johnreed take 25 - Atomic Electromagnetic Field Structures

johnreed take 25 - The Atom as a Compacted Electromagnetic Field
Structure - Part 1
July 4, 2008

Although I have previously posted my ideas on atomic structure,
explaining how I got here seemed to be a waste of time without first
providing a platform on which to base a wholesale modification of our
gravitational paradigm. I believe that my most recent gravitational
posts [1] are "sufficient", at least enough for now, where I can
develop the rational, preliminary arguments, that support an
electromagnetic, atomic field structure.

As a youth the primary problem I became interested in was conceptual.
In that regard I was a hold out long after everyone else had given up
on anything more than the least action quantum mechanical mathematics.
However, a conceptual clarity was argued and hoped for as late as
1926. During that year it was published in Nature that the quantum
view was not, "the last word on the subject, and that [physicists] may
yet be successful in expressing the quantum postulate in picturesque
form." However according to Dirac "...getting the interpretation
proved to be rather more difficult than just working out the
equations." (The quotes noted above are conveniently taken from the
recent 2007 book: "Uncertainty", by David Lindley.) So difficult in
fact, that we soon abandoned any idea that atomic structure could be
explained in a conceptually clear manner. Preceded by Planck,
Einstein, Bohr, Heisenberg, Pauli, de Broglie, Schrodinger,
Sommerfeld, Kramers, Feynman, etc. etc. and etc., by the time I
arrived on the set, atomic structure was explained primarily in terms
of quantum mechanics, and for the most part, endorsed to some extent,
by the legendary and accomplished "illuminati" listed above.

I wanted to understand quantum mechanics in terms of atomic structure,
rather than to understand atomic structure in terms of quantum
mechanics. So I continued to search for the conceptual idea in part,
because I did not consider the mathematics as an adequate, crystal
ball substitute, for a comprehensive conceptual clarity, and in part,
because the physicist mathematician not only considered the
mathematics adequate, but the only true path to physical knowledge.
And to that end, she/he would allow any mathematically consistent
fantasy (not outlawed by the mathematics), an extensive review.
Throughout my search I sought an atomic structure that would explain
the experimental spectra data, the wave function, the uncertainty
principle, and remain consistent with quantum mechanics in general.
Additionally and more broadly I sought a reason for the fact that the
mathematics represents the universe so well [2]. I was never under the
illusion that my task was going to be easy. My goal was seen by
mainstream science as a frivolous and impossible to obtain end. I
often received admonitions like: "What? Do you think you can do better
than the brilliant pioneers that preceded you?" and my often silent
response: "I hope so. For the sake of humanity, and for the sake of
science, I hope so." Yet today, through hindsight, the apparent
insurmountable difficulty is now seen by me, to be largely a matter of
perspective.

oOo

If we investigate matter initially, merely as substance extended in,
and displacing space, we can reduce matter to a 3D object. A subject
partially entertained in solid geometry. What is the simplest, most
efficient, representation for a 3D object? The immediate answer is a
sphere (although a torus is just as efficient at enclosing volume) and
the sphere is in fact the default shape for our particles, in our
charged "particles in equilibrium", atomic structure paradigm. However
the default shape for our fundamental particle does not define an
efficient structural representation for a 3D object. Rather, it
defines the efficient object as a fundamental given. This in keeping
with the indivisible atom of Democritus, and Isaac Newton's first law
on the conservation of momentum. Therein lies the problem. We build
divisible matter out of "so called" indivisible matter. Consequently
we think in terms of fundamental bricks. And like the lady with her
"turtles all the way down" offering, we have extended our fundamental
bricks "all the way down". And what makes a fundamental brick,
fundamental? According to Democritus a fundamental brick is not
further divisible. And the universe is composed of fundamental bricks.

And how do we know if a brick is not further divisible? We don't, but
we think that if we can devise a functional mathematical scheme that
is esthetically pleasing, based on the charged particles in
equilibrium we have designated as fundamental, the property of
indivisibility will follow, as a matter of course. This idea for
indivisible matter was fairly advanced in the time of Democritus. It
is totally primitive today. The best conclusion we can obtain from an
indivisible matter build, is that matter is made out of matter. If
you question the significance we attach to a particle's
indivisibility, note that our mathematical scheme for the Standard
Model has described electromagnetic charge in fractional units, solely
to allow our contrived material quarks the required fundamental
property of indivisibility. Nature has not provided us even a
suspicion for a fractional charge. We have been unable to
conceptually justify our charged "particles in equilibrium" paradigm
from its inception, except in classical terms. What keeps the charged
electron in orbit around the oppositely charged proton? We have
converted the classical quantities designated as energy and angular
momentum to the atomic electromagnetic quantities designated as
frequency and wavelength (via Planck's Constant), and essentially
think that it is the electron's energy of motion that keeps it in
orbit. This, where we cannot even isolate and identify an orbiting
electron, yet we explain how it would manifest if we could.

The questions arise: Is matter fundamental? Or is electromagnetism
fundamental? Are frequency and wavelength the properties that allow
the atom's absorption and emission of energy packets? Can we build, as
well as generate electromagnetic fields, with our indivisible bricks?
Or can we build our generating bricks from compacted electromagnetic
fields? If we can build our bricks from compacted electromagnetic
fields the property of brick indivisibility vaporizes. And the notion
of a fundamental brick takes its elementary place in the teachings of
Zen Buddhism, while we seek to build an atom from compacted
electromagnetic field structures, in terms of the principle properties
of frequency and wavelength, where mass is a consequence, rather than
a cause. Emergent [3], rather than controlling.

oOo
Consider that an enclosed area is a bordered extension of 2D space and/
or a displacement of 2D space limited by a boundary. A circle is the
simplest, and most efficient boundary for an enclosed area. We can
combine the 2D circle with another 2D circle, arranging them
orthogonally with each circumference passing through the center of the
other circle. If we allow for some as yet, undefined force here, we
can view the orthogonally chained circles as a representation for a
locked physical join. If we wish to build an efficient 3D object in
terms of a structured substance extension and force, this is one place
to start. An efficient Occam's Razor structural representation for a
3D object. Two geometric 2D circles joined solely to provide an
initial efficient buildable symmetric base.

Visualize the two orthogonal, center joined circles in any kind of
regular, mutually restricted motion for each circular element. For
example, we can set each circle circumference in a circular spinning
motion, allowing that circumference to pass through the center of the
other circle, or we can set each circle plane to travel orthogonally
along the circumference of the other circle. With respect to the time-
space properties between points on the joined circles the two motions
are symmetrically equivalent. Which I offer here momentarily as an
aside. However, note for starters that T^2/r^3 and E=mc^2 and
frequency, wavelength, 2pir, Plancks Constant as a conversion factor
for frequency to energy, the collapse of the wave function, and more,
can all be massaged into, and/or, out of, this simple, initial
structure. A rather nice elementary example of a correspondence
between the mathematics here and the stable system, least action
universe motion in general.

An ordered regular boundary requires a cause. Searching for some
semblance of a grounding physical meaning here, given the join and
each circle we can break the two circles down into two original
straight lines. Call them fundamental (indivisible?) electromagnetic
(energy) threads, that manifest independently in the absence (or
attenuation) of a controlling electromagnetic field (or in the absence
or the attenuation of any other background or controlling condition).
Say each thread is a like monopole, or unlike monopole, or a dipole (I
have a preference here but they each function in a subsequent build).
When each thread joins as two interlocked circles how do the two
circles manifest electromagnetically? Starting as dipoles, as joined
circles they are identical and may electromagnetically repel and/or
attract each other, depending on orientation. Perhaps as though they
were like monopoles, even as they share a locked physical join. The
rigid orthogonal configuration, each through the other's center, could
be maintained by mutual maximum repulsion of like monopoles. Or do we
have one circle contract while the other expands? The contracted
ring(s) serving as the nucleus. The expanded ring(s) separating
uniformly around the nucleus as orbitals? This could apply to dipoles
or monopoles. Can we massage the construct to represent the behavior
of like monopoles, elastically seeking maximum separation space within
the restricted parameters of the join? Or as unlike monopoles? In any
case, the model provides us a simple mathematical construct on which
to build an atom in terms of the properties of compacted
electromagnetic field structures. With this construct as is, starting
with hydrogen, we can directly and immediately mirror the periodic
table qualitatively (recall that in most mathematical models we use
stick figures rather than fully musculatured and innervated
representations) and with the assistance of Planck's Constant merge
the electromagnetic representation with the classical representation,
which is another nice example of least action primacy. My goal here
is to provide a conceptual carrier for oscillations, frequencies,
wavelengths, uncertainty, wave functions, their collapse, and quantum
mechanics in general.

We may call this primordial state of matter a particle, where the
property of extension in space requires some containing structural
principle. The single principle that threads through all our stable
system models is the principle of least action. Therefore that is the
principle I bring to the table. From this primordial particle
construct, representing an origin (a seeding) for an electromagnetic
field (rather than two joined quarks), we can duplicate the periodic
table and anchor quantum mechanics to a descriptive and continuous
picture, that accounts for most, if not all of the experimental
spectra results. Such a compacted electromagnetic structure will
account for all our experimental scattering results from Compton to
2005.

We have never before entertained such notions as these, choosing
instead to force our classical "object-space" view onto the universe
in terms of probabilities. That is to say that although our classical
"object-space" view is wrong, we have built a model consistent with
least action principles, showing the way it would be if it was
correct. And where our charged particle model runs aground we invent
special forces to get it to float. We just assumed that fundamental
indivisible 3D spherical objects existed, that served as the bricks,
by which all 3D atoms were built. So we built the 3D atom from 3D
charged objects in equilibrium, and 3D neutral objects to serve as a
mass adjusted filler. In short we built our fundamental bricks from
more fundamental charged and uncharged smaller bricks and we devised
suitable forces to enable them. Planck's constant provided us a means
by which we can convert the atomic electromagnetic properties of
frequency and wavelength into the classical properties of mass,
momentum, and energy. So that the proton is viewed as being composed
of little indivisible balls of stuff that, indivisibility
notwithstanding, exchange little balls of force. We call this
construction the Standard Model. Not so much as Democritus predicted
but again, like the lady who offered that "it is turtles all the way
down."

oOo

For several centuries we assumed that the universe is the "object-
space" mass driven world as subjectively quantified by Isaac Newton.
This was consistent with the world we perceived and measured and
quantitatively interacted with, as inertial objects. We sought the
nature of this universe in terms of components called matter,
quantified in terms of resistance (mass) within a field of space. An
"object-space" view of the universe where a notion for time direction
developed from the time lines of our lives. We are born. We live. We
die. We durate. We applied this sense of duration to our classical
view of the universe in terms of entropy. Where in an
electromagnetically controlled universe the dissipation of energy
becomes a cyclic phenomenon. And in fact the primary physical measured
counterpart of time is repetitive duration. This controlling aspect of
time, with regard to stable system action, was lost to our notion for
a direction in time and to mass generated gravity. The time-space
connection was amalgamated with our sense of direction and included as
a fourth dimension by Einstein and peers. In a least action universe
space and time and mass will reflect or operate within the least
action principles, where a subjective interpretation of these
quantities can easily ensue. Einstein attached great significance to
our subjective view, but that is the focus of another post.

oOo

We observe electromagnetic spectra data that is an electromagnetic
signature for each element. To explain the hydrogen electromagnetic
spectra data, Bohr introduced the idea that an atom's so called
orbiting internal accelerating electron could match the spectra data
if the pre-existing electron orbit was described proportional to its
frequency of rotation. Note how our assumption that the electron
manifests inside the atom as a charged particle has us tied to the
whipping post. Bohr does not deal with the problem associated with our
classical view but rather describes it in a manner that conforms to
spectral data. Our orbiting charged electron has severe problems and
should be discarded but Bohr describes mathematically how it could be
if it did exist. This stabilized the orbiting charged electron, by
defining it in mathematical terms that agreed with the experimental
electromagnetic spectra data. A defacto stabilization while carrying
our conundrums forward. This Bohr atom then crudely modeled the Balmer
series for the hydrogen spectra.

The Balmer series was an oversimplification as the spectra was soon to
be shown to be modified by externally applied electromagnetic fields,
into closely spaced doublets and triplets, etc. We had the
electromagnetic spectra of the atom modified by an external to the
atom electromagnetic field. Nothing unreasonable here provided we
regard the internal atomic field as a compacted electromagnetic field
structure. This is known as the Zeeman effect, and was thought to
result from internal charged electron orbits set at an angle to the
external fields causing the 'energy' of the orbit to change slightly.
What changes slightly are the frequency and wavelength characteristics
of the atom as shown by the spectra data. Here we further obfuscated
the fact that an orbiting electron could not sustain itself in orbit
without losing energy (not to mention just its attraction to the
positively charged proton), while allowing the external
electromagnetic field to modify that energy, rather than modifying the
atom's electromagnetic frequency and wavelength properties. Where the
entire atomic theoretical construct is based on discrete, non-
localizable, charged particles, in some kind of fantasy equilibrium,
and where the spectra data is clearly in purely electromagnetic terms.
Again, the crucial problem we must address is our assumptive a priori
belief that matter is made of matter? That it is "turtles all the way
down."

oOo

The questions we ask today to provide answers for the future, are
based on the conclusions of the present. The conclusions of the
present rest on our a priori assumptive foundations, and an attendant
supporting mathematics. As long as our assumptive foundations operate
within least action principles anonymously, the applied mathematics
will predict the relevant experimental results. Not because the
mathematics is a crystal ball on the universe, but because stable
systems are least action systems and the mathematics represents least
action well. Consequently we can have similar least action systems
where the comparative dynamics are not proportional with respect to
time and space.

oOo

We discovered that some forms of matter that we call elements reduce
to the smallest fundamental matter units we call atoms, and that each
atom is unique, as each element is unique. We define elemental matter
in terms of the smallest unit of elemental matter. The periodic chart
of the elements describes fundamental states of matter in terms of the
properties of atoms. We have described the fundamental elements of
matter in quantitative terms that we can perceive and measure, that
define the properties of the smallest example of the element. This is
where Democritus applied. We subjected the atom to intense
investigation and destructive scrutiny and learned that the atom was
not indivisible. And because it was not indivisible we concluded that
some, even more fundamental, form of matter, existed inside the atom.
We defined this form of matter in terms of the atom's naturally
ejected and naturally absorbed particles, and in terms of the atomic
electromagnetic shards we observed after high energy experimental
collisions. We reconstructed the atom using the particles and the
shards as the building blocks. We assumed that the particles and
shards maintained their discrete existence inside the atom. In the
process we invented more forces to overcome and explain the flaws in
our charged particle construction. Never recognizing that the charged
particle flaws required Herculean efforts to overcome, even as we were
led further into conundrum. This even after we accepted the
Uncertainty Principle where we admit that the internal to the atom
existence of our charged "particles in equilibrium" paradigm cannot be
verified, except in terms that again tell us how it would be, if it
did exist.

We search for the fundamental structure of atoms by destroying this
structure into shards of electromagnetic rubble and then we rebuild
the electromagnetic structure using the most prevelant recurring
shards, which we statistically apply to our "charged particles in
equilibrium" paradigm in terms that convert the electromagnetic field
properties of the atom to the object-space properties of classical
mechanics. Which "pre-existing" internal to the atom "object" we
cannot locate inside the atom, outside of statistical probabilities of
where it would be found if it did exist.

oOo

Using iron filings we observe the magnetic field structure that
emanates from a bar magnet. If we reduce our bar magnet to a single
atom and if we retain the magnetic field structure, it is reasonable
to suspect that the field structure reflects an especially stable and
efficient state of atomic structure, where atomic structure in general
conforms to the structural principle observed in the dipole field
itself, whether the atomic structure is especially efficient or not.
This idea is based on the well worn notion of form follows function. A
3D representation of this dipole field will serve the reader, for the
purpose of this post, as a general visual example of the
electromagnetic orientation for atomic structure.

oOo

The ultra violet catastrophe and blackbody radiation forced us to
conclude that there are severe conditions where the atom does release
excess absorbed energy in discrete quanta. We have no absolute reason
to believe that these ejected discrete packets of energy exist in the
packet form inside the atom. If the atom can release excess absorbed
energy in discrete quanta under varying and extremely adverse
blackbody radiation conditions, is it not reasonable to conclude that
the atom can also release standard packets of charged energy quanta
under a less adverse and more stable condition? And is it not
reasonable to suspect that the magnitude of the ejected excess energy
occurs as a consequence of the built in frequency and wavelength
limits attendant to the atom and to its compacted electromagnetic
atomic structure.

No one even considered that the electron might not be a charged
particle inside the atom. No one suspected that the electron might be
a standard packet of energy that the atom easily releases to maintain
stability, at the collapse of an internal orbital wave that serves as
an interface between the atom and its surround. No one thought that
the electron might manifest as a charged standard packet of energy
external to the atom, that the atom readily absorbs to regenerate its
collapsed energy deficient internal wave orbital. This, enabling the
atom to maintain stability, conduct current, and build the universe we
observe under non-severely adverse, reasonably stable conditions.

oOo

What is especially significant is the fact that the fundamental
elements share a common quantity of energy called the electron, that
manifests as a particle outside the atom, enabling the atom to easily
interface with its surround, maintain its core stability, conduct
current in special cases, and build the universe we observe. We have
no clear reason to suspect that this common packet of charged energy
manifests as a charged packet of energy inside the atom. The
Uncertainty Principle attests to this. Even so, our a priori idea that
the electron exists as a discrete charged particle inside the atom,
set our course of investigation for the entire 20th century. We had no
proof for this, and no compelling reason to believe it. But believe it
we did. Again, we just assumed that it was so because the isolated
proton and electron exhibit a mutual attraction that we measure in
terms of a standard unit we call charge. This, even when we knew that
an accelerating charged particle emits electromagnetic waves. So by
our thinking, the orbiting electron if it is a charged particle inside
the atom, should be losing energy and spiral into the nucleus in less
than a second. Since it does not lose energy, rather since the atom
retains stability (remember that we have only assumed that the
electron is a charged orbiting particle inside the atom) we could
easily question the existence of an internal to the atom, orbiting,
charged electron packet. More broadly since the electron is
negatively charged and the proton is positively charged when isolated,
if they each retain their integrity and charge when joined inside the
atom, what keeps these charged particles separated inside the atom?
Here it is the classical notion of the energy of motion that separates
the electron from the nucleus. And Planck's Constant is the
mathematically expedient conversion factor.

oOo

To match the electromagnetic spectra data the aspects of the imaginary
electron orbits were restricted to specific integer values, where each
integer is evenly divisible by Planck units. Recall that Planck's
constant allows us to duplicate the atomic emitted blackbody frequency
and wavelength radiation curve in terms of energy. Three quantum
numbers reflected orbit size, ellipticity, and orientation, each
divisible by Planck's Constant. A fourth quantum number is based on a
half integer unit with respect to Planck's Constant. This is the most
external orbital and can be viewed in terms of an electromagnetic
field structure as a compacted wave describing a torus around the
atom, where its point of anchor on its boundary, to the atom, passes
into and is influenced by the atomic nucleus. So only certain shapes
and sizes and orientation of orbits were allowed. And these measured
in units divisible by Plancks constant. It is significant that these
data were interpretted as though the electron maintained its discrete
charged particle status inside the atom. Where the conceptual problem
as I came to see it, was the difficulty in recognizing that emitted
electrons are particles and absorbed electrons are oscillating
compacted orbital waves.

Significant Indicators
Heisenberg gave us the limits that the atom set for us.The Uncertainty
Principle tells us that we cannot show that the electron exists as a
charged particle inside the atom. All we can get is the collapse of
the wave function which seeks its own regeneration and manifests as
charge, where the momentum and location of the emitted or absorbed
electron depends on where the wave orbital collapses or where it is
regenerated. Where in the photoelectric effect although the atom
always releases its standard packet of energy, the momentum of the
packet can vary to accomodate the point on the orbital plane where the
electron exits the atom (the integrity of the orbital plane is
maintained by the mutual repulsion between the planes). Or to
accomodate the release of excess energy that is not sufficient to
cause a standard electron packet to be emitted. So we are reduced to
probabilities that are consistent with the electromagnetic atomic
field structure dimensions, defined by frequency and wavelength, and
converted into classical quanta, by redefining the electromagnetic
controlling properties consistent with integer units, that represent
whole unit orbitals that are evenly divisible by Planck's constant.

oOo

A wave interpretation for atomic structure had previously been
directly approached. "Schrodinger insisted that a particle was not a
tiny billiard ball but a tightly gathered packet of waves that created
the illusion of a discrete object. Everything. fundamentally, came
down to waves. There would be an underlying continuum. with no
discontinuities. no discrete entities. There would be no quantum
jumps. But instead smooth transformations from one state to another
[restricted by the idea for an internal orbiting electron]. None of
this followed directly from Schrodingers equation. It was what he
hoped his wave equation would lead to." "Uncertainty", 2007, David
Lindley. (text in brackets added by johnreed.)

oOo

The idea that an external radiation field existed was put forward by
John C. Slater and picked up by Bohr and Kramers. The collusion
between the three became known as the BKS paper. The initial idea was
that an external field interacted with atoms internally, governing the
way the atom absorbed and emitted energy. This was later modified to
include the idea that the atom acted internally as though it
consisted of a group of "virtual oscillators". The physics for
oscillations was successfully used to explain the spectral lines of
the atom, absent any attempt to describe the structural aspect in
detail. This idea for virtual oscillators is the grandaddy of what is
now called string theory.

"We will assume that a given atom in a certain stationary state will
communicate continually with other atoms through a time-spatial
mechanism which is virtually equivalent with the field of radiation
which on the classical theory would originate from the virtual
harmonic oscillators corresponding with the various possible
transitions to other stationary states." BKS Paper, 1923 as quoted in
"Uncertainty", 2007, David Lindley.

Translating the above, it states that an atom is composed of
oscillators that match aspects of the external radiation field such
that an interchange between the two occurs, that is sufficient to
explain the observed emission and absorption spectra. This
complementary radiation field served to replace the idea for light
quanta. If Bohr could have articulated these ideas more precisely he
might have stumbled upon the electromagnetic field structure for the
atom. An oscillating (or rotating) electromagnetic atomic field, wave
orbital, would be selective with regard to the frequency and
wavelength of the radiation it could absorb and emit, as a
partitioned revolving door limits the rate at which each person and
the number of persons can enter and exit in the course of one complete
revolution.

For reasons I will not entertain here, by 1925 Bohr refuted the BKS
paper. The idea was continued by Kramers who rigorously demonstrated
that the atom's absorption and emission of energy at a certain
frequency could be precisely matched to the spectra data if the atom
contained a specific set of "virtual" oscillators. On the face this is
a major clue that supports an atomic electromagnetic field structure.
But Kramers still considered the idea merely as a mathematically
convenient tool for calculation. Although the oscillator idea
described the measured spectra quantities attendant to atoms, without
speaking to any conceptually clear internal structure, the overtly
spoken idea for discrete charged electron orbits was soon to be quasi-
abandoned and permanently enshrined, in our conceptual scientific
view. Replaced by the statistical probability of finding that pre-
existing charged electron at a particular location and at a specific
momentum, inside the atom. Which demonstrably shows that we will
build the universe after our own image in spirit, if not in fact, by
devising a consistent mathematical scheme that reduces that image to a
quantifiable mathematical statement. Where a sum of all possible
histories as a set of givens, will always provide a most probable, or
least action solution. How important is it that we obtain a correct
conceptual understanding before we incorporate mathematical methods
that lock us into bogus notions, that function solely from a
statistical consistency with least action events? My next post
titled "johnreed Take 25A - Radioactive Half Life", will show this
importance in terms of the many formerly closed doors that have been
opened by a mere change in perspective. In my opinion, the BKS work
provided the best clues for a coherent, conceptual, mathematically
verifiable, compacted electromagnetic field interpretation, for atomic
structure.

oOo

We have two structures in physics that jump out at us. The planet
orbits and the electromagnetic field structures. We have assumed that
atomic structure is composed of discrete charged particles in
equilibrium where the pure data reflects a composition that consists
of electromagnetic field structures. If we build the atom from these
electromagnetic fields it turns out that atomic structure does indeed
follow from Schrodinger's wave mechanics. It also follows from
Heisenberg's matrix mechanics. To see this we must "truly" abandon our
"particles in equilibrium" view of atomic structure and build the atom
from compacted and massaged electromagnetic fields [3]. This construct
will be consistent with our scattering experiments from Compton to
2005.

Inside the atom, the wave function, as opposed to Heisenberg, more
closely describes conceptually what is happening. For example: The
collapse of the wave function occurs when we cause it to collapse. We
can view this as a result of our interference or as a property of the
atom, or as both. In either case, it is the wave function itself that
fundamentally pre-exists and its collapse creates the particle and its
regeneration absorbs the particle. Consequently we must build the atom
structurally consistent with wavelike quantities. A compacted
electromagnetic field structure rather than an electromagnetic field
generated by charged objects in a Frank N.Stein cobbled together
notion for a charged particle equilibrium. Our conundrums are then
greatly alleviated and a clarity falls out of quantum mechanics that
can be visualized.

Endnotes
[1],[2],[3] If the reader wishes to review my earlier posts on atomic
structure, gravity, the measure of lightspeed, dark matter, etc.,
etc., and etc., she/he can do a Google.group search on "johnreed
take". Then sort by date to avoid my many earlier even more primitive
attempts to succinctly articulate these connecting ideas.
[3] Also see the paper by Andre Michaud at:
http://www.wbabin.net/science/michaud1.pdf
johnreed

.

Quantcast