Electric quadrupole moment of neutron? e.g. quarks need nonzero, algebraic argument needs zero ...

I think you're on point with regard to incorporating knot topologies into particle identity - it's out in the zeitgeist at some level. "Matter is energy tied in knots" can be taken quite literally and leads to interesting ideas which are only heretical according to the standard model (not according to experimental data as yet). I would probably disagree with you about the details, but it's worth hashing these things out and important to notice the larger vision which this idea gives some access to.

A number of people have come across this idea for the trefoil-proton association : John Duffield, Jack Avrin, and Larry Reed come to mind.

The identification of the electron as an intermediate topology between an unknot and a trefoil (mobius-like) was discussed in some detail by John G Williamson as a 'double loop', and there are some other authors who have also made a similar association. The proton spin crisis is a good reason to doubt quark theory, as Williamson (who worked at CERN for ~7 years) was quick to point out.

I have not seen too much discussion about what this implies for a neutron, but if you run with this (Kelvin-esque) idea the figure 8 knot is a natural candidate. I don't have a mathematical proof, but visually it's clear that the figure 8 neutron could take a tetrahedral-like conformation with two positive 'facets' and two negative 'facets'. This suggests a model somewhat like Edo's SAM in that some internal negative-positive binding is the explanation (no strong force), except that there are only ever 4 nearest neighbors for the neutrons, which can only accept up to two protons each as nearest neighbors due to the constraints described. I posted a thread about this but I don't think there's been any actual comment on the idea itself. This suggests something like a quadropole moment on the neutron, but with the charge centers located on the faces of d4 tetrahedron rather than on the corners of a square.

in this model, an H2 nucleus would look like one tetrahedral neutron with a single negative facet and 3 positive facets exposed, suggesting some dipole moment on that basis.

I struggle to see how halo phenomena has anything to do with knotting phenomena, but perhaps a case can be made. More importantly, they're probably not the most critical oddity/anomaly one might address (i.e. periodic half live variability, proton spin crisis, asymmetric fission, prediction of isotope half lives, segre chart behavior generally, etc.). A nuclear model which helps LENR would result in actionable theory and predictions that can be validated by existing data (i.e. segre chart) and used to infer something practical about isotope/element choice, or nuclear orientation within a lattice (something generally not considered in detail). It's hard to see how halo nuclei would be relevant to practical applications.

Once we can explain/predict tritium half life, and all the other long lived stuff, then I'll worry more about halo nuclei.

Quote from Jarek

While we agree 1D structures are crucial (called e.g. quark strings), I don't see charges in your model ... so your neutron has quadrupole moment or not?

Also: what are nuclei? To which particles correspond larger knots?

Charge is generated by the topology. Here is some idea of how it might be applied to the electron. In the context of the neutron you have to look at the spaces formed between the strands - figure 8 knots have 4 regions akin to the center of the trefoil knot, with pairs of each handedness. Larger knots are unstable as neutrons are unstable in free space, but with the addition of links and a modified Reidermeister 1 move, they could easily account for the particle zoo once the relationship between knot complexity and mass is better understood (mesons/baryons/hadrons if you like). The crossing/mass relationship appears at least monotonic for knots, complexified by the addition of links. I expect most electromagnetic topologies would be a bit simpler than most prime knots, including perhaps objects with twists which decay into more stable structures (pions come to mind here)

Quarks then can be interpreted as an accounting mechanism invoked to explain inaccessible topological structures with enough fitting parameters (supported by the addition of more quarks as needed). The crossings of the knot share the phenomenology of the quark - a critical part of the identity of the object which cannot be removed and isolated (per se) without totally changing the identity of the thing. As most of our probing experiments involve collision, you might see how projection (from a 3D knot to a 2D image) and collision are related - however you rotate a knot, some number of crossings will be encountered in that projection. You don't need to explain quarks if you're thinking in knots - it's an alternative concept for the observed data.

Best available evidence suggests that nuclei rely on only protons and neutrons. The knot model may be applicable to subatomics, but isn't as important to nuclear modeling excepting that a neutron structure informs the primary behavior of a nuclear model. This is not unlike Edo Kaal's model in this regard, but is derived from a totally different conception. If you have some D4 dice around (8-10 will get you pretty far) and some sticky tack, you can see for yourself. Just remember that for isotopes with n>1 you need at least 1 negative facet exposed. This defines the upper bounds of stability. The lower bound of stability is a bit squishier at present.... still tinkering.

I'm suggesting that the neutron probably does have something like a quadropole moment, but the key charge generating components would be described as located on the faces of a tetrahedra (derived from a figure 8 topology) and not on the corners of a square as in the traditional mathematical definition of 'quadropole moment'. Unlike E&M I'm not trying to introduce any point charges into the mix. Just local generation of charge across the whole topology. The entire neutron structure is still globally neutral of course. I only elaborate because to assert that specific charge configuration for the neutron without reason seems rather arbitrary, but it was implied from the larger hypothesis.

I guess I don't take the standard model at face value, as it's not a predictive theory. We need to account for observed data, including particles and their properties (charge, mass, moments, spin, etc.). This doesn't include quarks as they are a second order explanatory accounting mechanism. Even defenders of the SM will admit that quarks have not actually been observed or detected in isolation. Claims of seeing multiple groups of them might be interesting for what.... a nanosecond?

I encourage you to listen to John G Williamson and his take on QCD, in this very nice interview. He describes some of his time at CERN, and notes that part of why he decided to leave CERN was that the theory was not predictive. Because of this it has no practical utility and no legs and he decided to think differently and work elsewhere. (Don't get me wrong - the technical and experimental component of any accelerator effort has some merits, but the theory that is being used is of no use.) There is no technology which relies on quark-based explanations - all devices presently rely on photons, electrons, protons, neutrons and a mix of classical and QM derived theories arising independently from SM stuff. Most of our theory gets pretty far by assuming point-like charge, but we know this can't be the case, and instead of addressing this issue of charge generation theorists have been content to punt it down to the 'next lowest turtle'.

If you are running with the Kelvin hypothesis, the figure 8 knot neutron is more massive than a trefoil knot proton because the additional crossing contributes to the additional mass.

Charge comes from the writhe of the topology, and it is conserved on that basis.

I agree that images don't constitute proof, but they do help to communicate something difficult to capture mathematically using a defective R1 move. If you pinch the figure 8 knot, and imagine a vortex filament reconnection style event (i realize this is a bit of a loaded description), you are left with a trefoil knot and a mobius-electron similar to what John G Williamson was describing.

= +

I don't focus on neutrinos too much, but if individual photons are akin to loops, neutrinos might be like linked photon loops. This gives some insight into muons perhaps.

I encourage anyone vaguely curious about this suggestion to make some string knots and play with them for a while to improve topological intuition. It helps with visualization somewhat.

The best from our time is always...

Quote from Jarek

This is physics not mathematics, stable 1D structures, these knots are made of, are called e.g. quark strings/gluon flux tubes, e.g. decaying in LHC collision as string hadronization they assume: http://www.scholarpedia.org/ar…t_generators#String_model

Asking for their field configurations - why they are stable, because they are topological vortices like in superconductor/superfluid (e.g. https://www.sciencedirect.com/…cle/pii/S0370269399012083 https://journals.aps.org/prd/a…0.1103/PhysRevD.88.054504 )

These vortices can reconnect reducing and releasing energy ( https://en.wikipedia.org/wiki/Magnetic_reconnection ) - it is far nontrivial to form stable knots: not unknotting themselves.

Additionally, electric charges are there, e.g. of proton, which also has intrinsic electric quadrupole moment ( https://journals.aps.org/prc/a…0.1103/PhysRevC.63.015202 ).

The standard view is that quark string connects two quarks - so quarks are fractional charge excitations of such topological vortices, what can be done with inward/outward rotations like below: by pi would be hedgehog corresponding to elementary charge, by pi/3 would correspond to e/3 charge:

Display More

Hi Jarek

I'm not sure how to respond at this point. Are you asking a question? Making an assertion?

Magnetic Reconection would be the macroscale version of the phenomena as it relates to beta decay from a figure 8 topology, but yes, something along those lines is the mechanism I envision as being relevant to knot model of subatomic behavior.

FWIW physics without mathematics is typically of little use, and the mathematics of knots was derived from physical applications. Kauffman has an entire series of books about knots and physics. We shouldn't be surprised at the depth of the relationship.

Jarek you wrote in the far past :

---------------

So maybe we shouldn’t think about two-body p+e->n collisions, but rather about three body p+e+p or nucleus+e+p processes – because electron can attract both nuclei.

How to do it? Shooting electrons at nuclei, for some parameters we have backscatting: the electron goes back to the source. So imagine two closing nuclei and electron performing a few backscatterings between them: jumping between them, screening their Coulomb repulsion, making fusion much more probable.

Gryzinski’s model suggests this is quite a reasonable scenario, and his classical scattering paper has more than 1000 citations (google “Classical Theory of Atomic Collisions”).

Anyway, in contrast to other explanations of LENR, the only "exotic" assumption of electron-assisted fusion is considering trajectories of electrons.

Other non-standard assumption is adding electron's magnetic dipole moment to Bohr-like considerations (classical spin-orbit interaction).

-----------------

Okay, i well understood the Gryzinski thoughts however could you tell me more about the possible spin orbit interaction ? How that could help to fuse ? Another didn't ever studied the possibility this way could help to for tranmutation ? For example by releasing a P+e from a Li7 which "could go directly" to a Nickel 58 (59 to 62) ?

Quote from Jarek

I am saying your more complex knots would reconnect and vanish - themselves, or in scattering experiments - you need some stabilization mechanisms to prevent that, e.g. in mine you can see the two topological vortices have to be of different type, stably locking together when forming a knot ... still being (very deep but) only local energy minimum - such baryons could be destroyed/created.

So it is an open question if baryon number is ultimately conserved - it is violated in hypothesized baryogenesis (creation of more baryons after Big Bang) or Hawking radiation (massless from black hole created from baryons) ... but direct experimental search was unsuccessful ... if baryon number is ultimately conserved, they couldn't be knots.

And this thread is focused on charge distribution - so what is electric charge in your drawings? (in mine topological charges e.g. hedgehog through inward/outward field rotations)

And going from neutron to proton there is created electron and neutrino - how does this process look like in your picture? (below are mine)

Display More

Rather than could it be slowed down to simulate the same effect ?

If it is temporarily slower, it will spend more time between nuclei..

Quote from Jarek

For fusion we need electron to backscatter a few times between nucleus and proton, screening their Coulomb repulsion.

Even if you don't believe in the phonons involvement, electrons are their carriers.

Now, what should happen if some protons are heated at a certain temperature then vibrate at a certain frequency.

Now if they touch other protons more hot so what vibrate at an higher frequency.

Some heat will be transfered to the other protons to equalize the global temperature.

From the beginning we will have 2 differents frequencies next only one.

However just before the equalization we will generate a beat at few herz... So what that should say regarding the conduction electrons ?

Quote from Jarek

Sorry but electrons are ~2000x lighter than nucleons, making them super fast ... also they have powerful de Broglie clock/zitterbewegung which shakes everything around, allowing to escape potential minimums - it would be extremely difficult to imprison them e.g. between two protons, it is much easier to make them jump between through multiple backscatterings, like in the bottom simulation below: electron going to proton and back in nearly line.

Also, let's take such discussion to Electron-assisted fusion

Beats are electrons temporaly slowed down.

Quote from Jarek

Sure there are phonos, beat obtaining sum and difference of frequencies ... but I don't see how could it help with fusion?

... unless using extreme situation, like synchronized hydraulic rams creating spherical wave in https://en.wikipedia.org/wiki/General_Fusion