Painrx

PAIN: ITS QUANTUM NATURE AND FABRIC
RANDY BAADHIO
To Fanta and Kadi, two wonderful, supportive sisters; to Anne-Marie,
la doyenne of sisters-in-law, for the gifts of Caroline and Mimi.
Date: October 17, 2015.
1991 Mathematics Subject Classification. 14Gxx, 14H45, 14H55, 14D21, 14E15, 30F15, 32XX, 37A35,
51Pxx.
Key words and phrases. Quantum Biology; Pain; high temperature superconductivity; magnetic permeabil-
ity; lattice confinement, propagation of sensory signals; Riemann surfaces; curves; resolution of singularities;
zeta function convergence, divergence, residues; diophantine geometry; moduli space; quantum field theory; har-
monic, elliptic functions on Riemann surfaces and manifolds; lattices; entropy, invariants, information; dynamical
systems; ergodic geometry; algebraic, differential topology and geometry; Knot theory; quantum and topological
invariants; mathematical aspects of biological and neurological systems.
1

2
ABSTRACT. Quantum Field Theory, Differential Geometry, Topology, Lattice Gauge The-
ory, High Temperature Superconductivity, Magneto-hydrodynamics, are brought together
to unravel the complexity of Pain. Pain is shown to be a pressure-like harmonic oscillator,
akin to a primary seismic wave. The Aδ nerve, a prevalent carrier of pain signals, is shown
to exhibit characteristics of a high temperature superconductor, H T SC. Liénard-Weichert
equations for retarded time-electric, and magnetic potentials, are shown to govern Pain’s
three steps coupling, with its specialized receptors, and propagators. Phase One, a near
relativistic process, decouples Pain’s magnetic field from its electrical component, at the
singular point in which Pain latches on to receptors. Phase Two governs the absorption of
Pain magnetic fluxes, by boundary layers of myelin, a phenomenon known to physicists
as the Meissner effect. Phase Three describes the ingestion into the receptor interior, of
Pain electrical potentials. The Aδ benefits considerably from the coupling: Pain’s mag-
netic fluxes are used to sustain its physical integrity, even as its boundary layers undergoes
constant elastic deformations.
We resolved why a change in the weather, is often felt as acute pain. Barometric
pressure gradient variation of the atmosphere affects the magnetic fluxes configuration
of the atmosphere, often resulting in brute penetration. Navier-Stokes equation is used
to quantify actual deformations, subsequent elastic restoration, of equilibrium, of Pain
propagators. The telltale increase in Pain is shown to be proportional to the carrier’s rigidity
coefficient, to subsequent superconductivity nucleation of the Aδ.
Neurology most vexing problem, the Myelin Paradox is solved. Myelin is shown to be
a good insulator of Pain signals, in the large N-scale limits. Indiscriminate absorption, by
Myelin, of energy, spontaneous emissions, are explicitly derived, using a variant of Hawk-
ing formula for black hole emission, superconductivity lattice confinement, nucleation,
and the rigidity formula. The paradox, its resolution, highlights, the degree to which, we
have fundamentally misunderstood myelin; reveals in the process, a host of hitherto hid-
den properties about Pain, receptors, the brain; assists in unraveling complexities inherent
to the dynamics of sensory signals, specifically coupling constant of Pain, including con-
servation of scales, via Power Laws; provides an extensive treatment of the propagation,
diffusion, convergence, scattering, of Pain, within the Brain. The magnetic permeability
of a myelinated nerve, receptor, is what determine its ability to acquire, couple, propa-
gate, than deliver to he brain, Pain signals, without loss of signal integrity, or quantum
interferences; not insulation.
Why are certain nerves well suited to propagate pain? Aside from H T SC, complex
topological, differential geometry structures arises; among them, that of a Riemann surface
with a torus (a hole) of genus 1. Pain journey, inside of specialized nerves, is described:
the set of Z2 quenched lattices, describing the interior, separates Pain signals, by a distance
a, a factor proportional to the propagator’s radius, length. This separation coefficient de-
termines, via duality, the quenched order-disorder ratio, the threshold at which pain signals
are subject to quantum decoherence. We resolve why the B and C classes of nerves are
poor propagators of pain; resolve further, the salient contradiction: the Aδ, the B both, have
myelin layers. Yet, the B, is a poor conductor of pain signals. On the other hand, the C is
free of myelin. Nevertheless, it is also a poor conductor of pain, though curiously, shares
similar properties, where pain propagation is concerned, with the B. Obviously, myelin,
must be ruled out. The intrinsic radius, length of the B, and C, are small, in contrast
to the Aδ. Thus, the separation coefficient, a shrinks below a critical quenched order-
disorder threshold. This subjects a journeying pain signal to ricocheting, twisting. This
chaotic dynamic translates into energy depletion, divergence. This realization give rise to a
serendipitous discovery: in the B, C instances, pain has an amplitude, the configuration of
which is a knot. Whereas in the Aδ, it is unknotted. The celebrated Kauffman polynomial
detects these amplitudes. We shed some light on chronic pain fundamental nature as well.
Another of neurology standing problem is resolved: why Pain signals are forced out in the
open, in the bulbous area of the brain. We relates this peculiar mechanism to Cajal-Loewi
original discovery of the synaptic cleft. Demonstrates why it is required by physics, and
mathematics. The uniqueness associated to each pain signal is shown to be conserved, con-
tained in the Fisher Information formula, which is strongly entropy dependent. This lead
us to the discovery that human brains assigns a unique quantum algorithm, an individual
pain signal encryption key, to emerging pain signals. An extensive description of the dif-
fusion, scattering, convergence, decay modes, branching decays, of Pain, within the brain,
is provided, using a variant of Feynman diagrams, Wick-Gauss path integral formalism.

PAIN: ITS QUANTUM NATURE AND FABRIC 3
1. INTRODUCTION
To the persistent, age defying question, what is pain? the answer has remained quite
elusive. The brain central role in deciphering complex sensory signals, adds significantly
to the scientific dimension of the challenge. Pain is unique, as signals go. In the vast
majority of instances, sensory signals, such as temperature, gradient variations in humidity,
say, do not elicit the brain imminent response, mere specks in the background of sub-
consciousness. Pain is unique too, as biological sensors go for a host of other reasons:
biologists have spent decades, if not centuries, to decipher it outlines, to have worked out
the specialized apparatus at play, supporting it propagation up to the brain. Once triggered,
Pain is unique signal eliciting, equally exotic, complex, cascading processes, from body
and central nervous system. Biologists achievements here are truly remarkable. What is it
about pain that allow it to discriminate quite well, latching on to specific receptors, nerves,
neurons? Why those and not others? Is the reverse holding true? That the propagators of
pain are equally picky, prefers only to deal only with pain? What makes the brain equally
unique at recognizing, capturing, processing pain? At marshaling the body vast biological
machinery to react heal, as a consequence? What is it about pain that forces the brain
to assign a priority factor greater than other sensory signals? For instance, Why does it
not hurt to think? Why is are other sensory inputs, say pressure, temperature gradient
variations, do not hurt, so to speak; whereas pain does? What is it about pain that triggers
the brain conscious, complex and specialized areas, elicits an imminent and aggressive
response, whereas, in contrast, other inputs are assigned to the background? Why must
pain be required to undergo a complicated scattering to higher areas of the brain? Is there
something profound we may have overlooked about pain itself? What about insulation
of pain signals, especially in propagators with layers of myelin? Can we resolve biology
significant contradiction: that myelin is resistant to electrical sensory signals like pain, yet
somehow quite good at absorbing them, simultaneously? What gives? Have we missed, or
overlooked something fundamental here? Is physics able to unravel the nature and fabric
of pain?
This paper reports a number of new discoveries, thanks to converging, unusual factors:
(1) The author personal history of polio, subsequent acute, chronic pain, provided the
impetus. The author contracted polio at the tender age of two years, in Africa,
from improperly refrigerated Rabin vaccine. Since, polio sequelae have defined
the author life’s, pain spinal pain being the foremost manifestation. It’s devastat-
ing intensity, acuteness, persistence, its impact on brain malfunctioning, neurolog-
ical signaling, quality of life; its psychological, social dysfunction impact, whose
true dimension, is unfortunately difficult, if not outright impossible, for otherwise
healthier persons, to grasp.
(2) This has led the author to a quest for relief, a journey nearing five decades, marked
by ever sophisticated, specialized treatments, surgeries, thus far with limited suc-
cess.
(3) One final, radical at that, option, recently confronted the author: Selective Dorsal
Rhizotomy, the permanent severing of nerve bundles responsible (or suspected of
being) for the acutely, debilitating chronic pain. Questions I raised to biologists,
neurologists, clinicians in the medical field, were answered vaguely, confusedly,
and sometimes, contradictory; still, many simply had no answers, giving the cur-
rent state of knowledge in neurology and biology. So the author, a quantum and
mathematical physicist, began looking into (as we say in our field), the nature and
fabric of pain. Moreover, the connection with the pathways and propagators of

FIGURE 1. A disease with no cure or effective treatment, Poliomyelitis
in a young child.
pain could not be ignored. Neither could the brain, its capacity to make sense of,
and to process pain.
(4) Because I envision and assume a cross disciplinary readership audience of biolo-
gists, physicists, and mathematicians, I have departed from established standard of
styling for publications purely aimed at physicists and mathematicians, as I have
done in past work. They are not extensive however, therefore the mathematics and
physics professional audience should easily follow my arguments and results. On
the other hand, I am quite aware that the issues to be solved here are primarily bi-
ological. To resolve the difﬁcult task of addressing all audiences simultaneously, I
have resorted to a simple technique: whenever possible, I provide extensive back-
ground, often with visuals. For this reason, the article is rather long. Hopefully,
the efforts would meet objectives of clarity, and further much needed, cross disci-
plinary interactions between mathematicians, physicists, and biologists.
Without this personal and professional background, I doubt I would have been otherwise
privy to report something new on Pain.
1.1. A Personal History of Polio and Pain. Poliomyelitis [1, 2, 3, 4, 5, 6, 7, 8, 9] is a
virulent infection caused by an Enterovirus [7,8] in which vector form it is known as the

FIGURE 2. The adult and human face of Poliomyelitis, whose signature
sequelae, atrophy, paralysis, and deformities are quite similar to those of
the author.
poliovirus; the infection path begins with fecal matters in the water collected after miles
of walking, which you have no choice but to drink. There is no cure, medications, or
treatment for the infection, thus the importance of vaccination. The RNA viruses go on
to colonize the gastrointestinal tract, specifically the oropharynx and the intestine. Polio,
like HIV, or Ebola, is so peculiar in that it infects and causes disease in humans alone. An
often overlooked factor: malnutrition, immune deficiencies, hallmark of poor children in
tropical countries, significantly contributes to an increase in polio infection [6, 7, 3].
One of biology celebrated achievement has been the invention by Jonas Salk, of a polio
vaccine. Rabin later provided a refined, versatile variant. The Rabin vaccine, given the
author, is peculiar in a number of ways:
(1) Unlike Salk’s original vaccine, safer though less potent, it contains live polio
viruses. These have been genetically engineered. The original, virulent polio
parent strain, is known as the Mahoney serotype. Rabin modified the Mahoney
strain. By the second version, he was able to substitute two nucleosides [1, 2,
3, 4, 5]. Later, it emerged that people like me contracted polio as a result of his

FIGURE 3. Above, a recent MRI of the author back, showing a broken,
deformed, and fused spine, Polio most significant generator of Pain.
vaccine. The conventional, accepted rate, in the literature, for such, is one infec-
tion per 750,000; but as I make obvious above, this does not hold true for Africa,
and most third world countries [3, 4, 2], Rabin further attenuated the live viruses,
re-engineering them with 10 nucleosides substitutes.
(2) Second, the vaccine requires refrigeration, a true luxury, in sultry, tropical third
world countries,
(3) Third, the oral Rabin vaccine is only 50 percent effective per dose, to all three
poliovirus serotypes, meaning three doses are required, to be effective, another
challenge in taxed poor tropical countries with hardly any existing road infrastruc-
ture.
Ilizarov is the surgical procedure in which, to correct hip displacement and stress on the
spine in polio patients, the leg in question is broken into segments, than outfitted with a
huge frame, with rods piercing the leg. The eight wounds must be looked after and attended
daily, to prevent infection. Furthermore, twice daily, you are required to twist three bolts,
by a precise amount (essentially a 2πi twist in relation to the fixed Ilizarov frame), set via

(a)
(b)
FIGURE 4. A byproduct of polio, deformities of the spine often lead to
debilitating pain. Above, in this MRI of the author spine, pathologies are
obvious. The Caliber of Pain is made explicit by the 3 oval, white-ish
areas, radiating pain away.
tensile torsion during the five hours long surgery1
or not moving. Spine fusion may takes
away the most disabling of pain, and does away with the diseased and degenerated portion
of the affected lumbar disc(s), as it did the author.
When all have failed to relieve Pain, a risky, radical, and quite final surgery, to severe
offending nerves in the spinal cord, Dorsal Selective Rhizotomy (DSR) [9] can be consid-
ered. This is what confronted the author, and led to this work. As the theory goes, pain
is though to have an affinity for nerves lacking GABA, a prominent neurotransmitter (see
figure below). Nerves suspected of conveying the acute, chronic, debilitating pain to the
1To provide an accurate gauge of the torsion and associated force: flipping your arm with the elbow fixed (a
common practice of ballet dancers) with your palm and fingers facing away from the elbow. This is a 2πi twist.
A 4πi twist is impossible to do unless your arm is broken. The electron and other particles known as fermions
do so frequently. This was noted by the eminent physicist Paul Dirac [10, 15], is known as the Dirac string, or
chirality. It is among the mechanism by which particles flips into their anti-matter incarnation (the positron in the
electron case), and vice versa.

(a)
FIGURE 5. A patient fitted with an Ilizarov frame to correct bones defor-
mations. This process is used in Polio patients to generate bone growth in
order to compensate for polio-affected limbs that are shorter, and hence
a source of hip displacement and subsequent spine deformities and ex-
cruciating pain. The author was fitted with a much more complex frame
than above, for over 9 months. Below, in (b), Figure 6, X-Ray scans of
Ilizarov frame, bone fractures, holes.
brain, are permanently severed. You can deal of course with the possible loss of the good
leg, and so on. Then however, as you research all this, you began to realize that in fact
biologists do not know what pain really is, and how many pain signals a nerve can carry
to the brain. In other words, a bundle of spinal nerves may be severed that have nothing
to do with pain. This is because the principles used by clinicians in DSR actually uses
standards for muscles, in which roughly speaking, a short burst of electricity is applied to
the nerves and the resulting contractures, or physiological reactions, to the resistance from
the applied current, is the proof of guilt! To a physicist, this is akin to issuing a fatwa for
simply breathing!
DSR is no small affair. The spinal cord is exposed, after a cut; muscle nerves are iden-
tified, than pulled aside. Reaching further down, pain sensory nerves, directly connected
to the brain, are exposed, pulled out, than set aside. Muscle nerves believed to support
the diffusion of sensory signals are differentiated according to one of two classes; they are

pulled aside by the equivalent of a medical kitchen cutting board. Pain nerves are given a
fancy spa treatment, first with a bath of chemicals, then each and every one is pulled (or
a bundle of three at most). They are then zapped with a dose of electromagnetic energy,
precisely ones used for muscles [9]. Confusion is evident to a physicist. There is no mea-
sure of pain? No gauge of pain? Somehow, we have assumed, all along, Biologists knew
how many pain signals a nerve can carry. The question now becomes: just exactly what is
pain? Just what is the physics of pain? Why its choice of specialized couplings?
That we are able to report anything new on an academically mature subject as Pain,
speaks to the benefits of physics and mathematics being put to use, to solve biology most
pressing, unresolved, fundamental problems. Such a collaboration must be encouraged,
allowed to flourish, for it will benefit this field immensely. To the physicists and mathe-
maticians, there is also a net gain to be had, more satisfactory than the esoteric Cosmic
problems, with are professionally dealing with, daily. For obvious reasons, this has been
the least difficult ”physics problem” I had to deal with; yet it has also been the most dif-
ficult, in so many ways. Partly, from my background and perspective, I had no choice
when faced with a final last decision of life altering consequences, than to apply myself,
to make sense of what is already known in biology, than of course, reformulate it in its
proper physics and mathematics forms, prior to solving anything. The interdisciplinary
nature of this work albeit challenging, turned out to be intellectually stimulating and just
as satisfactory.
This is a personal appeal to my mathematician and physicist colleagues: step in. Your
contribution is sorely needed. Never mind if problems are vaguely defined by biologists:
we can redefine them in ways that meets our precise and exacting standards. As you read
this work, you will appreciate it can be done and quite easily. On the other hand, a number
of open problems will also become obvious to you. To pick random ones: working out
explicit generators (with torsion) of the homological cycles of pain nerves, and determin-
ing the vacuum configuration of pain itself when immersed in certain systems, including
the brain. The quantum topology of pain and nucleation of superconductivity; an exhaus-
tive treatment of the brain coherence/decoherence quantum encryption; the correlation and
dynamical coupling (or lack thereof) of brain lattices in which pain signals are confined;
the determination of just how many of these there are; and so on goes the list, touching on
numerous specialized fields in which you have earned a place of exceptional standing and
reputation because of your individual contributions. Either way, new learning is required
on both ends. But if history is any guide, there hasn’t been one advance in physics that has
not required ”new” mathematics, including Newton having to ”invent” calculus on his own
to make sense of gravity and later Einstein using Riemann’s. In physics, it is an open secret
that you are as good as the math you know. May the very same holds true for biology, that
is, you are as good as the physics you know. I am certain the advantage of bridging is that
the physicist will make it his worry, not yours, to bring in the complex mathematics to the
(party or table).
Because my audience is going to be a mix of biologists, physicists, and mathematicians,
I have taken care to provide an expanded review of the current state of nerve signaling and
pain. This foundation is useful to put the results into perspective. I have also departed
from normal norms of physics and mathematics academic articles so as to reach the dual
audience of biologists and physicists-mathematicians. The reason will become clear soon
enough. Unfortunately, as often is the case in cross-disciplinary outreach, the biologist may
be uncomfortable at first with the new language and dictionary of advanced mathematics
and physics, and the latter with that of biology. Thus, focus on clarity however of a laudable

(a) A multipolar neuron’s anatomy. Courtesy of Wikipedia.
(b) A myelinated motor neuron is depicted above. Note the synaptic cleft,
and the amount of dendrites. Courtesy of Wikipedia.
FIGURE 7
objective had to be supported by background whenever possible. Only then could the goal
of solving the problems at hand had engages my varied audience. I hope this effort resulted
in a better appreciation of the problems, and results. Biology can benefit a great deal from
physics and mathematics as it has from chemistry, no doubt. The reverse is equally true of
mathematicians and physicists. The emerging field of Quantum Biology is likely to be the
arena of such interdisciplinary efforts.
2. PAIN AND CHRONIC PAIN: NEW RESULTS
Pain is an unpleasant experience, the result of intense, sometimes persistent stimuli.
The body ability to take notice of pain, react, and began the process of healing, is per-
haps among pain most significant biological characteristic. In living forms, it has evolved
into reflexes, withdrawal from damaging situations. Yet, this must also be contrasted to
excessive impairments in attention, control, memory retention, in concentration, in mental
exhaustion, fatigue, depression, anxiety, fear, social withdrawal, unpleasantness anger; and
of course significant expenditures of medical resources for treatment.

(a)
(b)
FIGURE 8. Pain first emerges into the bulbous area (above in orange in
(a)), the very area affected by poliomyelitis; forced out into the open,
Pain must further contends with additional diffusion to higher portions
of the brain. Density gradient variations of the brain, (b), a previously
unrecognized, yet critical property, acts to control the process.
Close to the spinal cord, densely packed neurons are aggregated in the singular dorsal
root, a swelling most new students of biology recognize as the dorsal root ganglion [11].
These are mostly afferent neurons, connected to each other by axons from ganglion. Their
pathways is of great interest to us: from the dorsal root ganglion, they travel to the spinal
cord. We pause to rephrase this in a fundamental quantum description: the original sensory
signal (pain) is a first order harmonic pressure oscillator. It has a very well defined and
quantifiable Feynman path integral. Once inside the spinal cord, both the nerve fiber and
the pain signal travel upward to a part of the brain known as the medulla.
The pain original effective action acquires an additional term, an expansion factor, to
which degree of perturbation arises. Hence, an expansion operator within the Feynman
path integral [10, 15, 18, 20]. Once in the medulla, the signal gets directed to the medial
lemniscus of the mid brain (another perturbation), then on to the somatosensory cortex of
the parietal lobe.

Considerable energy has been expanded by biologists to make sense of the complexity,
the underlying mechanisms at work in nerves, neurons, their variants, where sensory sig-
nals are concerned. The crowing results, experimentally verified, are thus beyond factual
disputes [9, 11, 12, 21, 22]. To the exception of the central problems we are addressing
herein, for the most part, there is thus little for us to add. Cells in the dorsal horn are
physiologically divided by distinct layers, known as laminae. Nerve fibers (see the clas-
sification of nerves into types below) selectively synapses in different layers, using either
glutamate [13], or substance P [13], as their neurotransmitter of choice. For instance, a
prominent nerve fiber, known for its unusual affinity to effectively diffuse pain, the Aδ,
forms synapses in laminae I and V. The C fibers connect with neurons in laminae II, and
so on [13, 14, 21, 22, 23, 24].
FIGURE 9
Within the spinal cord, Pain couples to specialized laminae. According to our observa-
tion that Pain is akin to a ball or energy, moving about as a seismic-like primary wave, at
onset, it is a first order harmonic oscillator; which than couples with a nociceptor, projects
into a second order neuron, which than send the information via two different pathways to
the thalamus. There, it is processed into the ventral posterior nucleus, than further scattered
to the cerebral cortex in the brain [14] for final processing. Two things are noteworthy: one,
biologists believe the media-lemniscal system is reserved for non-pain, whereas the antero-
lateral is for sharp pain. To my knowledge, no experimental evidence, thus far, supports

FIGURE 10. Sketched above is Pain most famous nerve fiber carrier, the Aδ.
this claim. Second, when biologists states a neuron or pain signal projects into something,
they are in fact (albeit vaguely), describing the expansion of a potential function, whose
series expansion for the exponential path integral is well know [10, 15, 18].
What is so remarkable about pain and chronic pain?2
To the topologists, differential
geometers, and quantum physicists, I can truly only prove the maxim that a picture is
worth a thousand words. Here is a cross-section of the famous Aδ fiber:
The unusual Riemannian geometry of the Aδ nerve pain fiber3
is the first observation
which will also us to unravel the mystery of pain, the brain signals processing. Looking at
the cross section of the Aδ, the first reaction a mathematician, or quantum physicist, may
have, is, of course, to vaguely recognize the shape; nevertheless, pause, confusedly, say out
loud, to borrow a friend expression (who happen to also be a renown mathematician on his
own rights)4
: ”What is Randy talking about?” Implicit in that statement is that there seem
2Chronic pain is far more elusive. Nevertheless, as I show below, an emerging picture from quantum physics
provides significant clues.
3Also a personal friend of mine, lest we demonize it, as with the bad cholesterol, fats of any nature, even
the (non and) trans(itory) kinds, sodium (salt), and just about anything else under the sun. The Aδ is performing
an important function, should not be considered a sinister biological entity, nor a nemesis. To the contrary, it is
deserving of our deference.
4One that has also played a mentoring role from the late 1980s to the mid to late 90s (so from age 24, when
I began my professional research and academic career at Cornell as a mathematical-physicist, and later while
at Berkeley); one who can take some credit for teaching me, and hence satisfying my thirst for topology and
other esoteric fields of mathematics; one in fact, whose significant discovery, the Kauffman polynomial [29] has

FIGURE 11. Sketched above, the cross-section of the Aδ without its
complex cell machinery. Its Riemannian geometry and topological na-
ture are manifest. Einstein incorporated this formalism to make sense of
gravity and spacetime [16, 17, 18]. The hole, at the center, knowN as a
genus (of order 1), or the nucleus, by biologists, is equally critical, much
like a non-spinning black hole, against the background of spacetime. We
make full use of the Aδ rich mathematical complexity to unravel how it
couples with, than propagates pain.
to be something, to pause and to think about. Of course the mathematician and physicist is
thinking: ”Yes I recognize the shape, but so what?” She is doing so because, you see, she
is taking into account all the machinery that comes with: the fancy shades, the substantia
gelatinous, the dorsal nucleus, the central canal, the motor neurons of the anterior horn,
even the (torus) central canal and the strange curved lines (the I,II,···IX) and so on. She
is having trouble making sense of all this, because she is familiar with the shape empty (as
I illustrate in the immediate figure).
She vaguely recognize the curved lines, the contours as maybe some kind of generators.
But of what? There is no gauge group, no fields to speak of, no automorphism and diffeo-
morphism groups, no mapping class group5
Mathematicians and Physicists can be excused
impacted physics to a great extent [31] [30, 29]; the Kauffman polynomial [28, 29, 30, 31] is used to show that
the amplitude associated with the scattering of pain is unknotted in the Aδ nerve, whereas it is knotted in other
nerves; one who has reinforced in me certain fundamental human values by strength of principles in his daily life.
5If, as a kid, you wondered why a sock can seemingly and easily fit, opposite and misshaped, left and right
foot, you are witnessing the power of the mapping class group, among nature greatest of symmetries. If, on the

for further puzzlement, as would biologists, when the picture of the Aδ is redrawn, with ab-
solutely nothing in it, no fancy machinery, only the shape and torus, as shown above. Now
however, it is the turn of the latter to look in puzzlement at the figure below and wonder,
”What is this guy talking about? Is he crazy to show me this cross-section with nothing in
it?”6
The fact that it is empty is critical to understanding the extremely low scale of pain,
how it is able to affect a behemoth entity. The machinery is utterly useless: the relentless
focus on them, and on the scale of the nerves, has been the core reason, why, thus far, we
were unable to grasp the nature and fabric of pain (and it turns out, of the pain nerve, of the
brain abilities to process pain too). To get a sense of the scales, against this vast and com-
plex cross-section, pain will hardly be a point in that manifold. The dotted cross sections
drawn throughout the empty Aδ are certain important generators, known as cohomolog-
ical cycles (or by duality, homological), topological invariants which are fundamental in
describing physical properties of the nerve and of pain. Quantum physics essentially says
that it is not per say the volume, or area of pain in that nerve that matters: it is actually
the elastic, tiny, seismic-like deformations brought on by pain, as a wave, that matters the
most. And this is exactly what we have been missing for so long. In this optic, this is
exactly what pain looks like.
The physicist-mathematician (PM for short) is in this state, because training tells her
when to put something in, which will never be remotely close to the original Aδ nerve
cross section. That is, she must start with her own vacuum configuration of the nerve. On
the other hand, the biologist has worked very hard, to first detect, then later make sense of
all this fancy machinery [9, 10, 11, 12,13, 14,19, 23, 24, 25]. Thus, when I point out the
shape, he certainly is entitled to shrug it off: after all, they gave it to us, PM; and did so
after decades, if not centuries, of hard work. He is in very familiar territory, and deservedly
so. Or is he? The chasm, obviously, appear deep and irreconcilable, especially on both end
of the spectrum: if we leave everything, the biologist understand and is comfortable (but is
stuck to make sense of difficult, unresolved problems); whereas the PM is utterly confused.
If, on the other hand, we take everything out, leave out only the shape, the biologist is now
utterly confused (while the PM is happy), for what is an empty cell after all? What use
does it have? So what gives? Pain has remained a mystery because the focus has always
been on the scale of the nerve. You see, as long as you describe everything, and anything
in term of the nerve scale itself, even in relation to itself or to the brain, or a body at large,
the molecular scale is fine. But there is no way I know of, in which you can actually
understand pain (and other sensory signals) unless you take into account the very scale of
a pain itself: the quantum scale. The machinery is meaningless. Let me reemphasize this
statement: the machinery is useless. Indeed, you must come to the side of the PM. Why
is that? Let us look again at a depleted, crashing and dying ocean wave. Ingrained human
biases are such that we must first contrast the wave to the much larger systems it is evolving
in (oceans, shores). Time is factored in as well, but in a rather loop sided way: we see the
other hand, you have tried too, as a kid, to fit a left shoe into a right one, and wondered why it did not fit, in
contrast to the sock, you are witnessing, yet again the mapping class group, or lack thereof, at play. In the first
instance, the automorphism group agrees (in 2 + 1 dimensions) with the larger spatial diffeomorphism group,
and the translation of the sock from left to right is meaningless (the symmetry ignores the left or the right, a
fundamental property known as chirality in physics, and the reason for the existence of anti-matter, and a host of
very important cosmic features, when violated). In the latter instance, they do not because the diffeomorphism
group takes note of the fact the shoe is very large, in relation to the size of the foot, so its automorphism group, or
more precisely the ratio between automorphism and diffeomorphism groups is skewed. The physical importance
of this property is described at length in a discovery made in 1994 at Princeton [17].
6Maybe, but I will be very surprised to be proven wrong, and will bet my polio leg otherwise!

FIGURE 12. Quantum physics sees Pain as a ball, displacing the smooth
topological structure of the supporting apparatus it is coupling with, for
diffusion. Within the Aδ, Pain is shown to journey through a lattice,
illustrated above.
undulating wave crashing, disappearing, as we observe it. To grasp and appreciate the role
such a wave play in the erosion of continents, in soils-nutrients exchanges between the
continents and oceans, that they exist in great part to dampen kinetic energy from Earth’s
rotation, frictions between the atmosphere and the ocean surface, or that it is further the
result of the Moon gravitational pull, that demands we let go of our biases. Still, after such
consideration, no one can deny the central role a rolling, insigniﬁcant ocean wave has.
Look carefully at the cross section picture of the Aδ: it is big, even in relation to smaller
parts of its machinery. Pain is the scale of an electron, give or take a couple of orders of
magnitude up7
To understand its effect on the nerve (or for that matter nociceptors and
7The neutron is prohibited from been a pain signal (and any other sensory one) because it is electrically
neutral. It’s magnetic charge (expressed in relation to that of the electron), is non-existent, experimentally mea-
sured at [20] q = −0.2×10−21. The neutron, a composite particle, made up of three quarks (the (udd), or (up)
and (down+down) is much heavier than the electron, The proton (uud), though similar to the neutron in mass,
(within 0.01 percent), also in composite amount of quarks, is not neutral; it too is forbidden by quantum physics

neurotransmitters), you must first go to an extremely short scale (in relation to the scale
of nerves): the quantum scale. But what does that mean concretely? Roughly speaking,
a ball passing through, leaving in its wake a gentle, elastic wave, much like an ocean
wave rippling, than dying on the shore. The best analogy I can conjure is this: imagine
a city with a radius akin to that of New York city. Take everything out and put in a dot,
twice the size of the one ending this sentence. Of course it will take you a long while
to know there is a dot in New York city, let alone it does affect the city. Similarly, an
ocean wave, crashing on the shores possesses a scale quite infinitesimal, in relation to the
volume of the ocean. Waves however crash on the shore for a good physical reason: they
provide the very conservation of energy momentum in open system like a vast ocean. As
planet Earth rotates, oceanic waters swells, dip. Earth’s rotation forces the atmosphere to
swirl, a consequence of which, is the Coriolis force. Without the atmosphere, oceans will
still swell, and sway about. Interaction between the atmosphere and the surface of ocean
results in greater undulations. Waves on the beach appear all but innocuous to us: we tend
to systematically contrast them to the great vastness of the ocean (and shores). In doing so,
we neglect to see physics greater principles at work.
A dot in New York City share similar properties: hidden natural and physical riches. In
this, there could be no argument, because we are speaking with the conviction of over a
century of unwavering consistent experimental proofs, whose minute degree of accuracy,
still leave professional physicists in awe today [20, 10, 15, 18, 30]. In a nutshell, this has
been the reason why pain has remained so elusive; why the chasm between us and biolo-
gists has persisted for so long. The dot is the pain inside the nerve; not only that, it revet the
topology of an undulating seismic-like, primary wave. The quantum mechanics machinery
necessary to describe its effects on the nerve is vast, technical, complex. Nevertheless, it
has been available for over a century now. As with quantum physics, we can rely on such
formalism to explain pain’s fabric and nature, to an unparalleled degree of precision: yes,
the dot perturbs the cell, in the form of a tiny, compression like wave [22]. At this scale. it
is not a biology problem per say, rather a complex physics and mathematics one.
Incoming (or incident) pain waves amplify the Aδ intrinsic harmonic oscillation [22],
its vacuum, or minimal energy state, described by the celebrated BPS equation of state
[37]. The vacuum of any cell, nerve, is not empty at all: it has an absolute minimal en-
ergy [10, 15], the latter subject to quantum fluctuations at speed greater than that of light
8
. The vacuum of a nerve, or cell, must always fluctuate, within the range 0+ or/and 0−;
violation of Einstein’s postulate on light speed, by space and time, and energy, or combina-
tion thereof, remains a difficult, fundamental, yet unresolved, problem in physics, recently,
leading physicists to suspect spacetime to possibly be finite, composite of something more
fundamental. To compensate from tearing up its own cosmic fabric, and to satisfy the
universe’s conservation laws, time must borrow from energy to create virtual particles.
This profound consequence of Einstein’s discoveries, though popularly less known, ex-
plains why a far away observer, angling a certain way, can peer into our past, or future
easily: time travel; why time is relative, not absolute, expands and contracts; why space is
to be pain. The reasons for this exclusion follows from quantum field consistency conditions. They are derived
from saturated BPS states [37], in essence, a spectral signature condition which dictates the minimal amount of
magnetism a vacuum field can have; all indications (from the author) are pointing to the central role BPS may
play in chronic pain. Biology is primarily a cascade of photoelectric events from large molecules; living forms
are adept at interpreting these, via complex mechanisms. Pain is no different in that sense, that is, it is an electron,
or a collection of electrons.
8Heisenberg uncertainty formula for time and energy, quantifies such speeds at roughly ∆E · ∆t ∼= 10−24
second, or a trillionth of a trillion of a second. Light’s speed, by contrast. is a puny 299792458m
s−1 .

essentially the Federal Reserve, so to speak, a borrowing facility, akin to the biggest Cos-
mic Bank, in which both time and energy borrows freely. Against this background come
the dot, pain, with an even smaller scale, generating tiny perturbations or ripples. They
are absorbed by the cell. Just how, however, is not a trivial matter to describe [26, 27].
Nevertheless, this is our objective. An insignificant incoming harmonic disturbance is pro-
cessed as unique pain, all the way up to the brain. Fuzziness, vagueness, mystique, used
to describe pain, give way to quantifiable,explicit, computable, precise, and measurable
formalism. Not just from the pain itself, also from nociceptors, nerves, axons, synapses,
and from the brain itself. Reconciling all these scales, from pain, the body, nerves, the
brain, in a sensible, smooth, functioning way could only be done using physics. The aura
of vagueness, subjectivity, and mystery surrounding pain is gone.
The definitions of pain (and chronic pain) are as varied as the theories behind them.
Nevertheless, biologists, and neurologists, in particular, through experiments, have pro-
vided us with a clearer pictures of the pathways, chemicals, transition spread, general
propagation and diffusivity, and reception of signals into the brain [9, 11, 12, 13, 14, 19, 23,
24, 25]. We shall not rely on vague interpretations of pain, and of chronic pain, expressed
as function of duration (frequency), intensity, nor kinds of pain, for instance, neuropatic9
,
phantom, psychogenic, breakthrough, and incident pain. Instead, we squarely focus on
the physics and nature of pain itself, diffusion, processing by the brain. First, we unravel
the precise quantum processes at work, allowing nociceptors to discharge electromagnetic
currents, as initial pain. Second, mechanisms underlining pain fibers ability to absorb such
action potentials, preserve them, send them upward to the brain. Our focus does not end
with coupling, potential discharges of pain: we explain how neurotransmitters, within the
brain, are able to encrypt, than de-encrypt, and process pain. The quantum treatment of
pain signaling we undertake extends to explaining the physics of myelination of nerve
fibers: that is, we show why myelin, thought to be a good electromagnetic insulator, is
misleading, contradictory, and false10
.
Similarly, the often quoted explanation that pain nerves, such as the Aδ, derive their
properties as efficient propagators of pain, due to myelin, is misleading. Clearly, we have
missed something simple, yet fundamental about myelin. We explain the propagation of
pain, roughly as that of an harmonic oscillator, a primary, pressure like wave disturbance,
akin to an earthquake P, or primary wave; details the topology of the nerve fibers; explicitly
establish their high temperature superconducting nature. We further explain why variances
in atmospheric gradient pressure, (the weather), amounts to a deformation of the magnetic
(and actual physical boundary) layers of nerve fibers: the Navier-Cauchy equations, under-
lining this process, best describes the barometric pressure attempts to deform an otherwise
incompressible fluid in equilibrium, or near-equilibrium. Such a deformation often time
results in lower magnetic permeability (and higher attenuation coefficient, or dumping) Aδ
of the pain nerve fiber, resulting in acute pain.
For most of neurology infancy, it was assumed synaptic communications within the
brain was electrical. Ramon Cajal [21] discovered a 20 to 40 nm gap between neurons, the
synaptic gap. The suggestion that chemical messengers provides neurons with their unique
9Since I am working with pathway(s) of neurons and nerves, I will, from this point on, refer to the apt term,
neuropath-tic.
10The contradiction is obvious to state: if myelin sheathed nerves and/or axons or neurons have a protective
layer which insulate the electrical propagation of pain signals, in the first place, why are electrical pain signals
capable to violate that very protective layer or boundary? This simple observation shows the current explanation
does not stand a modicum of scrutiny.

FIGURE 13. Cajal-Loewi seminal discovery of a synaptic cleft in the
1920 − 30s, a 20 − 40 nm gap between neurons, in the brain, is crucial
to make in unraveling how the brain makes sense of pain. Cajal famous
drawing, above, of a pigeon’s brain nerve pathways is poignant, if for
one reason: a nature observer will recognize pathways traced by light-
ning during storms. The observant physicist and mathematician may
recognize the vague, albeit familiar, Gaussian matrix probabilistic dis-
tribution, manifest as Wick-Feynman path integrals, at work in Cajal’s.
When he drew the experimental sketch above, Quantum Mechanics was
still in its infancy. It would take decades more for physicists to work out
scattering and pathways of particles, their random nature, and still longer
for Feynman to come up with his seminal path integrals, Feynman’s di-
agrams, describing such processes. Cajal’s illustrates perfectly physics
hidden nature in biology most fundamental processes.
ability to communicate among themselves, was experimentally confirmed in 1921 by Otto
Loewi [21]. Loewi is further credited with the discovery of the first neurotransmitter,
Acetylcholine, or ACh. Cajal-Loewi discoveries upended biology: striking and counter
intuitive especially in light of our biases: our very brain first dump sensory signals in the
open, second, confines them to a noisy, highly entropic, dense, hot, small, bounded area, a
lattice.

FIGURE 14. Lightning, the flow of electrons, requires an electric poten-
tial generated by triboelectric effect, share significant similarities with
Cajal-Lewi.
It is counter-intuitive, because the body has also evolved to shield nerves with myelin,
to manufacture specialized transmitters, receptors, to force all sensory signals to be elec-
tromagnetic, shielded well enough to reach the brain, relatively intact, using an elabo-
rate, highly complex mechanism of physics and chemistry formalism: coupling, propaga-
tion, diffusion, scattering, with supporting chemical cascades. Why, than, are pain signals
dumped in the open in the brain? Could one seriously make sense of this bizarre mech-
anism? 11
To make sense of this, we must augment Cajal-Loewi with core principles to
physics.
Let us start with an analogy: your age, height, weight, choices of clothes, haircut, per-
sonality, the jewelry you wear, assuming the bling bling lifestyle is your cup of tea, etc,
defines you as a unique individual among seven other billion. In spite of this uniqueness,
11It does sound counter-intuitive and flat out crazy, right? You are unique, yet stripped of what precisely
make you so, your spectral signature, dumped in the steaming, noisy, dense brain.

FIGURE 15. Cajal-Loewi synaptic cleft is made evident in this drawing.
Quantum physics formalism is drawn upon to determine the coupling be-
tween communicating neurons. Entropy in latticed-areas in which they
are confined dictates the coupling (or discharges in biology parlance) as
function of the spacing, using Gaussian probabilistic formalism. The
first hint as to how the human brain makes sense of sensory signals can
be appreciated: however subtle, it is apparent.
you happened to be dumped in a vast, steaming ocean, containing literally billions of indi-
viduals, which, to some degrees, may be much like you, say by weight, height, and so on:
that is to say, your individuality is now seriously diluted. Not even your voice can be heard
against this background noise, so no one can tell if you have that exotic accent from the
Midwest, Brooklyn, Boston, France, or India, which the organizer of the event commented
on when she called you to attend.
However, please take a moment, to ponder, as I have. Against which background, or
referential frame, are we describing your uniqueness as an individual, or for that matter,
that of the pain? What is the point of telling a sea of billions, similar to you, that you
are unique? Certainly, your individual uniqueness is fine with you, as no one can describe
you better, in relation to yourself. However, the moment you step in in a venue, larger

than you, figuratively speaking, you must accept other participants are unique to. In other
words, you are been diluted against that background. Therefore, for you to persist in how
unique you are simply implies you are denying yourself (and others for that matter) theirs
and yours. They must compare how unique you are in relation to their own set of values,
or parameters, not yours. In this, there is simply nothing you can do. It is a prejudice
the Universe and physics requires. There is no Cosmic patent or license that says you
(or pain, or temperature) is unique. For instance, you share the same venue. Strike one.
You may also share the same geographical location, similar characteristics as language,
height, weight, etc. The dilution of your uniqueness cannot be denied. But that is not to
say the venue and sea of other similar individuals do not recognize you as an individual
with specific traits and personality, that will differ and vary from the norm. A dumped
Pain signal in the brain is in a similar situation. It is certainly fine to think of yourself as
unique. On this, even quantum physics, and the universe at large, is on your side. You have
the right to a favored referential point. The problem however, becomes quite problematic
and myopic for you, if you refused to accept the possibility, that your uniqueness must
be factored against a different point of reference, to make sense of how much of a unique
person you are.
The best way to illustrate this, is with the following analogy. When you are the recipient
of hospitality, say in a far off foreign land, you cannot insist on, say, ”I like my bagel with
Philadelphia cheese”. You just have to eat whatever is brought to you (or refuse, in which
case you missed the reasons why you traveled to a foreign land in the first place). Of course
your hosts know you are unique enough, against their own background, to have marked you
as a foreigner, the reason hospitality is being extended to you, in the first place. They do
not know cheesecake, bagel, or else; but they do know you are a human just like them,
albeit a different one. Your uniqueness stands up to mark you as a foreigner: you do not
speak the local language, nor dress like the locals, nor are your manners similar. Still, on
the basis of common traits, universal to humans, the locals know you must eat, drink, be
sheltered. The very fact you are feasting, an honor guest at their home, is a testament of
your uniqueness, though it has been diluted by the very observation you are human and
must eat, further by the language barrier, your hosts unable to comprehend ice creams,
Philadelphia cream cheese, and neither can you, of their exotic meals.
Such is the perspective from the brain. The pain is coming to its house. I explain this
in purely physics formalism below. Why is the brain resorting to the dump which, as one
would naively think, mix up the pain signals, hence dilute their individual uniqueness?
How are we, then, to make sense of Cajal-Loewi discoveries? Why are nerves, the body,
going through all this trouble to assure pain signals are deposited, as uniquely as they be-
gan their journey through the spinal cord, only to emerge out, dumped, confronted with
excessive background noise, akin to you diving in a steamy, hot, humid, densely packed
night club dance floor with blaring music? Why is the cleft spacing there, to begin with?
Were you a pain signal shooting up from the lower back into the CNS, having traveled first
class, so to speak, inside a pathway designed to preserve its very uniqueness, carefully sep-
arating you with other signals by a distance a proportional to its radius, a span necessary
to prevent quantum decoherence; the moment you exit and is confronted with a cacophony
of highly densely packed impulses, signals, ambient noise and heat, you obviously lose
certain spectral characteristics, unique to you, and only you, which are absorbed by the
larger lattice. The lattice, or brain at large, seems to be getting something out of this, si-
multaneously as you are losing your very identity. It does indeed according to classical and
quantum physics. Classical physics, thermodynamics laws, in particular, states the brain

has a net gain of energy. So far so good. Yet, we could not make sense of Cajal-Loewi,
the cleft, and dumping of signals thus far because indeed, stuck with classical physics, as
we all learned in high school, it is simply nonsensical and counter intuitive. What gives?
It turn out we have to descend to the scale of dumped signals to make sense of this puzzle,
You see, it is quite obvious then: quantum mechanically, there is no such object, not even a
black hole, that can take in net contributions of energy (or mass) without actually emitting
some of that away. For black holes this phenomenon is known as Hawking radiation. This
is indeed where entropy comes to the fore.
The picture gets murkier when chemistry is taken into account: some neurons commu-
nicate via electrical synapses, through the use of gap junctions, that allows specifics ions
to pass directly from one cell to another. Experiments has shown this spacing to be ac-
tion potential sensitive, to allow endogenous chemicals, neurotransmitters, such as GABA,
Glutamate, Substance P, Acetycholine, etc. [22, 23,24]. Again: why is a distance needed
between extremely tightly packed neurons, constantly firing off electricity in the open?
12
At first glance, such peculiar, bizarre spacing between neurons appear to enhance the
chaos, disorder of incoming signals, to give away their unique physical characteristics,
hence lead to more taxing processing power, energy expansion by the brain. Or does it? If
you are the brain, the perspective is very different: if you go back to dance hall example,
our human-centric logic was seriously flawed. You see, the room is happy to have all this
excess energy, this net gain, which it must convert to entropy. It is happy to get some en-
ergy out of you, out of the blaring music, the dancers, etc, so it can absorb it, put it to use
it, radiate away excess energy in the electromagnetic spectrum (infrared, ultraviolet).
The room does not care if you are human, the wall, blaring music, or other kind of
noises. It does not ”hear” music the way you know and enjoy it: say as Reggae, Disco, or
Rap. It does not ”hear” the beats, bass, nor the Brooklyn-accented voices. All the same,
it does ”hear”, quite well, vibrations from your feet, stamping the floor, your loud shouts,
the overhead lights flashing, burning away, the dozens of warm and misty breaths, the
expanded energy from momentum-laded dances... It does even ”hear” other unique char-
acteristics you are not aware of: a hybrid of your temperature, energy, for instance, sees
simultaneously the energy radiating away from within the room, in the entire electromag-
netism spectrum (Kirchhoff radiation). Yes, from the room point of view, though it does
not care the least if your are the Reggae, vibrating away from the speakers, or a human.
Not the least. It knows it has a net gain of energy, converted into entropy. It must measure
all that against the cold winter outside (or the heat of summer), as such gains (or losses)
impact its physical integrity, may expand or shrinks its walls, cracks it floors, and so on.
The room is not simply absorbing all this: it is simultaneously computing where that extra
energy ought to be put to use, it is making sense of all this by having all the noise, misty
breaths, cold drinks, shouts, out in the open13
. In a nutshell, the room care to know only if
your are adding or subtracting to its entropy. The moment you step into the dance hall, the
room perceives you only against its intrinsic temperature , entropy. You are simply what
physicists will call a vector, or energy potential ready to be discharged. It is not sexy to
12Akin to you shouting on top of your lungs in that packed disco dance hall floor, against the loud background
noise. If one pauses, one sees that you do have to compete against the ambient noise to be heard. However, upon
careful consideration, were you to actually pay close attention to the loud ambient noise you will detect different
voices, beats, the drums, bass, and so on. Thus it is not actually the ambient noise that matters per say, rather it is
its richness as a collection of individual noises patchwork.
13In other word, the dance hall has a utility bill to pay too, though not to the Public Service Electric and Gas
company in Princeton, or if you are in the mecca of nightclubs, Consolidated Edison in Manhattan, or its rival,
the Los Angeles-based Southern California Gas company.

say, but this is exactly the view from the entropy-centric dance hall and the brain where
pain is concerned. This is your id with the room (forget showing the official stuff to the
bouncer). Our bias has been so pronounced in biology, we have been unable to get away
from our arrogant, human-centric perspective. This example sums up perfectly why thus
far we have been unable to fully grasp the impact of Cajal and Loewi seminal work; why
quantum physics, entropy from classical physicsrequires the brain to force the signals out
in the open!
For the brain to make sense of incoming signals, the spacing is therefore vital (it just
cannot do so otherwise): it is a measure of the brain entropy, below, we explain how
the brain forces the incident signals to go trough a quantum-algorithm correction, than a
quantum gate, whose radius minimally, must be at least 2r that of the lattice from which
pain is emerging. We demonstrate how an entropy variant of the bounded regions in which
pain first emerges from, is none other than Fisher Information coefficient. The accuracy
and uniqueness of pain, owning to encryption and the brain quantum algorithm, reduces
the loss of information inherent when processing quantum information. The background
noise or error rate, is local, per lattice unit area, rather than the entire brain volume. The
brain is no fool. Blessed with amazing computing power, it is still a disciple of energy
conservation, waste little, by requiring signals to come out in a small area first, be tagged,
noticed, processed roughly, than scattered higher up for still further processing if necessary.
Remarkable indeed to confirm yet again, that hard working entities always find a way to
conserve in both work, and in energy expenditures. Quantum decoherence comes into play,
and precisely quantify the amount of time needed by the brain to receive and process the
pain signal: this accuracy threshold cannot be smaller than the time needed for synapses
to discharge, for the local entropy density function in which they reside, to take notice as a
gradient diffusivity ratio, something I make explicit in the sections below.
All this would not take place for an even obvious, yet overlooked physiological char-
acteristic of the brain: the variations in density. The lower parts, such as the spinal cord
connecting to the brain, the Cerebellum, Medulla, and Pons, have a much greater density
than higher ones, namely the Cerebral Cortex, Parietal lobes, and Neocortex. That the
overall gradient density of the brain must (and is) smooth (or linear, or homogeneous) is
a consistency condition for the brain, as an entity, to work with its various parts; also for
underlining processes (such as pain), to be made sense of. In a way, the analogy of the
variations in density between various segments of the human body (legs, torso, posterior,
stomach etc) is similar and just as edifying.
To summarize: the existence of a synaptic cleft seems to support both efficient dis-
charges and processing of sensory outputs, including pain. A hybrid, dual usage extends to
them, in that they equally rely on old fashion ionic exchanges and electrical ones. Why is
it the case? Shouldn’t a plurality of communications give rise to errors, misinterpretation,
entanglements, loss of signals purity, strength, lead to greater amount of energy expanded
in processing impulses, including pain? We prove why distance between synapses is a fun-
damental requirement of quantum physics, the only way the brain can process its extensive
overload of sensory inputs. Spacings act as ”dumping” mechanism, further helping the
brain to identify, tag, encrypt pain signals, using local entropy; quantum gates are created,
wherein, scattering pain signals are decrypted in the higher, entropy-poorer, less dense,
parts of the brain.
2.1. Pain, Nociceptors, Neurotransmitters, and Nerves. Nociceptors are specialized
sensory neurons sensible to (external or internal) pain. They are prevalent in the skin (cu-
taneous sensors), the cornea and mucosa, and internally, are also found in muscles, joint,

bladder, the digestive tract. The cell body of these neurons are located in the dorsal root
ganglia, or the trigeminal ganglia, which control nerves for the face. The axons extend
into the peripheral nervous system and terminate in branches to form receptive fields, a
peculiar topological configuration whose role in signal processing by the brain has been
overlooked and which we discuss below. The critical observation here is that to under-
stand pain, we must first explain why nociceptors have two different type of axons: the
Aδ fiber axons, which are myelinated, that is, exhibit the confinement and electromagnetic
shielding of signals, and the other kind, which possess little to no insulation or myelin con-
centration. In the first instance, the Aδ fiber allow for action potential to travel fast, about
20 meters/second toward the Central Nervous System (CNS).
In the second instance, impulse propagation is about 2 meters/second. The rate at which
pain signals are transmitted to the CNS has thus served as a fuzzy distinction between acute
and chronic pain, e.g. sharp versus dull pain. Up to now, the conventional explanation has
been that myelin plays a dual role in impulses propagation: shielding from ambient en-
tanglements with nearby particles, preservation of the signal fidelity, while on its journey
to the brain. This explanation is roughly crude, partial at best, and misses a much funda-
mental role: the confinement and induction properties of myelin cannot be denied. Nerve
fibers with such property turn out to be hybrid form of high temperature superconductiv-
ity (HTSC). We will discover significant properties of pain signaling, derived from this
observation, explain a host of issues thus far ”mysterious”, hallmarks of pain.
A pain signal traveling inside a myelinated fiber (its pathway, effective action, or La-
grangian in physics parlance), is a longitudinal wave, compressed with respect to the fiber’s
radius and length, roughly akin to a primary seismic wave. The fidelity of the wave is pre-
served within that medium, during its journey. Why is Pain a primary like seismic wave?
Pain signals are ruled out as secondary seismic wave, because they do not displace the
nerve, perpendicular to the direction of propagation (polarization) (upward to the CNS):
fluids inside the body tolerate little shear stresses. Pain signals, coupling, traveling in less
suitable medium, lent themselves to integrity, fidelity losses, quantum entanglements, and
decoherence.
The physical structure of secondary pain signals is in fact an interesting physics prob-
lem. The machinery requires a complex study of coupling constant using a variant of
Navier-Stokes equation, describing wave propagation in certain peculiar fields. One of the
serendipitous discovery herein, is the observation that once this technique is applied, we are
able to explain why variation in barometric pressures often induces pain. This sensitivity
is not fortuitous, as we will show explicitly.
The fiber is essentially an elastic medium with a certain rigidity coefficient. Pain inside
the fiber appear as a harmonic pressure oscillator, which we write down in general terms
as:
p(x,t) = λ cos(kx−ωt +φ);
in which we denotes the amplitude of displacement by λ, k stands for the pain wavenumber,
x is the distance from incidence to the time the signal reaches up the CNS, or propagation
length, ω the angular frequency; t the transit time; and φ the phase difference.
2.2. A Hint on the Fabric and Nature of Pain. A pain signal, or for that matter any
impulse, be it temperature signal, is thus a wave. It began as an electron, at the bare
minimum. While propagation inside a nerve fiber and the brain, it is a waveform, or
in simplest term, a quantum harmonic oscillator. The propagation inside the nerve fiber
and brain must be allowed impeded, at least to the extent interactions via Feynman path
integrals, and decays must be minimized This fidelity factor in turn dictates the pain nerve

fiber and the Central nervous System must act as highly efficient propagator of such signals.
That is, they must transmit electrical waveforms with little, to no deformation.
A number of salient observations follows:
(1) Pain, in its simplest from, is an electron, or a multiple thereof; that is to say, pain,
depending on the brain or nerves propagators is perceived as either a point-like
particle, or a wave (a harmonic oscillator). The momentum and position associated
with pain inherent phase space determines its wave function, which, by duality,
cannot be larger than 1/r the radius of the nerve (or the brain’s lattice in which it
is confined) in which it propagates. This dimension-centric coupling constant is
very important, as we will soon show.
(2) Second, the nerve fiber, inside itself, must have very little to no magnetic flux:
were magnetism permeating the interior, a process known as ”nucleation” or de-
fects, will conspire to decohere pain signal.
The Classification of nerve fibers by biologists as function of their radius (tough the
literature abounds with ”diameter”, most physicists and mathematicians use the more sen-
sible radius ()after all, why bother carrying two times the amount of anything, even in your
head, when one of one does just as well; d = 2r and of course r = d
2 ). The A group of fibers,
so prevalent in pain (and the focus of this research), begins the classification because they
possess a large radius–I will soon establish in relation to what and its importance.
The A fibers as a group carry pain impulses relatively fast, what in the biology academic
literature is referred to as ”high conduction velocity” (a term likely to gives physicists a
heartburn and lots of confusion), and are insulated, that is, their boundary is made up of
a thin layer of myelin of roughly in the range of 0.000001 to 0.000004 of a centimeter
[9,11, 19]. The α and β subclass have the ability of both carrying signals to (afferent) and
fro (efferent) the brain, whereas the γ subclass is only efferent, and the very interesting δ
subclass fiber only specializes in afferent propagation. It has been experimentally verified
[12,13,14, 19,21] time and again that δ carry not only pain, but sensory information related
to temperature, touch, and pressure. In a few sections below, I will draw on this peculiarity
to explain what has long been a puzzle and mystery in pain.
Next, down in the Classification scheme is the B Group. It has a small radius (again
in relation to what will be made clear soon). An interesting property of this group: it is
myelinated, although, in contrast to the A Group of Nerves, it is impeded by low speeds.
What gives? According to accepted belief, myelination act as perfect insulator of signals,
preserving fidelity during propagation. Clearly something is amiss. The myelin vs non
myelin role in pain, and generally sensory signals propagation, their interpretation, draw-
ing on the observation just made, is something I take up in an upcoming section, below.
Finally, we come down to the last of the Group, the C. Nerves in this class have a small
radius as with their B’s cousins. They have low sensory signals propagation as with the B.
The similarities ends there because they happens not to be myelinated. In the parlance of
physicists and mathematicians, they have a ”naked” or if you are prudish, a non-singular
boundary.
Let us pause and briefly review of what we have established:
(1) Nerve fibers are classified by radius size, among others;
(2) Nerve fibers do carry and propagate sensory stimuli of various intensity and forms
(pain, temperature, pressure, etc) to the brain, with various degrees of speed and
fidelity, or to be precise little error rate;
(3) Myelin does little to conserve these signals; at a minimum it does not speed them,
delaying initial coupling between pain and its propagators, splitting pain;

(4) The transmission speed is function of certain fundamental characteristics, topolog-
ical invariants of the nerve fiber. Our results agree, confirm, than shed additional
light on the classification scheme of nerves; furthermore, we resolve the long-
standing puzzle: nerve, endowed with large radius, propagates pain much faster
and with little error or bias, than their opposite;
(5) The observation that pain, is, at an absolute minimum, a multiple of electrons is
crucial.
The hint now.
The minimum size or quantum state of any pain, the quantum of pain in short, has basic
metrics. It’s absolute minimal radius for instance is easily derived from quantum physics
data:
re =
e
4πε0mec2
= 2.8179403267×10−15
m,
It follows therefore that pain has a minimal mass, roughly:
me = 0.510MeV,
or since as biologists are more familiar with mass expressed in kilograms,
9.109×10−31
kg.
These are the dimensions, or scale of pain. Instances where complex pain requires a greater
amount of electrons, still leaves the quantum dimension of pain is as a tiny speck, in con-
trast to its much larger pathways. The scale of pain is strongly correlated to the dimen-
sions of its respective pathways and propagators, a universal property known as duality
in physics: the coupling constant in force between pain and that of its propagators (and
the brain) is governed by duality [10, 15]. Roughly speaking, duality is the manifestation
of a fundamental symmetry among two seemingly different physical entities. Duality ex-
hibits an underlining, sometimes rigid, yet hidden, fundamental connection, linking two
seemingly disparate entities or processes: knowing just one entity scale, is sufficient to
determine the scale of the other. Consider energy and temperature, or entropy and temper-
ature; or mass and energy, examples of well-known duality-centric entities. It follows then
that: the radius of a nerve fiber must always be greater than that of a pain signal, as must be
its length, thus overall scale. The duality formula quantifying the relations between pain,
neurons, nerves, nociceptors I derive is rigid and leaves nothing to chance, owning to the
Universe’s strict laws [10, 15, 18, 23].
The intrinsic temperature of a pain signal is an equally important physics quantity: an
electron by itself is extremely cold, near absolute zero (K) (Kelvin). Dozen or thousand
more making up a collective pain signal would still remain quite cold14
. Nevertheless, the
laws of physics are precise: whenever two, or more particles interact, entropy is generated
by definition, followed by an increase in temperature. Nerves, on the other hand, carry a
much higher intrinsic temperature, owning to its greater scale and composites elements.
Further, it has a lifespan measured in months or years, whereas that of pain is measured
in fraction of a second. As such, nerves have a measurable temperature and a less elusive
spectrum. Again among the reason Pain remained elusive.
14Pauli Exclusion Principle, used to explain Pain confinement and preservation, within Aδ and related nerves
lattices, reveal such lattices as large, continuous ”band” structure of energy levels. Hence, a pain associated
wavefunction, φ(Pe) ⊂ L (Aδ) is degenerate, temperature-wise: journeying pain signals, within such medium, do
not contribute to the thermal capacity of its propagating medium. This observation is among the main reasons
the Aδ is a High Temperature Superconductor.

For pain to first come into existence, to further propagate all the way to the brain, ob-
structions during its journey must be kept at a bare minimum. Otherwise, pain will simply
cease to be the special signal, alarming, eliciting speedy answers from the brain; it would
have morphed into a regular signal. Hence, specialized nerve, the Aδ must contribute to
such complex endeavor. Therefore, its magnetic fluxes, including the dynamic of their nu-
cleation, must be such that, it results in a global push toward its boundary. Encapsulated
in this observation is the hint! The nerve is a High Temperature Superconductor (HTSC).
It display the very property of superconductivity (again in relation to the pain itself). The
illustration below provides a perfect illustration. Unfortunately, I know of no simpler way
to do so, other than to write down field equations. However, it will be worthwhile the
effort.
A nerve fiber has magnetic fluxes whose field is:
(1) ΦB =
R r
B(ξ,t)·dl.
B is the magnetic field, and B·dl is a vector dot product denoting the infinitesimal amount
of magnetic flux emanating from the pain magnetic charge; it is truly infinitesimal: for a
pain made up of just one electron, in the order of e = 1.602...×10−19J. Ordinarily, when
taking into account flow, or movement, physicists write down the field effective action
(Lagrangian) in relation to momentum (spatial vectors), and a time variable, t ∈ [0,1],
which follows from the fact time as a cosmic entity is just one dimensional (whereas space
is three-dimensional). This, however is meaningless at this juncture. The subscript R in
the first integral thus denotes the radius of the Aδ.15
We must (and are able) to keep track of (and to factor in) the radius of the pain itself,
r. The quantity ξ is something new altogether, a subtle, yet significant feature. It can be
viewed as a ratio of the various pain signals’ radius, contributing fluxes to the larger R.
In truth, it will turn out to be a fundamental quantity, known as a topological invariant, or
more precisely, a homological cycle, whose role in the superconductivity of nerves will
prove crucial and extensive. The reader should be mindful that, to describe the dynamics
and characteristics of pain, we will often need to do so in the least complex way, that is
with little or no time-dependent equations of motion. Freezing, or looking at a stationary
pain signal inside the fiber, or within the brain, is beneficial in deriving basic properties.
Often, the volume or surface area are used, at the expense of the length; similarly it does
matter little, at this point, if portions of the nerves are stationary or in motion. The formula
however is always radius-dependent, as is obvious from the duality formula below:
r → R;(2)
1
R
≈ r.(3)
What is striking, yet beautiful is this: since the radius of pain is very small, in relation
to that of the nerve, the rate of change of the nerve magnetic flux is constant, or negative
(from pain signals scale and transit time):
(4) ∇ ∼= cst−
dΦB
dt
.
In a nutshell, this is the reason the Aδ is a superconductor, a fact we make explicit be-
low. Critical values, given in the range R → ±0, R → ±∞, dictates the way in which its
15In the biology literature, the term for this nerve is Aδ. Naturally, I have used the physics-centric notation
Aδ with a subscript.

radius shrinks, or expands. A delicate, fast paced, complex phenomenon, fine-tuning oc-
curs, while the nerve simultaneously maintain, keep track, of its duality-derived coupling
strength with pain signals, that is it never loses track of the scales. Indeed, it is a challenge
to come up with instances where, as you are deforming, you are doing so in a way that
preserves your structural integrity; what is more, even as your contents are sloshing about,
you are careful to be rigid enough so as not to mix the contents, damage them, break, leak,
let them out. The best analogy is that of a modern jet, at cruising altitude, encountering
turbulence, bouncing about, while still keeping passengers within in their seats, secured.
3. THE QUANTUM THRESHOLD OF PAIN
What exactly is pain? Physics and biology diverges by degrees. Biology’s explanation
is rooted in a legacy of notable scientific accomplishments. It is no mere coincidence, how-
ever this explanation relies on physics insight by Albert Einstein [10, 15], which gave birth
to quantum mechanics: the photoelectric effect. A wave, or particle is strong enough to
knock off an electron from its atomic orbit. The overlooked point is: sensory signals, be it
pain or else, possess a fundamental scale; the quantum scale. Sensory signals force carrier,
so to speak, is the electron, or multiple thereof. To validate such declaration, pain must be
thoroughly incorporated, described, than treated, in purely quantum formalism, an achiev-
able objective. The common perspective: most neurotransmitters, including nociceptors
are extremely large, massive molecules, in contrast to the electron (or multiple thereof).
Indeed, a random neurotransmitter (endogenous chemicals that transmits signals from a
neuron to a target cell, across a synapse) is obviously several order of magnitude bigger
than pain itself. Consider the third most prevalent neurotransmitter in mammalian nervous
system, the neuropeptide, N-Acetylaspartylglutamic acid, also known, in different form,
as N-acetylaspartylglutamate, or NAAG in short (the Hindu word for cobra). Its chemical
formula, C11H16N2O8, is equivalent to saying it is made of eleven atoms of Carbon, six-
teen atoms of Hydrogen, two atoms of Nitrogen, and eight of Oxygen [13,21,24]. By any
standard, NAAG is large, as the figure below shows. The chemical depiction of NAAG is
aimed to convey my point of the scales involved. Compared to an atom, it is large. From
Pain scale perspective, NAAG is order of magnitudes larger.
The chemical structure is fine to look at. However, as with the dying beach waves, the
dot in New York City, or looking at a majestic mountain, our biases have prevented us from
the hidden richness of invisible effects or entities, affecting such behemoths. To incorporate
the perspective from pain itself, the scales, we must focus on NAAG molar mass [20],
roughly 304.25 gram by mol (in keeping with physicists norms, I have normalized by an
order of magnitude): A universal unit, the atomic mass (u) is defined as:
(5)
mass C12 atom of a carbon
12
=
(1g)
NA mol
;
It’s mass is [20]:
(6) 9931.494061MeV
or, put in the metric scale familiar to biologists,
1.660×10−26
gram.
An electron, on the other hand, has a mass of 0.5MeV or, roughly, in gram(s), 9.1×10−30.
Whichever your choice of perspective is, MeV or gram, one thing is inescapable, and that
is the vast difference in scale for pain, for its transmitters, its propagators in short, and for
the brain.

FIGURE 16. NAAG, a prevalent neurotransmitter in pain signaling and
diffusion, is depicted here in its atomic-molecular structure, showcasing
the contrast in scale with that of pain, nerves, and the brain.
Was I to factor in NAAG actual mass, or, for that matter, that of the humongous Aδ nerve
pain carrier, the inherent perspective from the pain signal will have shrank considerably. In
essence, this is what I meant previously: looking for a pain signal in the nerve fiber (or in
the brain ) is akin to looking for a single dot, in an empty city, the size of New York City.
To summarize: pain is a quantum ball, a ripple akin to a primary seismic wave; that is,
an harmonic oscillator, perceived by nociceptors, neurotransmitters, and nerve pathways,
as a pressure-like disturbance. Within the Brain however, pain takes on the nature of an
entity with unique spectral signature. In short it is a wave of energy with a fundamental
scale in mass, frequency, electric, and magnetic charges. The latter are absorbed, than
transmitted through processes governed by quantum mechanics. Put another way, pain is
a quantum state whose existence must correlates with the logN of the quantum states of
the nociceptors, neurotransmitters, nerve pathways, and that of the brain. This correlation
function in physics parlance, dictates the core processes by which pain is perceived, noted,
transmitted, scattered, than processed. logN, a measure of entropy, and of information,
is significant. This quantity gets larger as pain transits, first from its coupling, absorption
with nociceptors; second by being routed to the much larger nerve Aδ, and to the brain. The
coupling constant of pain, therefore is central to these processes. Nerves abounds in the
body, Pain must be shielded to some extent, while journeying upward. Within the brain,
this constant must be replaced by more exotic physical characteristic forms, in order to
make sense of its scattering, processing, in an organ awash with billion of sensory signals.

FIGURE 17. Gamma-Aminobyturin Acid (GABA),the foremost in-
hibitory neurotransmitter in mammals (including humans) regulates neu-
ronal excitability throughout the Central Nervous System (CNS). Zolpi-
dem tartarte, or Ambien, the popular sleeping medication, binds to
GABA to induce sleep. GABA plays an important role in pain, chronic
pain, though the precise ways in which it does so remain mysterious.
Pain would otherwise remain a background noise, much as small pressure or variations in
temperature are.
Thus far, we have shown why pain true nature, eluded us. We have pointed out to a
substantial issue with the problem of scales. To understand pain, biologist must first look
at it from the scale of pain itself, not the large scale of molecules (which they excel at and
which today defines the term biology) like NAAG, or even worse the Aδ nerve fiber, or
the much bigger scale of the brain. The quantum of pain is far from an abstract concept.
Unraveling the nature and fabric of pain is a paradigm shift, requiring the complex for-
malism of quantum field theory (QFT). Biology faces complex, longstanding, unresolved
problems; since traditional methods have failed to tackle the, let alone solve them, mathe-
matics and physics are needed. The influx of new ideas and techniques are thus certain to
benefit biology considerably16
.
16When the atomic structure of matter was being revealed by Rutherford, at Cavendish Laboratory, in Cam-
bridge, England, Chemistry was a vibrant part of physics. Maturing, it later became a scientific field, on its own
rights. Unfortunately, both biologists and physicists made the mistake of assuming there was no further rationale
for vigorous cross-field interactions. This may have been a welcome separation from the pure field of physics, as

FIGURE 18. Dopamine, another prominent neurotransmitter involved in
pain, whose societal cult status gave rise to the root word dope, is de-
picted above. As with GABA, Dopamine precise role in pain, especially
at the brain level, has yet to be fully elucidated. Dopamine can be found
in plants and fruits as well, including banana, and their peels.
The absence of interdisciplinary collaboration by and large has multiple roots, which I
briefly touch upon in this work. Among them, has been, so to speak, the ”dictionary” or
language between the disciplines. Aware of this, I have gone out of my way, and made a
point to illustrate,and convey, as much as possible, to both my biology and PM audience,
the discussion, problems, and solutions. Patience is required of both audiences reading
this work, to wade in uncharted territory, so to speak. The problems and results presented
are somewhat extensive. Tough I regret the sections below must be technical and cannot
be simplified, so to speak, I again reiterate to the attentive reader that the benefits will be
worthwhile the efforts.
Chemistry went on to focus on atomic binding (hence molecules); this of course later gave rise to modern biol-
ogy. While no one can deny the process of unraveling biological complexities took time, the unrelenting focus,
and dominance of molecular biology hindered cross-fields cooperation. We may now have come back full circle,
from the early atomic and nuclear era of the 1920s, as most fundamental and unsolved biology problems, such
as protein folding, diffusion of certain processes, cancer, sensory processing and pathways, and so, on requires
fundamental physics, and mathematics.

FIGURE 19
4. THE QUANTUM OF PAIN
To the question of what pain is, and what its threshold must be, the answer from quan-
tum physics is clear:
(7) Pain =
λp
S ∼ logN
·
ρ
·κ(λ).
The formula makes clear the extent to which pain and it’s fundamental minimal threshold
is function of S, the entropy density of the transmitter. The quantity ρ expressed in relation
to the normalized quantum Planck scale, ¯=c = 1 = 1/2h is roughly a factor that takes into
account the mass of the larger pathways. The quantity κ expresses a constant, which in fact
Mathematician and Physicist can recognize as a variant of the Wick’s-Feynman Gaussian.
Why is a nerve polymorphic? That is, how is a nerve able to simultaneously support
the propagation of various signals? Wick’s theorem shows why: it takes in contributions
from various incident fields signals17
. Pain, temperature or pressure gradients are seen
17In this quantum field view, a pain, or a temperature signals are external fields, coupling (i.e. coming into
contact with, than being absorbed by the nerve in question).

as quantum field to the larger nerves propagator. This field view, so to speak, provides
us with the formalism needed to work out otherwise complex, unexplained, sometimes
mysterious features. Consider a number of sensory signals, expressed as function of their
respective fields, in the nerve vicinity (in neurology terms, pain thresholds are generated,
and nociceptors excited):
φ(p1)···φ(T1)···φ(±1) .
The Wick Theorem, manifest in Feynman path integrals is a field operator ordering, that
is:
φ(Si)···φ(S2n) = ∑∏
ij
δ(Si −Sj)
S2
i
;
where S is any sensory signal. Wick’s equation, above, exhibit the polymorphic nature of
some nerves. As pain journeys to the brain, an important cumulative effect takes root: the
entropy density of its supporting propagators comes into factor. The entropy density of an
individual nociceptor, or neurotransmitter, adds to that of the Aδ nerve.
4.1. Feynman Diagrams of Pain. A pain signal p is part of the Feynman propagator ∇:
(8) ∂2
∇(xp) = iδ(x),
where,
∇(k) =
i
k2
denotes the Feynman propagator (expressed as a spectral invariant): quantum wavenumber.
The propagator is at rest, prior to coupling with pain; meaning the equation of motion
describing it (or its capacity to diffuse or propagate pain) is
(9) ∂µ∂µ
φ = 0.
Again perspective is important: when we state a propagator of pain is rest, we mean to
say it is so in relation to the scale and energy of pain itself. Obviously, propagators are
constantly in motion (in relation to larger entities whose scales are order of magnitude
bigger, for instance the ratio, or distance from pain’s point of origin to the brain, contrasted
to that of a nociceptor or nerve). A field at rest has zero expectation value. Expressed
differently, the fundamental threshold for pain to exist is met, when a signal P forces φ out
of its lazy, rest state, meaning P must be greater than:
(10) ∂µ∂µ
φ(x)φ(S)φ = 0.
The zero expectation value equation, above, sets a consistency condition: should pain re-
duces to P = S, obviously φ ability to absorb, let alone propagate anything is zero. There-
fore, in order to couple with nociceptors, the Aδ, pain is required by quantum field theory,
to have enough potential energy, to first disturb the nociceptors, awaken it, provoke it out
of its rest state. The analogy of a dying ocean wave, crashing on the shore is apt. Since pain
amounts to a potential electromagnetic current, it can be described as a vector potential.
Field theoretic techniques allow us to peer into the dynamic, of pain, within propagating
pathways. The unfolding dynamic takes into account pain behavior as it is being diffused
into larger systems, accounting for variations in its spectral, characteristic forms, among
them electric and magnetic field charges.
Pain, than, is expressed in terms of Maxwell time dependent equations. Pain, is actu-
ally ”read” by neurotransmitters, nerves, such as the Aδ that way. Maxwell’s importance
extends to explaining Aδ HTSC property. What is meant by saying pain, or, for that matter,
any other sensory signal, are ”fields,” contributing to a nerve, and to the brain? Why rely
on Feynman path amplitudes?

FIGURE 20. Aδ, the prominent nerve carrier of pain is contrasted to the
B and C. Feynman path integrals are drawn at the bottom (red, wiggly
lines). These are incoming pain signals about to couple with the nerves.
In this quantum field theoretic view, the Aδ, B, and C see them as field
contributors. Notice the spacing within Aδ, separating signals, by a dis-
tance a, proportional to its radius and length. Notice too the shrinking of
a depicted within B and C.
Naturally, our confusion is understandable. Were we to look, ever so carefully, a picture
does emerge, or should I say a hint: a bunch of wiggling lines going into a singular box,
spanning a finite length L, and radius r. Wiggling lines are separated, than forced into
specific channels,spanning a distance a, proportional to the nerve radius and length. What
I have just described is a complex problem, spanning the esoteric fields of topology, geom-
etry, known to mathematicians as Intersection Theory [34, 36]; in related arena of mathe-
matics, it can be described as homological cycles, and their intersections forms (something
we will make use of, below , in explaining the High Temperature Superconductivity of
nerves in relation to pain) [35, 18]; in another, Sheaf Theory [33]. Naturally, specialized
areas of physics are involved as well. Contributions between physics and mathematics are
exemplified by an African drum, a Congas, with has the unusual property of having a reg-
ular fastened membrane to beat, an open hole down at the bottom. Similar to how those

wiggling pain lines see the Aδ, above. Are the conservation laws for harmonics and ther-
modynamics, preserved in such a system? To answer requires the complex mathematics
we alluded to, above, further what physicists call the heat equation, or Laplace-Beltrami
operator. In the African Congas drum instance, this problem was solved in 1992 in a paper,
Geometric Topology and Physics of D = 2 + 1 Fractal African Drums [43]. The Fourier
operator in fact comes into play here, where pain diffusion and scattering is concerned.
We may dismiss all that as merely musings of people who have an affinity for abstraction,
but you may be surprised to know this actually sum up black holes emission of radiation,
decay, the wave you see crushing down on the shore: they are similar problems. Moreover,
this problem extends to the nature and fabric of time (especially at the very center of black
holes), and why it may in fact be a form of energy, after all.
Wiggling lines, harmonic oscillators, or pain exiting their propagators, undergo a scat-
tering process. The Daisy diagram, above, is a visual snapshot of this process. Fourier
transform comes into play, requiring the use of Harmonic Theory, an active field of math-
ematical physics [18, 31, 32, 33, 34, 35]. If you have heard of Andrew Wales 1995 proof
of Fermat last theorem, one that went unproven for 358 years, thus stood as one of math-
ematics three greatest challenges, than, to bring perspective, a special class of harmonic
oscillators, known as Shimura varieties [36, 35](a variant actually) were used in Wiles’
proof. Beginning with Einstein’s 1905 seminal discovery of the photoelectric effect, the
quantization of light, physicists learned that particles are not points, as previously believed.
Rather, they are tiny harmonic oscillators (or waves)18
. In the 1980’s, the point-wave du-
ality was extended to a string; the latter was further augmented, in 1995, with Membrane.
Both String and Membrane require extra dimensions of space, and points to the existence
of numerous extra universes. Einstein, however allowed his stubborn bias to refuse to ac-
cept the point-wave duality, a cautionary tale to us. The Daisy diagram shows a somewhat
vague affinity with the dynamic of nerves’ diffusivity property. In certain instances, pain,
barreling through nerves B,C, acquires the topology of a knot, as I explicitly demonstrate
below; that is, it’s amplitude is detected by the celebrated Kauffman polynomial, an ob-
servation which correlates with the Daisy diagram, Feynman’s, and the quantum of pain.
Roughly speaking, using a mathematical property discovered by Li [44] (see also [30]), we
can prove, from the perspective of the brain, that the Daisy diagram is the multiple point
set of lattices, encapsulating incident pain signals. Alexander polynomial invariant [30] is
sufficient to keep track of knotted pain in the brain, in contrast to pain inside nerves, which
call for Kauffman’s. The attenuation length of a pain signal is am important quantity.
Sketched in (a), a pain signal exiting the Aδ, entering a lattice area of the lower brain
(the bulbous area), emerging from the synaptic cleft spacing, splitting further on its upward
journey to higher (and less dense) parts of the brain for processing. This is a traditional
Feynman diagram in which the initial pain harmonic oscillator decays into multiple, differ-
ent, smaller harmonics channels (known as decay channel, or branching decay in quantum
physics parlance). In (b) however, the pain signal branches much less, a single resonance.
Note the choice of word ”resonance”. Sketched in (c) and in (d), are interesting cases in
which the pain is extraordinary strong as an oscillator, spurt out of the nerve, barely modi-
fied from its initial form, emerges out of the synaptic cleft essentially unscathed, continues
18The experimental proof resulted in Einstein’s award of his only Nobel Prize, though certainly he deserved
many more; the Nobel committee and foundation having an unwritten rule not to award more than one prize
to the same person. Physicists’ classic reference [20] is highly recommended, extensive, providing not only
an exhaustive treatment and classification of elementary particles, it also provide information on experiments,
cosmic and astronomical contemporary problems.

v
a
�
,..,,_ �-
J;�-
1·.,-v,
,I�
R-'.
1� �,,,N
" �
'I
t� +� .
� . <>
111
Ii 1'
� .;
I
.,
f �
)I -
I
t
�K ,•
i'
•'
;; v
...
�
FIGURE 21. The complexity of pain, its propagation , diffusivity, scat-
tering, decay, within the brain, above: this complex branching, known
to mathematicians as a Daisy diagram, reconciles, to an imaginable de-
gree of accuracy, all three sciences involved in life: biology, physics,
and mathematics. The Daisy of pain is a mathematical representation
of sensory signals kinematics in the brain, known to quantum physicists
as branching decay; also, similar to the phenomenon discovered decades
before quantum physics matured, by neurologists Cajal and Loewi. The
Daisy diagram depicts branching decays of lepton particles, for which
Feynman diagrams are extensively used. In mathematics, a number of
specialized ﬁelds provide the formalism to extensively work out such
peculiar decaying process. A net beneﬁt, of Pain complexity: all three
sciences, mathematics, physics, biology, are precisely merging at this
very intersection.

FIGURE 22
upward for final processing. These Feynman path integrals are know respectively, (in c),
as tree level decay; in (d), as a one loop decay. There is virtually an infinite number of
combination of Feynman diagrams for pain, and for other sensory signals. A noteworthy
case is the Feynman Penguin diagram, illustrated in (e). In most instances, Feynman di-
agrams shows an incoming and outgoing exchange (the arrows at the base). This is so
because there is no such a thing in a quantum system (like the brain), that is able to only
absorb everything (and anything), and to not let energy out. Stephen Hawking made use of
this fundamental property to demonstrate black holes emits radiation (the Hawking radia-
tion), hence, are not completely black, as previously believed, and do decay. As it happens,
Hawking result gave credence to a curious discovery made by Russian physicists, which
determined that a neutron star (the last stage of stellar collapse giving rise to black hole)
energy minimizer absolute relaxation, via its magnetic field, means decay. To emphasize
yet again the matter of scale and of hidden physics brought on by duality coupling: the
core of certain Type II neutron stars are superconducting, drawing precisely on the HTSC

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