# Similarity between particle physics and macroscopic quantum phenomena like fluxons?

## Recommended Posts

33 minutes ago, Prof Reza Sanaye said:

So therefore , let us not limit them into phase spaces . . . .

I didn't say they were so limited.

I said or meant I think that the term topological solitons refers to the same amthematical structure in abstract spaces (eg phase space)

• Replies 66
• Created

#### Posted Images

1 minute ago, studiot said:

I didn't say they were so limited.

I said or meant I think that the term topological solitons refers to the same amthematical structure in abstract spaces (eg phase space)

Topos can be solidly filled out with matter . . .

##### Share on other sites

3 hours ago, Prof Reza Sanaye said:

Topos can be solidly filled out with matter . . .

Topology is primarily concerned with shape and connectivity.

So yes, if the space you are working in has the requisite properties then you can 'fill' a shape in it with matter.

But if the shape you are working with is say a surface in an Entropy / Temperature plot, or an Energy Temperature plot how would you accomplish this feat ?

So to take my example of a hydraulic jump,

The shape of the energy density v distance along flowbed is indeed a physical step function in the water surface that stands still.

However for the equivalent phenomenon in a gas whilst it does indeed demonstrate the abstract step function neither stands still nor exhibits such a physical step function.
I am, of course, referring to a shock wave.

But the serious point I am making is that these abstractions are just mathematical models of the physical and only useful if they demonstrate the ability to predict something useful.

@Duda Jarek appears to me to want to model material particles with these mathematical abstractions so my question to Duda is

What properties can successfully be predicted by these models ?

Edited by studiot
##### Share on other sites

8 hours ago, studiot said:

What properties can successfully be predicted by these models ?

Sine-Gordon: just phi_tt = phi_xx - sin(phi) has already massive particles with quantized topological number, pair creation/annihilation, and entire special relativity: Lorentz contraction, time dilation, SR mass/momentum scaling ... studying this looking trivial toymodel is the best way I know to really feel the special relativity.

Going to higher dimensions, here is example of observing long-range F~1/D force for topological solitons in liquid crystal: https://pubs.rsc.org/en/content/articlelanding/2019/sm/c9sm01710k#!divAbstract

We can choose dedicated Lagrangian to get exactly Coulomb interaction for them with included charge quantization as topological - e.g. Faber's way ( https://iopscience.iop.org/article/10.1088/1742-6596/361/1/012022/pdf ) : define EM field as curvature of some deeper vector field, this way Gauss law counts winding number - topological charge.

But the goal is getting all the particles/interactions with dedicated field and Lagrangian - I have a framework, a sketch of Lagrangian, but getting the details + simulations was too difficult for me.

Here is the sketch of this general framework again I would gladly discuss - for superfluid biaxial nematic field - of 3 distinguished axes:

1) we get 3 hedgehog realizations of one of 3 axes - kind of 3 leptons (the same charge, different energy/mass), with magnetic dipole due to the hairy ball theorem, Faber's approach gives Coulomb interaction for them,

2) the simplest vortex loop resembles neutrino: stable - very difficult to interact with, 3 types: along one of 3 axes, can "oscillate" between them by internal rotation, are produced in beta decay,

3) loop with internal twist (hopfions?) might correspond to mesons, number of twists nicely fits strangeness - agrees with decay of mesons, strange baryons ( https://en.wikipedia.org/wiki/List_of_baryons ),

4) if another vortex goes through such loop, it nicely resembles baryons, interaction between its vortices creates charge inside (diagram below). Proton just closes this charge, while neutron has to compensate it - what is costly, explaining why neutron is heavier than proton (also quark-like fractional charge distribution),

5) combining baryons form nuclei as various size knots - binding them against Coulomb repulsion, including halo neutrons binded in much larger distance ( https://en.wikipedia.org/wiki/Halo_nucleus )

##### Share on other sites

I give up.

I have tried to discuss your points, but all you do is repeat them and ignore any comments.

There has just been a longish thread about what small particles might look like and the conclusion was that particles don't 'look like' their plots in abstact space any more than those pictures you keep reproducing.

Edited by studiot
##### Share on other sites

50 minutes ago, studiot said:

abstact space

I don't understand what do you mean by abstract space? E.g. sine-Gordon has mechanical realization as in the video, interaction between topological solitons is realized e.g. between fluxons in superconductors, long-range interaction is realized in liquid crystals (e.g. https://pubs.rsc.org/en/content/articlelanding/2019/sm/c9sm01710k#!divAbstract ).

This is about finding field and Lagrangian to get similarity with particles and fields - also the very real EM field.

About repairing this very real EM field: that Gauss law in nature only returns integer charges ... what is done here by interpreting charge as topological, with Gauss-Bonnet theorem as Gauss law ... then the simplest nontrivial charge becomes a simple model of electron.

This "biaxial nematic field" can be realized with a real symmetric tensor, exactly as stress-energy tensor in general relativity, by just using Higgs-like potential for it: preferring topologically nontrivial vacuum e.g. S^2, SO(3). But it is safer to be agnostic about its realization for this moment - first get the particles rights, then try to interpret the field e.g. with GR stress-energy tensor or some superfluid vacuum.

Edited by Duda Jarek
##### Share on other sites

2 hours ago, Duda Jarek said:

I don't understand what do you mean by abstract space? E.g. sine-Gordon has mechanical realization as in the video, interaction between topological solitons is realized e.g. between fluxons in superconductors,

........

This is about finding field and Lagrangian to get similarity with particles and fields - also the very real EM field.

If you didn't understand what an abstract space is why didn't you ask before  ?

Particularly as they were introduced by Lagrange, whom you mention.

Do you know what Lagrange's 'generalised coordinates' are ?

Lagrange's generalised coordinates were probably the first recognition of abstract spaces, I have already given an example of a plot of entropy v temperature.

What exactly do you think a fluxon is ?

Hint a fluxon is measured as approximately 2  gauss/cm2  (originally in CGS)  or  2  tesla/m2  (SI)

##### Share on other sites

13 hours ago, studiot said:

What properties can successfully be predicted by these models ?

I'm going to insist on this point just for a little while. I'm not completely sure that I'm faithfully echoing @studiot's concerns here, but I think my concerns and his at least partially overlap.

It is not enough to build analogical models of individual particles with every particle popping up in the model as an independent character in a play that could or could not be there. Kaons, for example, have known lifetimes, decay modes, etc., that must be accounted for. We know that kaons, and hyperons, and nucleons, are made of quarks. Where are these quarks, and the hadrons they give rise to in their decay modes?

These topological charges should have a multiplet structure to be fit into the known multiplets of the standard model, for example,

$\left(\begin{array}{c} e\\ \nu_{e}\\ u\\ d \end{array}\right)$

$\left(\begin{array}{c} \mu\\ \nu_{\mu}\\ c\\ s \end{array}\right)$

$\left(\begin{array}{c} \tau\\ \nu_{\tau}\\ t\\ b \end{array}\right)$

There are also tight constraints on chiralities for these leptons, so that right-handed leptons do not couple to the weak force. IOW: The weak force violates parity maximally. Then there's the question of the mixing angles: eigenstates of mass are not eigenstates of the gauge charge operators. Where are all these constrictions?

Don't get me wrong; I deeply sympathise with these topological efforts. The part that I'm missing is the one that makes them try to replicate more closely the known features of the SM and QM.

It's all a little bit as if an archaeologist unearthed a couple of broken columns under the ground of old Israel and proclaimed, "well I think I've found Samson!"

We're never short of people who make such claims.

Edited by joigus
##### Share on other sites

@joigus, these are matters of interpretation, e.g. in perturbative QED interpretation Coulomb interaction is performed with photon exchange ...

Should we really imagine some infinite sequence of exchanged photons e.g. between proton and electron in hydrogen atom?

Or maybe should we remind that it is perturbtaive approximation - like expanding into Taylor series and representing terms of this series - where Feynman diagrams mathematically came from.

In liquid crystal we get Coulomb-like long range interaction because the further e.g. opposite topological charges are, the larger total energy (stress) of the entire field is, e.g. with V(r) ~ 1/r behavior for Coulomb:

In perturbative approximation you could get Taylor series and imagine it as photon exchanges, but this is just a different interpretation.

So it is safer not to focus on interpretations first, but directly on particle behaviors like Coulomb interaction, decay modes - on agreement there first, then search for correspondence with perturbative QFT approximation of the Standard Model.

What particle behavior you think is wrong in the framework I have presented? It also e.g. gets fractional charges in neutron ("quarks") - explaining why it is heavier than proton. Its topologically nontrivial vacuum requires Higgs-like potential corresponding to mass of particles - it allows to deform electromagnetism into other interactions in the center of particles - to avoid the infinite energy of electric charge issue.

Edited by Duda Jarek
##### Share on other sites

Whoops, sorry.

An important error crept into my last post.

2 hours ago, studiot said:

Hint a fluxon is measured as approximately 2  gauss/cm2  (originally in CGS)  or  2  tesla/m2  (SI)

is measured as approximately 2 x 10-7  gauss - cm2  (originally in CGS)  or  2 x10-15  tesla - m2  (SI)

ie not per m2.
I was focused on getting the superscript 2, and the slash slipped in from habit.

1 hour ago, joigus said:

It's all a little bit as if an archaeologist unearthed a couple of broken columns under the ground of old Israel and proclaimed, "well I think I've found Samson!"

🙂

+1

48 minutes ago, Duda Jarek said:

It also e.g. gets fractional charges in neutron

What do you mean by this ?

Edited by studiot
##### Share on other sites

55 minutes ago, studiot said:

What do you mean by this ?

If you look at the big framework diagram above, for many reasons baryons resemble simplest knots: one vortex around another, proton/neutron should be such lowest energy pairs ... then they can form various size knots: nuclei (binded against Coulomb), including halo neutrons ( https://en.wikipedia.org/wiki/Halo_nucleus ) stably binded in distance a few times larger than standard nuclear force.

The external vortex loop enforces partial hedgehog-like configuration in the center vortex - proton can just enclose it to entire hedgehog, what means +1 topological charge - corresponding to elementary e electric.

But neutron has to compensate this partial hedgehog/charge to zero, what requires increased size and so larger energy/mass ... while asymptotically we have charge quantization (as topological), locally there can be such partial configuration/charge like quarks, but it comes with additional energy.

Here are a few sources also claiming such charge distribution for neutron: positive core, negative shellhttps://inspirehep.net/literature/1377841http://www.actaphys.uj.edu.pl/fulltext?series=Reg&vol=30&page=119 , http://www.phys.utk.edu/neutron-summer-school/lectures/greene.pdf  :

Edited by Duda Jarek
##### Share on other sites

Any perturbation of effect on what is normally called "matter" has to have  back"wave  modified repercussion as an integral part of its function(ing). Atoms under consideration to process imprinting formats of any kind of wave , say solitons or magnetons in this case , ought to be able to revert differing retracting-extending forces over to the lattice created only as a local manifold for emanating vortices in complex line bundles on the general  Riemannian manifold(s) . If levels of flux are (to be observed) to die away in units disregarding temporal dimensionality , as for example gauss/cm2  (originally in CGS)  or  2  tesla/m2  (SI) , then it would be real interesting to  study the composition of two wave velocities v and u in the cases when:  v<c and u = c;  when  v>c and u>c;  when  v>c and u = ∞;  when  v = ∞ and u = ∞. What happens with some of the basic  laws of physics in each of these cases? Are  we to simply dismiss the present symbolization of true Toposes in favor of radically revolutionary mathematical  syntaxes ?

Can we , then ,  not make changes mathematically take place but topologically/physically not appear at all ?

Have interlocutors in this present discussion thought of these broader schemata of the way (wave) physics is dealt with ?

##### Share on other sites

33 minutes ago, Duda Jarek said:

But neutron has to compensate this partial hedgehog/charge to zero, what requires increased size and so larger energy/mass

Thank you for confirming we are talking about an overall electrically neutral neutron and proposing a structure that accomplishes this.

32 minutes ago, Duda Jarek said:

Here are a few sources also claiming such charge distribution for neutron: positive core, negative shell

Seems to me, however, that the jusry is still out on the structure, although we are presumably all agreed on the 3 quarks ?

Quote

Wikipedia

### Structure and geometry of charge distribution

An article published in 2007 featuring a model-independent analysis concluded that the neutron has a negatively charged exterior, a positively charged middle, and a negative core.[72] In a simplified classical view, the negative "skin" of the neutron assists it to be attracted to the protons with which it interacts in the nucleus; but the main attraction between neutrons and protons is via the nuclear force, which does not involve electric charge.

The simplified classical view of the neutron's charge distribution also "explains" the fact that the neutron magnetic dipole points in the opposite direction from its spin angular momentum vector (as compared to the proton). This gives the neutron, in effect, a magnetic moment which resembles a negatively charged particle. This can be reconciled classically with a neutral neutron composed of a charge distribution in which the negative sub-parts of the neutron have a larger average radius of distribution, and therefore contribute more to the particle's magnetic dipole moment, than do the positive parts that are, on average, nearer the core.

ref 72:
Miller, G.A. (2007). "Charge Densities of the Neutron and Proton". Physical Review Letters. 99 (11): 112001. arXiv:0705.2409. Bibcode:2007PhRvL..99k2001M.

38 minutes ago, Duda Jarek said:

while asymptotically we have charge quantization (as topological), locally there can be such partial configuration/charge like quarks, but it comes with additional energy.

Seems to me that all your information is of a geometrical nature, not a Topological one.  ?
For instance you talk of "increased size" which is definitly a geometrical attribute, not a topological one.

Finally you still have not stated what you understand a fluxon to be.

Do you regard it as a particle ?

If so why does it not have the appropriate dimensions ?  (using my coreected definition, sorry about that error).

39 minutes ago, Prof Reza Sanaye said:

as for example gauss/cm2  (originally in CGS)  or  2  tesla/m2  (SI)

Please note I misquoted the units and corrected them in my subsequent post.

is measured as approximately 2 x 10-7  gauss - cm2  (originally in CGS)  or  2 x10-15  tesla - m2  (SI)"

Further,

I don't see what is 'dying away' in  a fluxon ?

##### Share on other sites

48 minutes ago, Prof Reza Sanaye said:

study the composition of two wave velocities v and u in the cases when:  v<c and u = c;  when  v>c and u>c;  when  v>c and u = ∞;  when  v = ∞ and u = ∞.

I again recommend sine-Gordon model to understand massive particles - containing rest energy which can be released in annihilation, also working as inertial mass due to Lorentz invariance ... and such particles can only approach the propagation speed c, at cost of energy growing to infinity, it cannot exceed this velocity.

8 minutes ago, studiot said:

Seems to me, however, that the jusry is still out on the structure, although we are presumably all agreed on the 3 quarks ?

It is safer to directly target experimental properties like charge distribution - which is also suggested in this"biaxial nematic field" ... then interpret fractional charges as quarks, interaction between them as gluons and pions.

Another big hint is deuteron - we know it has large electric qadrupole moment ( https://en.wikipedia.org/wiki/Deuterium#Magnetic_and_electric_multipoles ) - hard to imagine for just proton+neutron, but suggested in the discussed model: neutron needs charge, so proton shares part of its charge - leading to savings as binding energy, and observed quadrupole moment.

16 minutes ago, studiot said:

Topological charge is the winding number for function f:S->S from e.g. sphere around some point, into e.g. sphere of vectors

Winding number of this f:S->S functions can be obtained by integrating over Jacobian, which is curvature of this vector field - getting Gauss law as Gauss-Bonnet theorem, with built in charge quantization as topological:

##### Share on other sites

quote from duda jarek

"I again recommend sine-Gordon model to understand massive particles - containing rest energy which can be released in annihilation, also working as inertial mass due to Lorentz invariance ... and such particles can only approach the propagation speed c, at cost of energy growing to infinity, it cannot exceed this velocity." [ End of Quote]

Many thanks Duda for this hint......... I shall soon start going this way in order to see what types of outcome will possibly manifest . . . .

quote from studiot :

"what is 'dying away' in  a fluxon ?" [End of Quote]

I was talking there of the dissipation of kinetic energy. . . . . . ..

##### Share on other sites

13 minutes ago, Prof Reza Sanaye said:

quote from studiot :

"what is 'dying away' in  a fluxon ?" [End of Quote]

I was talking there of the dissipation of kinetic energy.

So what is kinetic energy in a fluxon ?

28 minutes ago, Duda Jarek said:

It is safer to directly target experimental properties like charge distribution - which is also suggested in this"biaxial nematic field" ... then interpret fractional charges as quarks, interaction between them as gluons and pions.

Thank you for an answers to one of my questions and this response to a comment.
You did not comment on my question as to whether you agree that one neutron contains' 3 quarks  ?

You have yet to answer my simple question as to what you think a fluxon is  ?

Further I have no idea what the pretty blue arrows at the bottom of your last post in repeated several times now are meant to represent.

Some pictures may indeed be worth 1000 words, but most pictures, including yours need at least some words for explanation.

##### Share on other sites

quote from studiot :

what is kinetic energy in a fluxon ? "

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

The total energy at its originary point to surmount the locally barrier-acting manifold and (thus) overcome prospective dissipative effects ( you know  , they have to "climb" barriers )..   ..     ...    ...

Edited by Prof Reza Sanaye
##### Share on other sites

58 minutes ago, Prof Reza Sanaye said:

quote from studiot :

what is kinetic energy in a fluxon ? "

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

The total energy at its originary point to surmount the locally barrier-acting manifold and (thus) overcome prospective dissipative effects ( you know  , they have to "climb" barriers )..   ..     ...    ...

Seems a meaningless statement to me since, as a primary unit of energy, a fluxon can surely neither gain nor loose kinetic energy.

##### Share on other sites

Just now, studiot said:

Seems a meaningless statement to me since, as a primary unit of energy, a fluxon can surely neither gain nor loose kinetic energy.

It is NOT a Primary Unit of Energy(PUE).

##### Share on other sites

59 minutes ago, Prof Reza Sanaye said:

It is NOT a Primary Unit of Energy(PUE).

So what is it then and why does it have the dimensions of energy ?

##### Share on other sites

26 minutes ago, studiot said:

So what is it then and why does it have the dimensions of energy ?

Very Dear Studiot ;

It is, in fact, flux. To be even more precise , it is electromagnetic flux.

The negative flux only equals the positive flux in magnitude, so that the net flow or the cumulative flux is null. If a net charge is present inside a closed surface, the overall surface flow is proportional to the load used, positive if positive, negative if negative.

Electric flux has SI units of volt metres (V m), or, equivalently, newton metres squared per coulomb (N m2 C1). Thus, the SI base units of electric flux are kg·m3·s3·A1. The dimension can however change when you are actually talking of topological fluxion on manifold(s). You may , for example , go from Dimension-3 to Dimension-2 or even to 1. One should not expect the dimensions all remain the same with these changes. You can even do the reverse and go to higher dimensions , like D-4. I would , however , not introduced this ideatic entitiy into modern day physics. I do agree with you that objective utility must be the criterion. What is the purpose of inviting in even yet more conceptualisations when we have too many of them in physics of electricity ??  !!

Seems some PhD theses have to be written some places for filling out positions in some "other" places.

I do not agree with the over"mathematisation in general , either.

Where are we going with this many sub-sub-branches of physics ( and science in general ) and with so much of theorisationary  Mathesis  ??   !!

##### Share on other sites

10 hours ago, studiot said:

First and foremost fluxions are something Newton invented to do with calculus.

Well spotted. Precision in terminology is essential in science.

##### Share on other sites

20 minutes ago, joigus said:

Now, if you don't mind, I would like to discuss some of the finer points @Duda Jarek is making. We may disagree about some ways in which to tackle this question, but I want to learn more about his approach.

Sure the basic one is why I haven't moved it forward with simulations ... because the details are tougher than it sounds.

To make Gauss law count winding number/topological charge as in Faber's approach, we need to define EM field as curvature of such SO(3) biaxial nematic field, then use EM energy density: as sum of squares of these curvatures.

Below is such approach, using representation as 3x3 real symmetric tensor, with Higgs-like potential: preferring some set of 3 eigenvalues - shape of nematic in SO(3) vacuum.

One difficulty is translating such energy density from rotation matrix O to the actual tensor M (quite subtle). Second is getting Euler-Lagrange equation (I wasn't able to get), or work on ansatz avoiding them. Third is choosing details of this Higgs-like potential, in fact containing weak and strong interactions. It was too tough for me and I gave up, hoping to find help.

##### Share on other sites

A request to whoever split this thread

I have just spent quite some time setting up and plotting plotting a time independent (ie standing) solution to the sineGordon equation to post here for discussion.

I also had comments to make on the understanding on the Physics of fluxons.

I now don't know what to do since some of the stuff is left in this thread and some is in the split thread, in the Trash can for some reason.

Please explain what is going on.

Thank you.

Meanwhile here is the beginning of my discussion on the sineGordon equation, if anybody actually wants to discuss it here.

As can be seen this is the required step function but the question really is,

What does this solution represent ?

##### Share on other sites

!

Moderator Note

If you’re discussing fluxons and the topic introduced by the OP, it goes here. If it’s about the “electricity physics” terminology, introduced by someone who is not the OP, don’t post it

## Create an account

Register a new account