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FQXi FORUM
May 23, 2019

CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: Topological Solitons of Ellipsoid Field - Particle Menagerie Correspondence by Jarek Duda [refresh]
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Author Jarek Duda wrote on Aug. 23, 2012 @ 11:50 GMT
Essay Abstract

Universal formalism of QFT operates on abstract entities like point particles, not asking about their spatial structures, dynamics behind processes like photon production. Topological soltions, vacuum analogues of Abrikosov vortices, bring hope to understand field configurations behind Feynman diagrams, by the way explaining many fundamental assumptions, like spin, charge or strangeness quantization by constructing them as topological charges. Skyrme has made popular this kind of approach to mesons and baryons, while perfect situation would be a single field which family of topological solitons corresponds to our whole particle menagerie and their behavior. Here is discussed such unifying all interactions simple attempt - practically by just expanding field of unit vectors of Faber's electron model, which can be seen as reformulation of electromagnetic field to enforce charge quantization, by a single degree of freedom corresponding to quantum phase: of rotations around this direction (vacuum dynamics changes from $S^2$ to SO(3)). This simple model also suggests intuitive answers to many fundamental questions of physics.

Author Bio

I am theoretical mathematician from Jagiellonian University (Poland), who, thanks to broad education, decided to focus on practical problems. My interest in information theory, besides Ph.D. in Computer Science, has lead me to Maximal Entropy Random Walk for Ph.D. thesis in Physics, suggesting there can be an objective, deterministic and local physics below quantum description. Previous interest in topology has pointed me to use mathematical analogues of particles: topological solitons. While searching for such complete model, a really simple candidate occurred to be extremely promising, also leading to intuitive understanding of many fundamental questions of physics.

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Frank Makinson wrote on Aug. 23, 2012 @ 18:58 GMT
Jarek,

Congratulations, this is the second essay in this contest that mentioned solitons, and your material is substantive. I would like to get a few individuals to recognize the presence of electromagnetic (EM) solitons. I had stated in an earlier essay comment that Einstein was in one of the lost generations that seemed not to be aware of solitons.

Groups of particles as a fluid are responsible for the recognition that solitons exist in the first place.

Top of page 6, "Thanks to lack of viscosity of EM field, instead of dispersing, such twist-like wave can travel undeformed through light years."

I appreciate you introducing the readers to the world of helical EM waves and putting the terms "electromagnetism and gravity" in your Conclusion title. On page 9 you stated, "Obtaining electromagnetism (+gravitomagnetism) is relatively simple, while fitting them to known properties (also de Broglie's clock) seems difficult, but could lead to reduction of required constants of standard model - effective in presented approach." You might be interested in the approach used in the two papers in the links below.

Electrifying Gravity

Newton's Quantum Coupling Constant

I used the two papers as references [6] and [7] in the paper in the link below. I note in the paper why Einstein, and others of his generation, did not consider EM as the force that creates the gravitational influence.

Helical Electromagnetic Gravity

I notice that the bottom illustrations on page 7 seems to be in a Mobius form. You do not mention a Mobius form in your essay. It appears you presented the page 7 illustrations in a Mobius form to fit the "twist" you used in the illustration on page 6.

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Jarek Duda replied on Aug. 23, 2012 @ 21:44 GMT
Frank,

Thank you for your comments. It is indeed really strange and sad that while solitons are widely used in many fields like superconductors, hydrodynamics, optics etc., people are well aware that they behave just like particles ... but still using them as just particle models seems to be an exotic topic.

I was on "Emergent quantum mechanics" congress last year (proceedings) and...

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Frank Makinson replied on Aug. 24, 2012 @ 00:59 GMT
Jarek,

I saw the illustrations and did a search for Möbius but failed to put in the umlaut.

The photonics folks use the term Orbital Angular Momentum (OAM) to describe optical frequency EM waves with a helical wavefront. The wavefront is no different than circular polarization which has been utilized many decades for radio communications. I am aware that optical frequency beams with OAM are used as optical tweezers.

Please note that the helical EM (HEM) structure of the one EM field provides the unique chirality feature that allows two fields of the same type at 180° to couple. Next to chirality, the angular phase position characteristics are very significant. I quote from my paper "Whether an electric or magnetic field, the angular phase position (APP) of the EM field vectors will be fixed relative to the HEM source orientation. In comparison to the simple pull characteristic of gravity, the APP is a HEM field trait that will cause a more complex interaction between objects with different APPs."

I notice your one Möbius illustration has a double twist. A "Möbius space" requires a 720° path to achieve a 360° rotation of a plane object in the space.

Do you realize that you are presenting material as to why ionizing radiation is so destructive to biological tissue, the rotational form of the energy field allows it to efficiently couple to DNA and other helical structures within the body.

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Ted Erikson wrote on Aug. 23, 2012 @ 20:04 GMT
Jarek:

Your mathematics is beyond me. I approach the problem from an emergent (growth) and panpsychistic (memory) view geometrically.

Perhaps my "model" of chaos deterministically could be handled as 1-D, 2-D, and 3-D probabilities. See: To Seek Unknown Shores

   http://fqxi.org/community/forum/topic/1409

Good Luck

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Jarek Duda replied on Aug. 23, 2012 @ 22:03 GMT
Ted,

What is nice about topological solitons is that you can get intuitive understanding without going into sophisticated mathematics - here you have Wikipedia article with nice animation of solition-antisoliton pair creation or annihilation. The field prefers to be in -1 or +1, but sometimes external conditions enforce it to charge these energy minimums - soliton is the least energetic way to do it. This minimal energy is its rest mass. Such topological constrain can be released while annihilation - releasing energy in form of non-topological waves: photons. If you want to understand more dimensional solitons, you can start with this simple demonstration.

Thanks,

Jarek

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Jeff Baugher wrote on Aug. 23, 2012 @ 22:50 GMT
Jarek,

Your essay will take quite a bit of time for me to digest. After viewing your ease with vector fields, I would like your comments on stress tensors (which may help me relate my own essay to solitons). If I were to model particles as instead holes traveling within a medium, would it be correct to model the stress tensor for the hole
or for the remaining medium
(where the "res" is for the residual medium and Omega is the non-stressed medium in the immediate neighborhood)?

Regards,

Jeff Baugher

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Jarek Duda replied on Aug. 24, 2012 @ 14:54 GMT
Jeff,

You can try to imagine yourself the behavior of this simple real symmetric tensor field preferring some set of different eigenvalues - its family of stable structures and their dynamics ... and compare it with known physics (please let me know if you find some essential discrepancy).

I don't think there is a simple correspondence between this real symmetric tensor field and energy-momentum tensor (much closer is stress tensor): very different values appear in them, the second is effective while the first is intended to be much more fundamental, energy density is directly written in the second while in the first you need to use potential energy for that etc.

The kinetic term in Lagrangian is probably also quite different, like -Rab Rab of prof. Faber ... but it should lead to gravitomagnetism on more effective level, which is good approximation of GRT (up to our measurement possibilities).

The question of choosing both kinetic and potential term is extremely subtle here - I would be grateful for some suggestions how to do it right - I think similarly as in the Faber's model, but include the difference between axes, making e.g. that energy density of electric field of electron, muon and taon charge are a bit different.

Thanks,

Jarek

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Edwin Eugene Klingman wrote on Aug. 24, 2012 @ 00:42 GMT
Dear Jarek Duda,

I found your essay quite interesting. I too believe that topological soliton-like structures are the best approach to particle physics, and I agree that focus on a de Broglie 'clock' is appropriate, and there is a need to explain Zitterbewegung.

I found your figure 5 on page 6 also interesting and will give that more thought. Of most importance to me was your mention of gravito-magnetism on your last page. With this in mind, I invite you to read my essay, The Nature of the Wave Function, which does not deal with particle creation but with the quantum mechanics of existing particles.

Good luck in the contest.

Edwin Eugene Klingman

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Jarek Duda replied on Aug. 24, 2012 @ 16:11 GMT
Dear Edwin,

Thank you for your comments and interesting essay. We know that particles are localized field configurations, what is also definition of soliton and e.g. charge quantization leaves no doubt that we should use the topological ones - I don't think the question is if we should use topological solitons to mode particles, but how.

Sadly very few people search for such finally objective, local and deterministic physics from which QM would emerge on more effective level - e.g. while most of speakers in recent Congress of Emergent Quantum Mechanics was still focused on double-slit experiment (like thanks of recently weakly measured from the first page of your essay - it was the second achievement emphasized there after Couder), very few is searching for this physics below quantum description.

There are important questions how this de Broglie's clock should look like. For example are these produced waves only local (vanishing), or maybe single electron in the universe would make the quantum phase rotates everywhere ... the second option seems nonintuitive, but in Schroedinger's picture this single electron would also enforce quantum phase of the whole universe to rotate. Fortunately electron is created together with positron, which should compensate rotation caused be electron to nearly zero.

Thank you for the wishes, but I'm fully aware that solitons are not a popular subject and good luck won't change it - I'm here for a discussion rather.

As you know where to search for real understanding of particles, I wish you good luck with finding the proper one ...

Jarek

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Israel Perez wrote on Aug. 29, 2012 @ 07:44 GMT
Hi Jarek

Very interesting work, I liked it very much. I must confess that I am not an expert in soliton theory though I understand the fundamentals and the virtues of solitons as an intuitive picture at the microscopic level. I have read your previous comments to other contestants and I am aware that not many physicists embrace solitons as an alternative formulation to describe the...

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Jarek Duda replied on Aug. 29, 2012 @ 08:47 GMT
Hi Israel,

I think the problem with appreciating solitons is the feeling that models should be derived from e.g. the standard model, like in the most popular: Skyrme approach. The philosophy I present is just opposite: accept that modern physics has grown by building the believe in the previous assumptions and then building new ones on the top while something occurs to be wrong/missing ......

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Israel Perez wrote on Aug. 29, 2012 @ 21:53 GMT
Hi Jarek



Thanks for your reply.

You: "I think the problem with appreciating solitons..." I agree with this. I have promoted the replacement of particle by solitons though many physicists instead have the notion of quasi-particle, and therefore this labeling demote them to a second rank below a particle. I recognize the potentiality of solitons as a fundamental conception in...

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Jarek Duda replied on Aug. 30, 2012 @ 14:08 GMT
Hi Israel,

Indeed the soliton approach is still seen as an exotic concept by particle physicists. They are satisfied with QFT description, but it is only a general mathematical tool to work on completely abstract entities (like algebra) - not asking what particles really are. Skyrme model is still alive for short range interaction of baryons, but its specialists emphasize that it is...

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Israel Perez replied on Aug. 30, 2012 @ 21:51 GMT
Hi Jarek

Thanks for your the links and the article, I found them very interesting. I was unaware of the discovery of the voyagers, definitely they will change our perception of the universe. In relation to the aether I assume that you refer to the old aether notion that Lorentz supported. In 1951 Dirac (and many others later, such as Bell, etc.) speculated that the aether could be reconsidered in physics. In my essay I argue in favor of a preferred frame of reference (the aether) and I provide some arguments to elucidate some misunderstandings around this concept. I would be glad if you could make some comments about my work.

I appreciate your comments and I wish you the best

Israel

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Jarek Duda replied on Sep. 1, 2012 @ 21:36 GMT
Hi Israel,

Yes, the discovery of Voyager is very interesting and should motivate to think about these magnetic structures, like if they could remain such complexity in standard electrodynamics. Anyway, I think the corona heating problem should bring much more attention - showing that we don't understand something looking very fundamentally: just dynamics of EM field with charges.

About aether and your essay, Lorentz invariance seems really natural assumption in field theories - I honestly don't see a need for some more preferred frame of reference.

Generally I really appreciate philosophical disputes, but there was more than a century of similar ones and they hasn't changed much ... like most of speakers on recent "Emergent Quantum Mechanics" speaking about double slit ... I think it is enough of general discussions - if we want to move toward a better understanding, we need to propose concrete alternative, concrete models ... e.g. if you agree that we should search for field configurations behind particles (soltions), try to work in this direction. Having really understood microscopic physics, astronomical should appear naturally.

Cheers,

Jarek

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Sergey G Fedosin wrote on Sep. 18, 2012 @ 16:41 GMT
Dear Jarek,

Of course mathematics is a good tool for describing of phenomena with the help of formulas. But the problem is with the real models of particles. When the model is wrong mathematics can not help. See substantial model of electron in § 14 of the book: The physical theories and infinite nesting of matter. Perm, 2009-2012, 858 p. ISBN 978-5-9901951-1-0. By the way the problem of electron spin is explained in the book.

Sergey Fedosin

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Jarek Duda replied on Sep. 18, 2012 @ 19:02 GMT
Dear Sergey,

I don't understand your point - if you are implying that my model is wrong, I would be really grateful if you point me some discrepancy with the reality?

Maxwell's equations allow for any charge, while we know that they appear only in integer multiplicities of elementary charge - we need to reformulate/improve Maxwell's equations to have this quantization already deeply written - it was done by prof. Faber: http://iopscience.iop.org/1742-6596/361/1/012022

Now charges can appear only in portions: particles (and have mass) ... but only electron-like.

What I propose is its simple expansion to get all particles as we know - and I'm open to other such expansions.

Jarek

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Sergey G Fedosin wrote on Sep. 26, 2012 @ 12:33 GMT
Dear Jarek,

In the Theory of Infinite Hierarchical Nesting of Matter (my Essay) neutron stars at star level of matter are analogue of nucleons at particle level of matter. In a neutron star a lot of protons and electrons. But for the star level of matter there is stellar charge as a maximum charge of a star, see Stellar constants . In the average we can say that charge of star objects composed of neutron star must be integer in units of stellar charge. But in reality the charge of one star is never equal to charge of another star, the coincidence has small probability. The same is for the charge of a proton which consists of charges of numerous particles in substance of the proton. So I want say that elementary charge of electron, proton and other particle is approximation, in reality the particles have somewhat different charges.

Sergey Fedosin

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Jarek Duda replied on Sep. 26, 2012 @ 20:11 GMT
But the particles have charge being integer multiplicity of elementary charge (or 1/3) - this quantization is the most essential fact to understand particles. Quantization itself makes charges need to come in portions - became particles.

Before nesting further particles in electron, start with improving electromagnetism to have quantization written (e.g. like prof. Faber) ...

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Ed Unverricht wrote on Oct. 1, 2012 @ 18:18 GMT
Hi Jarek,

Just read and loved your essay "... there are three basic families of soltions, simplest charge will topologically need to have spin, ... While dynamics of rotations of the original axis will correspond to electromagnetic interaction ... the additional perpendicular rotation corresponds to quantum phase, enforced by the soliton to constantly rotate as for de Broglie's clock of particle."

I liked your drawings and if you ever consider trying to animate them in real time, please send me a note.

You can see some examples of my animations in the links at my essay #1306.

Regards, Ed

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Jarek Duda replied on Oct. 2, 2012 @ 01:30 GMT
Hi Ed,

Thanks for the comforting comment, especially that I was counting on a real discussion, while I mostly got posts from people seeming not even to look at the essay but only wanting to advertise own ... and mostly interested only at fighting with special relativity ...

What you call the need of animations, I would call the need for numerical simulations - I would like to work on it as soon I will have some time, but it is difficult question how to precisely choose both kinetic and potential term of the Lagrangian.

I have looked at your paper and nice animation. As you are interested at classical atomic models, you should look at: http://en.wikipedia.org/wiki/Free-fall_atomic_model

You want to see particles as vortices - seems similar to what I'm writing, but standard vortices don't enforce quantization e.g. of the charge - for that you need to use topological vortices/solitons, like Abrikosov's.

Regards,

Jarek

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Member Benjamin F. Dribus wrote on Oct. 2, 2012 @ 04:26 GMT
Dear Jarek,

This is a fascinating paper; the ideas involved are very pleasing aesthetically. It's very different from my own ideas about fundamental physics, but I wouldn't be at all disappointed if your ideas turned out to be right. A few remarks and questions.

1. Do Hopf fibrations play any role here? Adding an S^1 degree of freedom to S^2 immediately suggests this.

2. Have you looked at the essays by Torsten Asselmeyer-Maluga and Jerzy Krol? They discuss another (also aesthetically pleasing) "pure manifold" idea about fundamental physics: exotic smoothness structures.

3. Given your information theory background, you might find my essay interesting, although as I said, the ideas are much different.

Thanks for the great read! Take care,

Ben Dribus

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Jarek Duda replied on Oct. 2, 2012 @ 09:12 GMT
Dear Ben,

Thank you for your comments. I have looked at your brave essay about rejecting most of assumptions and starting with new ones. Personally I prefer approach of making small steps - basing and comparing to known physics, and really deeply understanding their consequences.

For example we know that electromagnetism is generally right, but it disagrees with nature by allowing for any charges, while the nature allows only for integer multiplicities of elementary charge - correcting/reformulating electromagnetism to have included this fundamental principle was made by prof. Faber in natural way - make that Gaussian law counts topological charge (Hopf number). This improvement itself makes charges appear in portions - became particles. But there is something missing - some expansion is needed, so I've started with experimenting with adding single dof - and using just kind of anisotropic stress tensor seems to fit perfectly to recreate our particle menagerie and their dynamics...

About e.g. Hopf fibrations, prof. Faber uses quaternions in his representation and told me he experimented with octonions. I just assume a simple field and try to understand consequences to topological structures it can create and their dynamics.

I've looked at Torsten Asselmeyer-Maluga and Jerzy Krol essays, but similarly to yours, I see them too abstract - there is a lot of a general talk these days, but what we need to fight with the orthodox physics, is a concrete working microscopic model which can complement the Standard Model.

Thanks,

Jarek

ps. I see causality is one of your rejected assumptions - there is extremely powerful Walborn's version of delayed quantum erasure you might be interested ...

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Member Benjamin F. Dribus replied on Oct. 2, 2012 @ 16:09 GMT
Dear Jarek,

Thanks for the link... I do find things like this interesting. There were a lot of popular articles last year about a psychology experiment that supposedly demonstrated precognition; interesting, but I never took it seriously. I did repeat the experiment myself for fun, but of course got the expected answer.

Just to clarify: I certainly do NOT reject causality; rather, my entire approach (causal metric hypothesis) is based on taking causality to be fundamental. I do reject manifolds as fundamental, and there are certainly good physical reasons for doubting the infinite divisibility of space, but the principle reason is because they possess properties that seem physically irrelevant or even absurd (see Banach-Tarski paradox, for instance).

My view is that the physical ideas should be simple and well-motivated (e.g., cause and effect), and the mathematics should be whatever it has to be to get the job done. I believe many scientists view continuum manifolds as "natural" out of habit because the structures involved are often mathematically convenient enough to permit nice, exact, combinatorial-type calculations. I think this is partly "anthropocentric:" our brains "like" manifolds, but automatically protest at a causal structure with even a few thousand elements, even though examples of the latter are all over the place.

Oh well... I wouldn't much mind if I were wrong about manifolds: most of my mathematical work deals with them! Your model will be wonderful if it works out. Take care,

Ben

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Jarek Duda replied on Oct. 2, 2012 @ 21:51 GMT
Dear Ben,

About causality, what I believe in is the Lagrangian mechanics we use from QFT to GRT. It gives very clear time symmetric picture, for example through action optimization formulation: the present is the equilibrium between past and future - both are equally important.

We have natural intuition of time asymmetry, there is no doubt in the 2nd law, but the fundamental equations are time/CPT symmetric. It means the asymmetry is a property of the specific solution we live in: relatively close to Big Bang having everything in one place - low entropy and so creating entropy gradient. It also started reason-result chain leading to our intuition.

Much better controlled situation (than precognition) to search for this symmetry is e.g. quantum erasure, especially in configuration we can later control the earlier outcome I've linked.

And I'm not saying that your approach is wrong, but that you should make it more predictive for comparison with the reality.

Thanks,

Jarek

ps. Here is great thought experiment to het intuition about this time-symmetry: GRT doesn't forbid nonorientable spacetime: with time-reversing loop ...

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Sergey G Fedosin wrote on Oct. 2, 2012 @ 10:23 GMT
After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.

Cood luck.

Sergey Fedosin

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Jarek Duda replied on Oct. 2, 2012 @ 11:41 GMT
Please feel free to ask question if you don't understand something. I would be also greatful for remarks related to my essay (in opposite to your previous one).

Jarek

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 06:27 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
and
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:
or
or
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. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Jarek Duda wrote on Oct. 4, 2012 @ 07:06 GMT
Sergey,

I'm not here ... I'm not doing science for 0-10 score, but to find a better understanding. I'm here for discussion - counting e.g. for a single constructing counter-argument to my reflections ...

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Anonymous wrote on Oct. 6, 2012 @ 00:44 GMT
Dear Jarek

Congratulations for your essay - I am proud that I alerted you to this fqxi contest. While I only understand it qualitatively, I can see that you have excellent grasp of your ideas and have presented them consistently in the text, and beautifully in the illustrations.

As I mentioned in our previous discussions, I agree with your idea about a particle as a soliton pushing...

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attachments: 5_Particledoubleslit_.jpeg

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Inger Stjernqvist wrote on Jan. 31, 2013 @ 23:00 GMT
Dear Jarek

Excuse me for throwing in some yeast after the bread is long since baked! I have only recently read your essay. It is thought-provoking and in a peculiar way both visionary and basic. Most interesting. And - yes! - intuitively very attractive.

I like the way you show a seemingly non-violent way to unite the theories of micro- and macro cosmos. I also like the way you go back to basic, not least to de Broigle, whose particle-wave duality was far more direkt than it (too soon?) became in the hands of Schrödinger, Heisenberg and Bohr.

This far I have no clever questions to ask, but for sure I look forward to read your other publications on this subject. Until then, thank you for good reading!

Best regards

Inger Stjernqvist

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Jarek replied on Feb. 1, 2013 @ 07:44 GMT
Dear Inger,

Thank you for the comforting comment. I deeply believe we should try to get below abstract models of QFT - search for internal structure and dynamics of particles: localized constructs of the field (solitons). Just repairing Maxwell's equations such that Gauss law no longer allows for any real charge, but only integer multiplicities of elementary ones as in the nature - e.g. by making that Gauss law counts topological charge like in Faber's approach. These elementary charges already became primitive electron models - now we need to expand the model to get all the particles and ellipsoid field is not only the only such expansion I could find, but surprisingly, while being extremely simple, it seems already qualitatively extremely promising - giving intuitive answers to many fundamental problems of physics ... as the right model should do.

However, while finding by simulations the proper form and constants of both potential and kinetic term of Lagrangian requires huge amount of work, it seems nobody is interested in understanding internal structure and dynamics of particles. And so I have to leave it for now, I'm starting information theory postdoc. But I would always gladly discuss about soliton particle model approaches.

Best regards,

Jarek Duda

http://th.if.uj.edu.pl/~dudaj/

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