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

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studiot, I had long fluxon response, response about baryons and strangeness - both disappeared.

This sine-Gordon kink represents solution minimizing energy e.g. in lattice of pendulums: of phases while twisting by pi. But this is the most basic model - you can find it in hundreds of books and papers - please start with looking closer at external sources.

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What is the topic of the OP please  ?

I have already mentioned that it is rather wooly and wide ranging so difficult to have a focused discussion about.

Further I don't see the available definitions (Wikipedia) of fluxons bear much relation to standard textbooks eg Kittel.

This also impedes discussion.

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Let me bring back my two responses, both are crucial for the model:

Quote

But has there been any attempt at building the multiplets that I'm talking about with topological equations?

The number of found particles is in hundreds/thousands now. Some are virtual, like 80GeV boson W in beta decay of 1GeV neutron - this mass should be rather imagined as only shape of energy dependence like for https://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics)

What we should target (as configurations being local energy minima) are especially more stable particles and their decay modes e.g. from https://en.wikipedia.org/wiki/List_of_baryons ... and a general behavior in this table is decay with pion or kaon to baryon with lower strangeness.

As discussed, there are many reasons to imagine baryons in this biaxial nematic perspective as loop of one vortex around another vortex. We have three types of vortices, allowing for quark-like interpretations.

Possible complication of such simplest knot is additional internal twist of its vortex loop around - it should be obtainable in high energy collisions, and should relax by releasing part of this twist as particle - pion, kaon (bottom of diagram below) ... getting nice agreement if interpreting the number of internal twists as strangeness.

There are considered strageness 4 baryons (e.g. https://arxiv.org/abs/2011.05510 ). The space of local minima of configuration space can be quite complex: 3 types of vortices, they can contain charge (e.g. hedgehog), additional twist for loop around - can lead to hundreds of metastable states for baryons.

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So what is kinetic energy in a fluxon ?

In these models we have energy density (Hamiltonian, can be translated to Lagrangian) - usually with some spatial derivatives like stress, temporal for kinetic behavior, and potential (e.g. Higgs-like) ... integrating energy density we get mass of particle, usually scaling as in SR thanks to Lorentz invariance. Unfortunately it is quite tough calculation, I have attached for kink of sine-Gordon a few posts ago.

We can parametrize with positions of ansatz configurations like hedgehog, Lorentz transformed for velocities, getting classical mechanics approximations ... with kinetic energy going into mass exactly as in special relativity.

Fluxons are quite complex. While they are usually studied in superconductors/superfluids, here they are also needed in vacuum, e.g. to bind nucleus against Coulomb repulsion.

Probably the best experimental argument are "magnetic flux tubes" - nearly 1D shining structures seen in Sun's corona, they carry energy density per length - which can be released while shortening in https://en.wikipedia.org/wiki/Magnetic_reconnection

Quote from "Physics of Magnetic Flux Tubes" by Ryutova:

"Vortices in superﬂuid Helium and superconductors, magnetic ﬂux tubes in solar atmosphere and space, ﬁlamentation process in biology and chemistry have probably a common ground, which is to be yet established. One conclusion can be made for sure: formation of ﬁlamentary structures in nature is energetically favorable and fundamental process. "

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Quote from Duda Jarek

So what is kinetic energy in a fluxon ?

" In these models we have energy density (Hamiltonian, can be translated to Lagrangian) - usually with some spatial derivatives like stress, temporal for kinetic behavior, and potential (e.g. Higgs-like) ... integrating energy density we get mass of particle, usually scaling as in SR thanks to Lorentz invariance. Unfortunately it is quite tough calculation, I have attached for kink of sine-Gordon a few posts ago. "

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Keep in mind the Hamiltonian actually refers to absolute energy. In other words, the sum of potential and kinetic energies. The disparity between kinetic and potential energies is known as Lagrangian. Hamiltonian equals total energy in an optimal, holonomic, and monogenic system (the normal one in classical mechanics) when and only when both the limit and the Lagrangian are time-independent and the generalized potential is absent. In any coordinate system, the Lagrangian is optimal for systems with conservative forces and for bypassing restriction forces. Generalized coordinates can be used for ease of use, to take advantage of device symmetries, or to take advantage of the geometry of the constraints. However, in Lagrangian mechanics, a quantity known as the Lagrangian is used to explain the behavior of a system. Both Hamiltonian and Lagrangian mechanics allow you to reduce complicated x, y, and z coordinates to the system's most fundamental properties. The problem is that in mechanics, the term "physical" refers to something that follows the laws of physics and/or is detectable and observable. It has nothing to do with whether or not you are matter or energy. The problem is that the Lagrangian is defined as kinetic energy minus potential energy: L=T-V. As a result, several science students, including myself, will ask, "Why would you do that?" Since energy is preserved, it makes sense to incorporate potential and kinetic energy, so why would you deduct them? Many physicists regard the Langrangian as a more basic phenomenon than energy, despite the fact that it does not appear to correlate to something physical. It's all the coordinates and variations in coordinates here.  Acceleration, for example, is called "physical" (in the sense of being measurable), while speeds greater than the speed of light are considered "non-physical". We may , of course , apply cyclic coordinates or symmetries for reducing the number of variables in dealing with how particle physics and macroscopic phenomena look like. Would you offer elucidation(s) on these , please  ?

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Energy density, Hamiltonian is a first step - convenient to start with as all the terms have positive conteibutions. It is often timespace symmetric - not distinguish time and space directions.

But for solving such model we indeed usually go through the Legendre transform to Lagrangian - both for the least action formulation, and the Euler-Lagrange equation.

I have tried to go this way for the biaxial nematic with Coulomb interaction, but it was too tough for me.

Hamiltonian alone can be used to find static solutions, like this kink in sine-Gordon as minimal energy transition between two vacua. However, electron should be finally a dynamical solution - with this zitterbewegung, de Broglie clock ~10^21 Hz oscillations, confirmed experimentally: https://link.springer.com/article/10.1007/s10701-008-9225-1q

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28 minutes ago, Prof Reza Sanaye said:

Quote from Duda Jarek

So what is kinetic energy in a fluxon ?

" In these models we have energy density (Hamiltonian, can be translated to Lagrangian) - usually with some spatial derivatives like stress, temporal for kinetic behavior, and potential (e.g. Higgs-like) ... integrating energy density we get mass of particle, usually scaling as in SR thanks to Lorentz invariance. Unfortunately it is quite tough calculation, I have attached for kink of sine-Gordon a few posts ago. "

_________________________________________________________

Keep in mind the Hamiltonian actually refers to absolute energy. In other words, the sum of potential and kinetic energies. The disparity between kinetic and potential energies is known as Lagrangian. Hamiltonian equals total energy in an optimal, holonomic, and monogenic system (the normal one in classical mechanics) when and only when both the limit and the Lagrangian are time-independent and the generalized potential is absent. In any coordinate system, the Lagrangian is optimal for systems with conservative forces and for bypassing restriction forces. Generalized coordinates can be used for ease of use, to take advantage of device symmetries, or to take advantage of the geometry of the constraints. However, in Lagrangian mechanics, a quantity known as the Lagrangian is used to explain the behavior of a system. Both Hamiltonian and Lagrangian mechanics allow you to reduce complicated x, y, and z coordinates to the system's most fundamental properties. The problem is that in mechanics, the term "physical" refers to something that follows the laws of physics and/or is detectable and observable. It has nothing to do with whether or not you are matter or energy. The problem is that the Lagrangian is defined as kinetic energy minus potential energy: L=T-V. As a result, several science students, including myself, will ask, "Why would you do that?" Since energy is preserved, it makes sense to incorporate potential and kinetic energy, so why would you deduct them? Many physicists regard the Langrangian as a more basic phenomenon than energy, despite the fact that it does not appear to correlate to something physical. It's all the coordinates and variations in coordinates here.  Acceleration, for example, is called "physical" (in the sense of being measurable), while speeds greater than the speed of light are considered "non-physical". We may , of course , apply cyclic coordinates or symmetries for reducing the number of variables in dealing with how particle physics and macroscopic phenomena look like. Would you offer elucidation(s) on these , please  ?

I wanted to give you +1 in your last post, now in the Trash can.
But I find even more to agree with in this post and would like to note that these last two posts have been so much more cogent and coherent.
So +1 here.

On 3/6/2021 at 3:48 PM, Duda Jarek said:

studiot, I had long fluxon response, response about baryons and strangeness - both disappeared.

This sine-Gordon kink represents solution minimizing energy e.g. in lattice of pendulums: of phases while twisting by pi. But this is the most basic model - you can find it in hundreds of books and papers - please start with looking closer at external sources.

I also lost several posts but I have managed to get your developing presentation from dropbox and I am currently studying it.
I note that at least one of of the links in it have been since discredited ; I refer to couder's experiment.

But I think perhaps matters are begining to come clear at last.

I remain concerned with you interpretation of fluxons, and also the introduction of the sine-Gordon equation, or any of the non linear Gordon type equations.

Utt - Uxx = sinU

It is important to understand what is meant by the variable U, just as understanding what is meant by Ψ in the wave equation.

Since we are discussing magnetic fields, I think is beneficial to avoid phi as the dependent variable.

Edited by studiot
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I can respond tomorrow, but in sine-Gordon the field can be interpreted as of phases of these penulums in lattice - with minimum of gravitational potential every 2pi.

For Couder and other hydrodynamical QM analogues (Casimir, Aharonov-Bohm etc.), here are gathered materials: https://www.dropbox.com/s/kxvvhj0cnl1iqxr/Couder.pdf

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Another long-range interaction in liquid crystal paper: "Long-range forces and aggregation of colloid particles in a nematic liquid crystal": https://journals.aps.org/pre/abstract/10.1103/PhysRevE.55.2958

Edited by Duda Jarek
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There are more long-range interactions for liquid crystals, e.g.:

dipole-dipole: "Novel Colloidal Interactions in Anisotropic Fluids" https://science.sciencemag.org/content/275/5307/1770

Coulomb (!): "Coulomb-like interaction in nematic emulsions induced by external torques exerted on the colloids" https://journals.aps.org/pre/abstract/10.1103/PhysRevE.76.011707

Skyrme models are for strong interaction ... so why can't we model all?

These liquid crystal systems are for uniaxial nematic - one distinguished axis everywhere ... bringing a question about natural generalization: biaxial nematic: 3 distinguished axes in 3D (4 in spacetime adds gravity) - giving particle-like configurations resembling 3 leptons, neutrinos, baryons, nuclei ...

Edited by Duda Jarek
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• 2 weeks later...

You might find today's new from CERN interesting.

This BBC report is probably more sensationalist than necessary so caution is needed.

Physicists have uncovered a potential flaw in a theory that explains how the building blocks of the Universe behave.

The Standard Model (SM) is the best theory we have to explain the fine-scale workings of the world around us.

But we've known for some time that the SM is a stepping stone to a more complete understanding of the cosmos.

Hints of unexpected behaviour by a sub-atomic particle called the beauty quark could expose cracks in the foundations of this decades-old theory.

The findings emerged from data collected by researchers working at the Large Hadron Collider (LHC). It's a giant machine built in a 27km-long circular tunnel underneath the French-Swiss border. It smashes together beams of proton particles to probe the limits of physics as we know it.

The mystery behaviour by the beauty quark may be the result of an as-yet undiscovered sub-atomic particle that is exerting a force.

But the physicists stress that more analysis and data is needed to confirm the results.

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I though "beauty" was abandoned long ago in favor of "bottom" (along with "truth" as an alternative to "top")

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studiot, thanks, probably as usual it is matter of adding/modifying terms to Lagrangian - in practice used in perturbative approximation, literally adding terms to Taylor expansion.

But this is description not understanding, neglecting basic questions like of field configuration behind given Feynman diagram, mean energy of fields in given distance from electron etc.

Or renormalization literally subtracts infinite energy by hand - where exactly it subtracts it? Shouldn't it in fact subtract some energy density - from e.g. energy density of electric field, to make it integrate to finite energy.

Search for deeper models - effectively described by something close to Standard Model, is just no longer ignoring such basic questions.

Like of regularized EM field around electron - including renormalization procedure, this way integrating to finite energy.

Or explaining basic properties of physics - instead of inserting them by hand, e.g.:

- Why electric charge is quantizatized? In liquid crystal experiments: because it is topological charge.

- Why we have 3 leptons? In biaxal nematic view: because we have 3 spatial directions.

- Why leptons also need magnetic dipole. ... because of hairy ball theorem.

- Why proton is lighter than neutron? ... because baryons require charge, which in neutron needs to be compensated.

- How nuclei overcome Coulomb repulsion? ... by being bind with fluxons.

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You might find this book worth reading

Variational Principles in Dynamics and Quantum Theory

Yourgrau and Mandelstrom

The authors take a Lagrange - Hamilton - Jacobi approach to the development of both classical dynamics, relativistic dynamics and (relativistic) quantum dynamics.

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On 3/23/2021 at 1:26 PM, studiot said:

You might find today's new from CERN interesting.

This BBC report is probably more sensationalist than necessary so caution is needed.

Physicists have uncovered a potential flaw in a theory that explains how the building blocks of the Universe behave.

Ok, I have finally looked closer (paper: https://link.springer.com/article/10.1140%2Fepjc%2Fs10052-018-5918-6 ).

So basically they believe that B mesons should decay symmetrically to electrons and muons, but they observe slight asymmetry: ~15% more to electrons with 3.1 sigma (~1/1000).

Mesons is huge family: https://en.wikipedia.org/wiki/List_of_mesons

Beside kaons (~500Mev), we mainly know pions: charged have ~140Mev, ~10^-8s lifetime, mainly decay to muon + neutrino ... but also have rare decay to electron + neutrino ( https://en.wikipedia.org/wiki/Pion#Charged_pion_decays ).

B mesons ( https://en.wikipedia.org/wiki/B_meson ) have ~5GeVs ... while pions have very asymmetric decay into leptons, I have to admit that I don't understand why slight asymmetry for other mesons is surprising (?)

Anyway, in discussed "biaxial nematic perspective", mesons nicely fit fluxons forming loop with additional internal twist (corresponding to strangeness), maybe hopfion (diagram below from https://en.wikipedia.org/wiki/Hopf_fibration ).

The three types/quarks are from performing such loop along one of 3 axes of biaxial nematic. Mesons are configurations being local energy minima - their asymmetry of decay into various leptons is completely unsurprising.

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• 4 months later...

I have finally worked out mathematical framework up to Euler-Lagrange for this ellipsoid field/liquid crystal like approach:

- field of 3 distinguishable axes using 3x3 matrices preferring fixed set of eigenvalues,

- hedgehog of one of 3 axes for 3 leptons - charges governed by Maxwell equations, with magnetic dipole moment due to hairy ball theorem,

- then expanding to 4x4 matrices we get second set of Maxwell equations for GEM ( https://en.wikipedia.org/wiki/Gravitoelectromagnetism ).

The approach generalizes Faber's from vector to matrix field.

Electromagnetic (A vector, F tensor) are no longer just (connection Gamma, curvature R), but additionally include dependence of rotated shape (eigenvalues).

This way we can get vacuum dynamics of 3 strengths: EM >> pilot wave >> GEM.

Below is the main diagram with concepts.

I have submitted to arxiv but is "on hold" as usual, so I have put it here: https://www.researchgate.net/publication/353932148_Framework_for_liquid_crystal_based_particle_models

It is initial version I will work on especially:

- the details of potential to choose is the main open question, and very difficult one - it contains weak/strong interactions,

- explaining gravitational mass - spatial curvature caused e.g. by energy density, activation of potential,

- finally numerics first aiming agreement with electron, 3 leptons, hopefully enforcing intrinsic periodic process: de Broglie clock.

Edited by Duda Jarek
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• 5 weeks later...

Hypothesized further particles, e.g. proton lighter than neutron - because baryons structurally require charge here, neutron has to compensate it what costs energy ... in deuteron two baryons hare single charge - getting electric quadrupole moment and aligned spins as in physics:

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• 1 month later...

Some updates - interactive demonstration to play with such topological charges of liquid crystal biaxial nematic - of 3 types resembling 3 leptons, requiring magnetic dipoles, with analogy of quantum phase evolution: https://demonstrations.wolfram.com/TopologicalChargesInBiaxialNematicLiquidCrystal/

Derivation of Klein-Gordon-like equation for this evolving phase (slide 15 of https://www.dropbox.com/s/9dl2g9lypzqu5hp/liquid crystal particles.pdf )

Edited by Duda Jarek

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