electromagnetic vibrations which would constitute the strings or filaments of the vortex knots

described above. Additionally this is not a topologically sound proof, as any knot theorist might

attest. With a similar disregard for rigor, consider the annihilation of an electron and positron

pair:

In this case, the mirror particles ‘match’ each other and have some predilection for ‘unknotting’ each

other, producing photons/unknots in the process.

If, despite the absence of theoretical calculations, the reader maintains some interest or

willing suspension of disbelief, the remainder of this work will detail some of the inconsistencies

and heresy associated with fusing this reasoning to the current state of the Standard Model. It

must be considered tentative speculation at best. If one begins to consider this electromagnetic

vortex knot model as having potential merit, it immediately wreaks taxonomic havoc on the

familial designations applied by the standard model, in addition to the obviously radical

reinterpretation of quarks. While quarks are a convenient accounting system (made even more

flexible through the use of anti-quarks) they are re-envisioned through a knot model as a

misinterpretation of the admittedly murky and complex experimental data about internal particle

structure that was expanded as needed to accommodate the increasingly energetic zoo particles

created throughout the evolution and enhancement of accelerators/ colliders /high energy physics

technology. This model served its purpose in giving a framework to the experimentalists doing

the observations.

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

15

The lepton-hadron family structure is seen to be somewhat unnecessary (as would

become the distinction between mesons and baryons). All known particle phenomena could

conceivably be unified under a single conceptual form. The characterization of particles as being

‘bosons’ or ‘fermions’ can be interpreted as a misunderstanding about what it means to exhibit

certain types of statistical behavior in different contexts. Bosons exhibit ‘bosicity’, a certain type

of statistical behavior, in that they are best described by Bose-Einstein statistics. This retains the

utility of the distinction without allocating unnecessary reverence toward their statistical

behavior, and could provide a re-interpretation of superconductivty in the BCS model. If you’re

not enslaved to the idea of fermions and bosons, you may interpret what invokes ‘fermicity’ or

‘bosicity’ in a particle as a context-dependant process, rather than an inherent property of the

particle.

Another heretical development from this thought-experiment deals with reformation of

what makes up the strong and weak forces. For example, if your fundamental particles (the term

fundamental being somewhat disputed) are not conceived as balls but as electromagnetic knots, it

may be possible that their interaction and decay can be mediated without recourse to additional

forces. With regard to the nuclear force, these knot constructs give some alternative possibilities

(One will be proposed here, though others can be imagined).

If one assumes that the proton and neutron are identified with the previously described

knots, a certain kind of geometry develops for the nuclear structure which would otherwise have

no apparent source: Imagine that these two knots (trefoil, figure 8) can be approximated by a

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

16

geometric shape derived from the symmetry of their respective knot (triangle, tetrahedron),

whose surfaces are decorated to exhibit the respective charge of the particle. For protons, each

face (top and bottom) would be of +1/2 charge, with the entire particle charge ‘integrating’ to +1.

For neutrons, the four faces of the tetrahedra would be mixed, with 2 faces appearing as +1/2

and two faces appearing as -1/2, with the entire particle charge ‘integrating’ to a net charge of 0.

If one uses tetrahedral dice (D4) to construct these nuclear models, accounting for the positive

and negative faces according to the proscribed numbers of protons and neutrons which yield

stable isotopes, this seems to yield a viable system for describing nuclear structures.

Within this model of nuclear attachment, localized charge approximations give a

mechanism for nuclear bonding, with the standard rule of charge: opposites attract, like charges

repel. Two protons cannot coexist in a nucleus as a lone pair, as there are no negative faces for

their positive faces to attach to. Deuterium would be considered stable, as its single proton could

attach to either of the two negative faces of its neutron. Similarly with Helium 3 - though no

more protons can be added from that point, without the addition of more neutrons. To this point,

no more rules are required, but the instability of Tritium (Hydrogen 3) requires some thought but

can be rationalized in this way: if a neutron is unstable in free space, and even in certain nuclear

settings, there must be something about its natural configuration which leads to instability. In

terms of this toy model, the rule might be described as the exhibition of two negative faces by a

single neutron - something which is guaranteed with a lone neutron, or in neutron-rich isotopes.

Within this model, it is easy to imagine two configurations of tritium in which this neutron

condition is either satisfied or not satisfied, with relative stability or instability as a function of

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

17

the given configuration. Sandwiching the proton between the two tetrahedral neutrons would

(n~p~n) would be stable as each neutron exhibits only one negative face, while a configuration

in which the proton ‘decorates’ one of the two neutrons would have stability dependent on which

neutron was being decorated. In this scheme, an asymmetry is introduced by connecting two

neutrons to each other directly - one must donate a + face, one must donate a - face. The result is

that one neutron keeps both of it’s negative faces, while the other only has one. As the proton in

the tritium nucleus must ‘attach’ to one of the exposed negative faces, the neutron stability

condition will either be met (p~n+~n-, where the sign of the neutron denotes the sign of the face

contributed in their ‘bond’), or one neutron will be in a condition where two negative faces are

exposed, similar to that of a neutron in free space (p~n-~n+). This neutron instability (beta

decay) rule helps set the upper limit on the number of neutrons which can be added to a nucleus

before decay becomes possible, and then increasingly probable. One might imagine that

neutrons on the surface of a nucleus have some flexibility in terms of their position, provided

that there is a nearby face of appropriate sign for them to switch to, and that this neutron

migration on the surface has something to do with statistical probability of decay.

To continue onward with this, Helium 4 would exhibit only one negative face in any

configuration, and would be considered to be particularly stable, though perhaps prone to being

ejected from heavier isotopes (alpha decay). When considering this system, both Deuterium and

Helium 4 are useful constructs, as they each are the simplest configurations which exhibit only

one negative face. This becomes useful when considering that the process of connection of

neutrons and the addition of protons has a tendency to ‘eat up’ the negative faces exhibited by the

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

18

nucleus. To move from one isotopic structure to another, having these ‘base units’ (along with

protons and neutrons) is of great use, in that they can be attached to light isotopes to make

heavier isotopes without breaking any previously defined rules provided that a simple connection

is made in which only one face of the base unit (p,n,D,He4) is in contact with the lighter isotope

to construct the heavier isotope.

This model has been applied with some rigor up to isotopes of Argon and seems to

hold with some notable exceptions. Helium 3, with no negative faces remaining exposed, seems

to be an exception rather than a rule, with other isotopes seeming to prefer to keep at least one

negative face exposed on their surfaces. It is expected that certain local arrangements may allow

more than one negative face to be shown, provided that no single neutron exhibits both of them

at the same time (this was touched on with Tritium, and also seems to apply to Lithium 7). If one

models Beryllium 8, it becomes clear why this might prefer fissure into two Helium 4 nuclei

while Lithium 7 and Beryllium 9 do not. Using home-made dice models, gedanken experiments

have yielded fruitful descriptions of the simpler isotopes, and these efforts imply that a full

attempt at applying this model to the entire isotope map might best be done with the assistance of

computers. Assistance from interested parties is welcomed, as the idea is easier to form than to

test rigorously.

Leaving this hypothetical nuclear model (derived from a hypothetical vortex knot

model) aside, it is worth remembering that some similar ideas have been floating around online

which propose to merge these string/knot/vortex concepts in various ways. Several theories have

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

19

been proposed which seem to weave the knot metaphor into a conceptualization of fundamental

particles through some mechanism or another. Christoph Schiller has developed his strand

model, which describes particles as crossings or tangles of cosmic strands. This shares some

similarity with the ideas above in that they describe perceived particles as string-like interactions,

much as quarks are re-interpreted above as a projection-like, string-crossing phenomenon (see

Motion Mountain). Clifford Ellgen is possessed by a very similar sort of thoughts, as is

everyone else listed on M. Erk Durgan’s page (http://www.unitytheory.info/

similar_theories.html) Mr. Durgan himself having a related thread of thought. (sorry)

These models tend to build on the standard model as practiced currently, without much

development regarding reinterpretations of what quarks are in light of a new knot model. But a

certain amount of scepticism and critique has been evoked over the years, often simply by

examining the drastically evolving states of the standard model over the course of its

development. Three quarks became four, then five, then six. The number of quarks seems to

trend with our accelerator and detectector capability, in as much as they describe anything about

the universe (or so one might argue). There is a physics poem, rare among journal submissions,

which is tacked onto the end of the paper by H. J. Simon, D. E. Mitchell, and J. G. Watson,

“Surface plasmons in silver films---a novel undergraduate experiment,” (Am. J. Phys. 43,

630-636 (1975) [doi:10.1119/1.9764)]. This poem reads:

J or psi(A physicist’s four-footed sonnet)

Where is the thing beneath the thing?

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

20

When can we say we have found it all?Is there an end or just a stringThat dangles down like an endless fall?

Molecules, yes, and atoms, to,Electrons we know, and nuclei;Neutrons, protons, the particle zoo,And now enter now the J or psi.

Can we not try to knot the same string,To start from a bottom and see what grows?Plant us a seed and see what we getWhen unity doubles and does its thingAnd triples, quadrubles, quintuples. Who knowsWhat patterns will show? What world is there yet?

- Roger E. Clapp

The J/Psi particle was the impetus for acceptance of the addition of a fourth quark to

the standard model to account for another particle, and apparently also the impetus for Roger E.

Clapp’s poem*** above. Consider the degree of technical and scientific capability before quarks

were king: the development of molecular analysis and synthesis (organic and inorganic), isotope

separation, and beam handling (electrons, ions or otherwise) did not require quark models nor,

for that matter, do any of our current electronic or photonic technologies. In some sense, the

utility of the standard model and the quark metaphor has been limited to projecting descriptions

onto the smallest known constructs with no real impact in terms of atomic applications and no

clear macroscopic comparison. Perhaps this is the true dread secret of the high energy physicist.

But all hope is not lost, beam-line workers! This re-envisioning of Kelvin’s Vortex

knot model, if taken seriously, could provide a powerfully simple re-interpretation of the

Standard Model of fundamental particles. As no mathematics has been employed to give rigor,

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

21

there is plenty of room for additional thought here, with a possibility that the desired equations

may already be known through prior mathematical labors. In an ideal future, this might simplify

fundamental physics to a level accessible to savvy school children, as nuclear structures and

elementary spectroscopy have been to be for some time. The nuclear structure model proposed

here requires more development, but might provide a similar level of educational accessibility.

Any serious effort to develop such a model would surely motivate dozens of graduate theses -

even if it was eventually considered no more useful than string theory and cast aside as fruitless.

With this in mind, the elaboration of mathematical models for the vortex knot idea and

subsequent invocations of heresy toward the standard model are left as an exercise for the reader.

The nature of infinity is this : That every thing has its Own Vortex; and when once a traveller thro' Eternity

Has passed that Vortex, he perceives it roll backward behind His path, into a globe itself infolding, like a sun,

Or like a moon, or like a universe of starry majesty, While he keeps onwards in his wondrous journey on the earth, Or like a human form, a friend with whom he liv'd benevolent. As the eye of man views both the east & west encompassing Its vortex: and the north & south, with all their starry host: Also the rising sun & setting moon he views surrounding

His corn-fields and his valleys of five hundred acres square. Thus is the earth one infinite plane, and not as apparent To the weak traveller confin'd beneath the moony shade. Thus is the heaven a vortex pass'd already, and the earth

A vortex not yet pass'd by the traveller thro' Eternity.

Excerpted from ‘Milton’ by William Blake

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

22

Footnotes:

*Vortex rings are exploited currently in certain toys (http://en.wikipedia.org/wiki/

Vortex_ring_toys), and used occasionally by dolphins in a similarly playful fashion (http://

en.wikipedia.org/wiki/Bubble_ring).

**We must also eventually consider the nature of kaons, J/Psi particles, and other

particle characters with less prominent roles than the more readily observed photons, electrons,

protons, neutrons, and neutrinos.

*** Clapp seems particularly sceptical of the quark idea, as one can read in his

“Nonlocal Structures: Bilocal Photon” paper, though his own explanation for particle behavior is

fairly dissimilar to that of the knot/string/strand/tangle models described/referenced here.

Fiasco Press www.fiascopress.org Journal of Swarm Scholarship

23