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Anonymous: on 10/7/12 at 19:39pm UTC, wrote Dear Kenneth Snelson, If we want to consider classical atomic models, we...

MV Vasilyeva: on 10/6/12 at 1:31am UTC, wrote Mr. Snelson, I very much admire your work. I always had a thing for art,...

Sergey Fedosin: on 10/4/12 at 4:10am UTC, wrote If you do not understand why your rating dropped down. As I found ratings...

Vijay Gupta: on 10/2/12 at 18:58pm UTC, wrote Mr Kenneth Snelson SORRY THE ABOVE MESSAGE GOT REGISTERED AS ANNONYMOUS. ...

Anonymous: on 10/2/12 at 18:48pm UTC, wrote Mr Kenneth Snelson It was a pleasant surprise to read your article. Your...

Juan Ramón González Álvarez: on 9/29/12 at 18:08pm UTC, wrote Dear Kenneth, Thank you for a very thought provoking essay with a welcome...

Kenneth Snelson: on 9/28/12 at 22:15pm UTC, wrote Dear Andeas, What a great compliment --"Christmas eve feeling". I...

Vladimir Tamari: on 9/26/12 at 8:34am UTC, wrote Dear Kenneth thank you so much for your kind words. It is great that you...


Rajiv Singh: "Dear Stefan, Sometimes, the website does not offer a login option, so you..." in FQXi Essay Contest 2016:...

Anonymous: "Dear Stefan, So far, I had been avoiding to comment on certain aspects of..." in FQXi Essay Contest 2016:...

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April 27, 2017

CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: An Artist's Modest Proposal by Kenneth Snelson [refresh]
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Author Kenneth Snelson wrote on Sep. 6, 2012 @ 10:59 GMT
Essay Abstract

Niels Bohr's atom model of 1913 was abandoned by science over eighty years ago yet it is still introduced in all science classrooms and it remains famous the world over as the cartoon-symbol meaning "atom". In the dramatic causal/acausal debates of the 1920s, the Copenhagen people who argued to disallow any further "reality" atom models were declared the victors. Among the ideas left behind in the rush to get rid of physical models entirely was Louis de Broglie's adaptation of Bohr's model in which he replaced orbiting electrons with matter-waves. De Broglie's atom is remembered in classrooms but is given short shrift on the way to introducing wave mechanics that Erwin Schrödinger developed in 1926 after learning of de Broglie's matter wave theory. As an artist whose work and interest concerns fundamental structure, I became fascinated as far back as 1960, in developing a more complete picture of an atom for those still willing to speculate about a reality model, the kind physics gave up on so very long ago. This is what my paper is about: a qualitative reinterpretation of de Broglie's model of the hydrogen atom.

Author Bio

My name is Kenneth Snelson, born the year of the Fifth Solvay Conference. I am a working artist best known for building large outdoor sculptures of steel pipes and aircraft cable, many of them standing in museums and public places around the world. Each of my sculptures is a prestressed tension/compression network of steel pipes and aircraft cable, a principle known as tensegrity, one of my several inventions. I describe them as diagrams of physical forces in three-dimensional space.

Download Essay PDF File

Frank Makinson wrote on Sep. 6, 2012 @ 18:24 GMT

Your presentation of electron "energy loops" is one of the better explanations I have read about.

I remember being exposed to the planetary concept of an atom and electrons in my early education. I realized later that this was unrealistic. Physicists then used the energy level jumps, but then I realized they never identified how something as small as an atom could produce a wavelength that was humongous relative to the atom's size. The 21 cm wavelength from the neutral hydrogen atom is a case in point. There has to be an energy structure in place that can support the generation of the EM field that has that particular spatial dimension, and I had never found a satisfactory explanation.

The discussion related to Figure 10 is informative. Fig. 11 depicts shells within shells.

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Author Kenneth Snelson replied on Sep. 11, 2012 @ 16:06 GMT
Dear Frank,

Thanks very much for your recollections of being taught early on about planetary electrons. It's the picture we all carry around to some degree I believe. After years of talking with people about their own inner image, most say they see planetary electrons. I rather think that no one is likely to change that very soon.



Anonymous wrote on Sep. 6, 2012 @ 20:34 GMT
That was a very informative essay, and the illustrations are superb! That's awesome.

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James T. Dwyer wrote on Sep. 7, 2012 @ 00:34 GMT
Hi Kenneth,

Thanks you for addressing this neglected issue. I'm certainly not a physicist, but in my experience I've found that even highly successful mathematical representations of a system may not accurately represent all processes and elements involved in producing the system's observed characteristics. I think most physicists would consider me naive (or more directly, ignorant) but I...

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James T. Dwyer replied on Sep. 7, 2012 @ 13:26 GMT

BTW, I did find a Wikipedia entry, Atomic orbitals that presented a great deal of additional considerations I had certainly been unaware of. You might also find it a useful read...


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Kenneth Snelson replied on Sep. 18, 2012 @ 18:35 GMT
Dear Jim,

Thanks so much for your thoughtful comment. Sorry it has taken me so long to respond. Yes, even the Figures 7 and 8 are meant to represent a blurred electrical charge. They aren't blurred in the illustrations largely because of I wanted to emphasize the numbers of de Broglie waves and they become less clear by blurring them. It's a question choices of graphic style. I've attempted in so many different ways over the years to represent these invisible things. Did you ever Google "images" for "atom"? It's hilarious how many different ways people try to picture atoms.

Best wishes,


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Vladimir F. Tamari wrote on Sep. 7, 2012 @ 09:21 GMT
Dear Kenneth

Your essay is a pleasure to read both for the clarity of the presentation and illustrations, and the originality and relevance of the ideas presented. I hope readers more qualified than I about atomic structure will give their feedback. I specially love the magnetic spin system shown in your Fig. 10. You have provided more details on your website this wonderful invention (discovery!?) which may well describe in a physical way how nuclear particles and electrons actually behave at the smallest scales.

On your website you have also fascinating studies of weaving patterns which in a spherical configuration become topographical knots. Some years ago there was a Scientific American article showing how various quantum states are represented by the topology of knots. You were already there too in that area straddling art and science to the benefit of both!

In this magnetic conception tensegrity plays a role because of the (+) (-) repulsive- attractive forces. These forces are hard to 'see' in the gear-like top configuration you provided because the gears are always in contact, but may be easier to visualize if you think of the tops as free-floating rotating rods set normal to the rotation axis, moving in unison with their neighbors. Inspired by your work this is how I presented my universal building blocks in my Beautiful Universe Theory

Hats off and good luck in continuing your wonderful inventions and artistic creations.


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Author Kenneth Snelson replied on Sep. 18, 2012 @ 19:40 GMT
Dear Vladimir,

What a wonderful and complimentary comment, and especially from a fellow-obsessive trying to figure out if there's a logical mechanism that we might one day understand out of all of this complexity.

I do think that the culture of quantum physics too willingly shifted in the direction of non-visual tools by the Copenhagen people who succeeded in forever filtering out of the system many bright minds who rely on their visual faculties as well as their left-brain skills. Einstein was such a mind. The enduring reverence for the uncertainty principle seems strange considering that no other realm of science recognizes such a restriction on the imagination.

I was watching a PBS documentary, "Naturally Obsessed" about a class at Columbia trying to discover the workings of a complex protein molecule. One of the students, who eventually got his doctoral for solving the problem, said at one point, "Its properties are never going to be properly understood until we can see what it looks like". When I heard that I thought, "Why was that idea, that goal, abandoned by quantum physics when other sciences HAVE to understand what the thing looks like and how it works". In my naivete I remain baffled.

So, bully for your Beautiful Universe Theory!

Warmest and best,


Vladimir F. Tamari replied on Sep. 26, 2012 @ 08:34 GMT
Dear Kenneth thank you so much for your kind words. It is great that you are getting so many visitors to this page who offer support and understanding of your atomic model. Your clear uncluttered model is the result of deep thought about structure and the forces that keep various components in tensegretistic balance (to coin an adjective from your noun !). This has served you well in the conviction that the atom is no different than any other structure.

Bravo for ignoring the negativity of the probabilistic Copenhagen interpretation towards physical reality. That took some strength of mind. On the other hand non-academic researchers like you and me have the advantage that we can go on a limb and present our ideas without worrying that it will cost us a University position, and the like.

The visual approach is more important than other kinds of math (geometry might be considered a visual discipline) because Nature has structure in 3D. This we believe.



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Cristinel Stoica wrote on Sep. 8, 2012 @ 07:13 GMT
Dear Kenneth,

Louis de Broglie is underappreciated - his contribution was essential to quantum mechanics. I guess that this lack of appreciation has to do with the rejection, by the scientific community, of his idea of double solution and of de Broglie-Bohm theory. In my opinion, the debates which took place at Solvay, and continued after that, had a very important role, and all criticism brought by Einstein, de Broglie and others to the Copenhagen interpretation led to the understanding we have today. It is a shame that they are so often regarded as opposing the new and the truth, and that their contribution is so underrated.

I am amazed by tensegrity and your sculptures, as well as your visual model of the atom - beautiful and inspiring.

Best wishes,

Cristi Stoica

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Cristinel Stoica replied on Sep. 9, 2012 @ 13:57 GMT
P.S. I feel that I should add this, to avoid any misunderstanding. I fully endorse the atom as it is pictured by quantum mechanics, based on the Schrodinger and Dirac equations. I can appreciate though an artist's modest proposal.

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Kenneth Snelson replied on Sep. 10, 2012 @ 23:57 GMT
Hello Cristi,

Thanks for your kind messages. Yes, clearly, physicists need the mathematical tools of the standard model to solve problems.

I’m wondering though if my visual model, as you see it, is totally resistant to calculation? For example do you think it might be possible to calculate the orbital magnetism -- the azimuthal, l (small L), quantum-number value -- for the 3s, 3p, 3d de Broglie-wave “halo” orbits in my model; in order to compare them with Sommerfeld’s elliptical orbits? Or does the question make any sense?

Thanks and best wishes,


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Cristinel Stoica replied on Sep. 11, 2012 @ 09:29 GMT
Dear Kenneth,

You asked:

"I'm wondering though if my visual model, as you see it, is totally resistant to calculation? For example do you think it might be possible to calculate the orbital magnetism -- the azimuthal, l (small L), quantum-number value -- for the 3s, 3p, 3d de Broglie-wave "halo" orbits in my model; in order to compare them with Sommerfeld's elliptical orbits? Or does the question make any sense?"

In my opinion, the parameters of your model can be calculated and compared with Sommerfeld's elliptical orbits. I don't know if the direct calculations can give the known values, but I think it worth checking how far is possible to go in this comparison, and if there are some natural adjustments which can help. My intuition saids that your artistic depiction extracts some essentials features of the atom and makes them somehow more visible. It may be possible even to exist a mathematical correspondence between the standard atom model and yours. If this turns out to be true, your model can complement the standard atom model, and have some pedagogical advantages.

Best wishes,

Cristi Stoica

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Peter Bauch wrote on Sep. 12, 2012 @ 17:43 GMT
Dear Kenneth

It's nice to see a fellow proponent of science-art. We both offer graphic interpretations of physics' hidden realities. It is my belief that the circle is the cornerstone of all creation, its form repeated ad infinitum in nature, and I think that if you use it in a reasonably intelligent way you stand a greater chance of hitting the mark in an attempt to describe a hidden reality. Higher-dimensional string theory that began with Kaluza-Klein introducing the fifth dimension only became possible when Oskar Klein in 1926 proposed that the fourth spatial dimension was curled up in none other than our friend the circle. Looking at your website, I found it fascinating how you were bitten by the physics bug when you began a study of the circular aspects of your tension structures by experimenting with plastic rings. I am of the notion that if you correctly depict a hidden reality it should be as visually appealing as a landscape painting and strike a chord of resonance within the viewer. Your Fig. 11 is a perfect example.

All the best,

Peter Bauch

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Kenneth Snelson replied on Sep. 18, 2012 @ 19:05 GMT
Dear Peter,

I agree about nature's fundamental shape -- the circle -- in creating many kinds of structures. About fifty yeas ago I became fascinated with "circlespheres" -- for lack of a standard name -- and the plastic rings you mention. Circlespheres are cousins of to regular platonic and archimedean polyhedra but they also offer a number of peculiar variations. Anyway, that is how I discovered the magnet spherical mosaics and got involved with atoms.

Thanks so much for your kind comments,

Best wishes,


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Peter Jackson wrote on Sep. 19, 2012 @ 11:00 GMT

Both good reading and valid electron conception. Congratulations. Unfortunately it seems my long post last night got lost in cyberspace. The basics;

Have you considered possible helical fields around a more 'substantive' version of your ribbon. This would form a toroid, which I've found as a fundamental structure from single particle through nuclear tokamaks, Earth's em field, through to AGN's and indeed probably the universe. You don't of course suggest what the ribbon may be 'made of'. Thoughts?

Secondly. I commend your comment;

"As with macro pieces of matter, de Broglie waves occupy exclusive space. Orbits cannot be in the same space at the same time."

And suggest it may have far deeper meaning than you discuss, which I outline in my essay, considering the implications of spatial exclusivity of matter an states of motion. I do hope you'll read and comment on (and score!) my essay.

Well done. And congratulations for such a flexible and perceptive mind, putting many physicists 50 years younger to shame.

Best wishes


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Edwin Eugene Klingman wrote on Sep. 19, 2012 @ 21:07 GMT
Dear Kenneth Snelson,

I very much enjoyed your essay and your artwork. Your summary of de Broglie is excellent. If you have not already read it [it's not in your references] I think you would enjoy reading "Quantum Theory at the Crossroads", a recent analysis of the 1927 Solvay Conference and re-evaluation of de Broglie, available at Amazon.

Like you, I am convinced that the "atom is an elegant submicroscopic mechanism" that can be visualized, much as you have done. The question of how this related to probability is treated in my essay, The Nature of the Wave Function. In fact we visualize the orbits [which have recent experimental support!] in much the same way. Based on my interpretation of the physical field that is the basis of the wave function and upon Joy Christian's framework that focuses on a 'volume element' instead of a 'vector' description, I derive a 'volume conservation' relation that, visually, preserves a cylindrical volume that gets narrower as the cylinder gets longer, fatter as it get shorter, corresponding to your figure 4 and to your figure 3. [see the diagrams on page 5 of my essay.] The volume represents the actual (helical) wave in space whose strength is proportional to the particle momentum and hence to the de Broglie wavelength. You seem to capture this in your figure 3.

Like you and several other authors here, I consider the de Broglie waves to be physically real -- a physical field that is induced by the mass in motion according to an equation of general relativity. I believe that your work with tension/compression networks [tensegrity] have provided you with an excellent intuitive understanding of the relevant atomic relations.

I invite you to read my essay and hopefully comment upon it and give it a [high] community score.

Thanks for your analysis and your artwork, and good luck in the contest.

Edwin Eugene Klingman

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Robert Webber wrote on Sep. 21, 2012 @ 22:51 GMT
Dear Kenneth,

Thank you for pointing out that physicists should be held accountable for refusing to think about small objects in real space and time! As you suggest, it was de Broglie who first conceived of the quantum wave and deserves credit for starting the field of QM. I see you give your quantum objects (or at least electrons) a quality such that they cannot share space with any other quantum object, rather like discreet solid objects, whether or not they have differing quantum numbers; this, of course is contrary to the accepted view. Whether or not you are right, I agree that the Pauli exclusion principle, so fundamental to the nature of matter, needs to be thought about more deeply. It surely must be hiding a lot of physics, but when being taught, it is presented without any reason or further comment.

I think you would be very interested in reading Alan Kadin's essay on the rise and fall of wave-particle duality: The Rise and Fall of Wave-Particle Duality. He also builds a real-space picture of electrons based essentially on de Broglie waves and suggested that electrons are not point particles, but are made of a distributed rotating vector field. According to Alan, this real field, which can be represented as a picture in 3 dimensions IS the quantum wave function. However, it is not so easy to draw a picture of a distributed rotating vector field. You might have the insight to be able to represent these fields in 3-D.

Best regards,


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Member Hector Zenil wrote on Sep. 23, 2012 @ 22:01 GMT
Dear Kenneth,

The representation and hypothesis you propose for the model de Broglie suggested seems quite interesting, since it covers some of the problems one could find when trying to model it. It was also very useful all the images you provided to show your ideas. I think this reminds us that different models, even if not mainstream or toy models, may have greater pedagogical advantages than others in order to work towards the understanding of more complex topics.

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Andreas Boe wrote on Sep. 23, 2012 @ 22:17 GMT
Hi Ken!

Reading your essay and enjoying the illustrations gives me a kind of Christmas eve feeling. I am not sure it convinces me to change view of the atom, but it sure helps me with the out of the box thinking. Just like good science fiction.

A short SF story I think you might enjoy is "The Tower of Babylon" by Ted Chiang.

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Author Kenneth Snelson replied on Sep. 28, 2012 @ 22:15 GMT
Dear Andeas,

What a great compliment --"Christmas eve feeling". I downloaded Ted Chiang's "Stories of Your Life and Others" from iBooks. Interesting reading.

Thanks for the recommendation -- and Merry Christmas!


Member Benjamin F. Dribus wrote on Sep. 24, 2012 @ 03:38 GMT
Dear Kenneth,

Vladimir Tamari was kind enough to mention your artistry over on my thread, so I came over to see what he meant. I have no idea how long it took you to create this, but it was well worth it!

By the way, I agree with the notion that physics ought to be based on simple physical principles (I like to describe things as much as possible in terms of cause and effect). However, I have found that choosing the physical principles to be simple rather than choosing the mathematics to be convenient can result in some very complicated mathematics! I noted the discussion in your thread above about trying to precisely quantify your model, and it looks to me as if the math involved might be a bit steep. No matter, though; the math ought to be whatever it has to be to get the job done.

On a lighter note, if a picture really is worth a thousand words, then I'm afraid you've exceeded the length limit for the contest! Take care,

Ben Dribus

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Joel Levinson wrote on Sep. 24, 2012 @ 14:15 GMT
Hi Kenneth,

What a surprise to see you authoring an article in this contest. I have known and admired your sculptures for many years and was delighted to see that you, like me, take our artistic/visual talents and our interest in science to deal with questioning the foundations of modern science. I have an article in this contest you might want to check out. It's brief and easy reading. I haven't been able to read and comment on many of the entered essays because I've been busy promoting my just released debut novel, The Reluctant Hunter, which tells the odyssey of a young aspiring architect with an interest in cosmology who is caught up in the Bosnian War. It has five stars on Amazon and Barnes and Noble and was voted Editor's Choice by my publisher.

But I was so excited to see your name here that I had to write even before I read your article. I will go there now. You've been one of my heroes -- your sculptures are exquisite.

Joel Levinson At this website you'll see articles I've written on architecture and other subjects.

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Juan Ramón González Álvarez wrote on Sep. 29, 2012 @ 18:08 GMT
Dear Kenneth,

Thank you for a very thought provoking essay with a welcome conclusion.

When being a student I was taught Bohr early model and subsequent atomic models based in Schrödinger quantum mechanics. The models left many question without answer and the teacher most common recommendation was "don't ask". In my essay, I criticize some aspects of quantum mechanics, which are often assumed but which are not valid.

In recent years, I have been approaching more and more to Bohm and DeBroglie ideas. Up to the point of develop my own formulation/interpretation of quantum mechanics, which I present in my FQXi forum (1356) and available here Positive Definite Phase Space Quantum Mechanics. I obtain a correction to the classical Hamiltonian which shares many properties with Bohm potential.

One interesting aspect of this correction term is that it can be splinted into two components: the electronic density, its Laplacian and its gradient. When we represent the density for an isolated atom we a scientific representation (see attached fig. density1) that resemble figures such as your 2 (of course yours is much more beatiful, what I provide below is raw black and white).

I think that you will find very interesting how spherical symmetry of isolated atoms is lost in molecules due to perturbations from the other atoms. For instance, the scientific representation (see attached density2) for ethene molecule reflects the inner spherical symmetry near nuclei and the highly non-spherical 'valence' shell.


attachments: density1.gif, density2.gif

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Anonymous wrote on Oct. 2, 2012 @ 18:48 GMT
Mr Kenneth Snelson

It was a pleasant surprise to read your article. Your quest for understanding the working (relative stable atomic structure) is exemplary. As you have properly put the question & result of Solvay Conferences of 1927 and 1930 in perspective in these words ' "real" atom models versus abstract non-visual mathematics in favour of Niels Bohr and his Copenhagen world view....

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Vijay Mohan Gupta wrote on Oct. 2, 2012 @ 18:58 GMT
Mr Kenneth Snelson



Please accept my gratitude for the enlightening essay.

Thanks & Best Regards,

Vijay Gupta

Proponent - Unary law

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 04:10 GMT
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is
was the quantity of people which gave you ratings. Then you have
of points. After it anyone give you
of points so you have
of points and
is the common quantity of the people which gave you ratings. At the same time you will have
of points. From here, if you want to be R2 > R1 there must be:
In other words if you want to increase rating of anyone you must give him more points
then the participant`s rating
was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process.

Sergey Fedosin

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MV Vasilyeva wrote on Oct. 6, 2012 @ 01:31 GMT
Mr. Snelson,

I very much admire your work. I always had a thing for art, geometry and physics, and your work beautifully reflects it all.

I too have a visual approach to physics, but what I found lately is that placing it all in 4D (all spatial dimensions), dispels paradoxes and explains things from small to large. Thus I have a hunch that your ideas can find mathematical expression in 4 dimensions, not 3 (+ time, of course, there is never escaping it :). Regardless of what you may think of my essay ( ), I think you will enjoy the 4D geometry and find the projections of 4D objects onto 3D fascinating in your work.

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Anonymous wrote on Oct. 7, 2012 @ 19:39 GMT
Dear Kenneth Snelson,

If we want to consider classical atomic models, we need to remember that electron has also very strong dipole magnetic moment - is tiny magnet. Placing reference frame in the electron, proton travels in this magnetic field - there appears Lorentz force which is far non-negligible: it makes circular orbits unstable. Such classical electron would like to fall to proton, but the Lorentz force bends the trajectory so finally it misses the proton and return to the initial distance:

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