A Strand Model Published: Physics of Particles & Nuclei 50 (2019)

[physics8553]

So now we finally agree that electron neutrino tangles are chiral but not topologically chiral and that thus assigning zero electric charge makes sense. Phew, that took quite some time!

Now the next step. That is the electron tangle. Please draw it in Mathematica or make one with ropes.
There is no projection that has only two crossings. (You are obviously not allowed to shift crossings out of your field of view with the aim of not counting them.) The condition is that three ends/tethers are above and three ends /tethers below the paper plane, as set out in the definition. (And by the way, I do have three ropes to play near me.)

The mistake with the "MilkyWay" reasoning is that you are pushing crossings out of the MilkyWay by doing this. You have to count all crossings, not only the ones you like. When one says "locally", one has to look at the whole region that has crossings. This definition of "locally" is what corresponds to "locally" in usual physics. (If you want another definition, "locally" is that region which includes all curved sections of strands when you pull their ends.) The electron tangle is topologically chiral, in contrast to the electron neutrino tangle. That is why the electron is electrically charged.

Another topic you brought up: A photon tangle indeed has zero crossings in certain, even most projections; it is a single unknotted strand, after all. Any helix also has vanishing crossing number. The corkscrew model of the photon is old, and works well, if some additions (hopping) are made. And because the photon has zero crossing number, it has zero mass and zero electric charge. The labeling is consistent.

Just to be clear: Crossing number is a topological invariant. It is the number of crossings in the minimal projection. It is not the number of crossings in every projection. Electric charge in the chiral crossing number. That is another topological invariant. It is not the number of crossings in every projection. Many projections have more crossings than the minimal one.

 

[HBrown]

So now we finally agree that electron neutrino tangles are chiral but not topologically chiral and that thus assigning zero electric charge makes sense. Phew, that took quite some time!

Now the next step. That is the electron tangle. Please draw it in Mathematica or make one with ropes.
There is no projection that has only two crossings.

String was too floppy, I had to play with this in mathematica and rigidly rotate around for a bit with different strand configurations to see what you were describing. You are correct about the electron tangle not having a projection with only two crossings. That was my mistake.

The mistake with the "MilkyWay" reasoning is that you are pushing crossings out of the MilkyWay by doing this.

Since you assign the W+/- a unit charge, you must agree that the minimal projection for this has three crossings. "Flatenning" the electron locally, and then later letting the strands go off to infinity at the "above/below" paper level does not change any crossings, or push any crossings out beyond the Milkway. It still appears that the only thing distinguishing them is off at infinity.

So it still appears to me that we cannot distinguish a fermion and a boson locally.

Another topic you brought up: A photon tangle indeed has zero crossings in certain, even most projections; it is a single unknotted strand, after all. Any helix also has vanishing crossing number. The corkscrew model of the photon is old, and works well, if some additions (hopping) are made. And because the photon has zero crossing number, it has zero mass and zero electric charge. The labeling is consistent.

That does not sound like consistent characterization of particles to me. If it was consistent, then you would call that vacuum, not a photon.
It looks like it is not possible to distinguish vacuum from photons and neutrinos everywhere.

Just to be clear: Crossing number is a topological invariant. It is the number of crossings in the minimal projection. It is not the number of crossings in every projection. Electric charge in the chiral crossing number. That is another topological invariant. It is not the number of crossings in every projection. Many projections have more crossings than the minimal one.

I'm not sure how to even word this. Is it possible for some of the crossings of a tangle to be topologically chiral while others are not? It seems like it would have to be all or nothing, so why doesn't your muon tangle have charge -2 ?

And please, I still would like a description of the stochastic motion. You seem to assume that if something is rotating one way that it will continue rotating that way. How is that encoded in the stochastic motion? Is there something that gives a bias towards moving in a particular direction? Do the strands themselves have momentum or something to prefer continuing movement in the same direction?

And what about left chiral vs right chiral electrons. Are they different tangles? Since only one couples with the weak force, shouldn't that be some other charge associated with the tangles?

 

[physics8553]

The last questions are the most important ones, so let me start with it. Yes, the conjecture assumes/asserts that if a particle tangle is rotating while advancing, that it will continue rotating and advancing. No, strands have no mass, so they have no momentum; the reason for the continuous advance is just one of probability: probability leads to continuous rotation.

The simplest case is the photon: it is a corkscrew advancing through the ("very thin") vacuum. The chiral shape of the corkscrew makes it advance by rotating (imagine the vacuum as a very thin mattress, with no friction). And just to come back to the topic: a photon strand and a vacuum strand are topologically identical, as you point out. Thus they both have no mass and no charge. But a photon strand, due to its localized helix, has curvature and rotation, and therefore has energy, wavelength and spin. A vacuum strand does not. And a helix is the same after rotation by 2 pi, so a photon has spin 1.

The more complex case are fermions. Here, in addition to the core motion and core rotation, there is also the belt trick. The belt trick produces the spin 1/2 properties: return to itself after 4 pi, not after 2 pi; the belt trick in its two-particle variant also yields the fermion behaviour under particle exchange. These two properties can of the belt trick be visualized easily with animations: see for the 4 pi invariance, i.e. the spin 1/2 behaviour under rotations, and the much rarer animation showing the invariance after double exchange of two particles, leading to fermion statistics. But you can also do this easily yourself at home, with ropes, or with paper stripes (must be long enough; and use different colours, so to keep track properly). In the embedded animations, imagine two or three strands instead of each stripe.

Let us start with the core rotation of fermions. Simply said, the core rotates when advancing because its shape is chiral. This gives the rotation bias you asked about. Antiparticles are mirror tangles and thus their cores rotate in the opposite direction - due to the same bias. (Note that the idea of a rotating advancing particle is standard, and encoded in the Dirac equation; strands just reproduce the usual narrative.)

But the belt trick also occurs for fermions. And the belt trick itself can also go in two directions. You can see the two different options for the belt trick and core rotation in these two animations: https://www.infinitelooper.com/?v=qgEaNm-3Lis&p=n (core and belt trick in same direction) and https://www.infinitelooper.com/?v=-KGW3QvwFuE&p=n (core and belt trick in different direction) These two animations show a cubic core with bands; just imagine a chiral tangle core with strands instead.

For the weak interaction, the idea is that when rotation and belt trick have the same sign, the weak interaction behaviour is one, and when the two signs differ, the weak interaction behaviour is another. This yields the maximal parity breaking of the weak interaction.

In the next days I have less time. I'll tell more about the other issues as soon as I can.

 

[HBrown]

I feel like stuff is being swept under the rug just because I made an incorrect claim about your electron tangle.

If the neutrino and its reflection are topologically equivalent, then it must be possible to recreate any projection.
But these two projections seem to distinguish the two:

Starting on a strand and going over, under, then switching to the strand it went under, then going over, under, repeat ... for the left it takes me counter-clockwise, and for the right it takes me clockwise.

I have tried rotating the left one all over and I never see anything like the right.
They still appear topologically distinct to me.
We got off on other discussion because of a mistake I made, but let's please return to this fundamental issue.

And to 100% make sure that we're on the same page:
If the tangle on the left is topologically distinct from its reflection (the tangle on the right), then you consider its crossings "topologically chiral" and thus this tangle is charged, correct?

The counter-clockwise over-under seems topologically distinct from the clockwise over-under pattern. I do not see why you claim these are topologically equivalent. Please specify how to rotate the left one to make it look like the right.

 

[HBrown]

The more I read, the more I am worried your definition of a "tangle" and "equivalence" of tangles is different than everyone elses. Usually for tangles, the boundary is chosen and fixed, and then various configurations of the ropes inside are studied. Many of your ideas feel like a mish-mashing of rational tangles with your previous knots ideas.

So let's try to agree on some basics.
Step 1. Can we agree on this definition of a tangle from wikipedia?

In John Conway's definition, an n-tangle is a proper embedding of the disjoint union of n arcs into a 3-ball; the embedding must send the endpoints of the arcs to 2n marked points on the ball's boundary.

Note that the boundary (marked points) are fixed (otherwise all rational tangles would be equivalent). For example when discussing 2-tangles, even the two "zero-crossing" tangles below all considered distinct ( https://arxiv.org/pdf/math/0311499.pdf )

Step 2. Can we agree that only the stands should be allowed to deform and move (not the marked points), when trying to determine equivalence of tangles?

Step 3. Once we can agree on the foundations, let's revisit the neutrino "crossing chirality" in depth.

Here are some spheres with marked points, and strands for neutrino and the reflected (r → -r) version of that. Do you still maintain these are equivalent tangles? If so, how can you deform the strands on the left to make it look like the one on the right?

If you'd prefer, we can put the marked points on the 6 points where the x,y,z axis exit the sphere. But then I need to use curved lines, and I'd prefer to not have a side debate about that if its an issue. But if you'd prefer, here they are:

If you disagree, I would appreciate if you give clear definitions of your terms to help get us all on the same page.

 

[physics8553]

The paper states several times that mirror tangles correspond to antiparticles. These two tangles correspond to electron neutrino and antineutrino. The curved lines imply that they have mass. The difference between the two tangles imply that they are Dirac neutrinos, not Majorana neutrinos. In the present experimental situation, these statements should be seen as predictions.

The tangle model further predicts that the mass order of neutrinos is normal (because more complex tangles correspond to higher mass). The tangle model also predicts that the mass values of the neutrinos is much smaller than that of any other elementary particles (essentially because the tangles are so close to that of the vacuum). The tangle model also predicts neutrino mixing (essentially because of the possibility of tangle tether deformations) and a mixing matrix that is unitary (both for quarks and for neutrinos) because unitarity follows from the deformation model of mixing.

 

[HBrown]

It would help if you answered the pertinent questions instead of providing more predictions.

You stated:

Electric charge: 1/3 for each topologically chiral crossing (in minimal crossing projection) in a matter/fermion tangle. Charge can be determined by computer.

Despite saying that, you have yet to define a clear procedure that would allow a computer to determine this. When I tried to bring actual math in, you instead then suddenly claimed that trying to compute this given a tangle embedding is an open question.

As the neutrino and its mirror appear to be topologically distinct, and you agree that the minimal crossing projection is non-zero, then by your definition there the neutrino tangle is charged.
You disagreed, and so I asked for what your definition of "topologically chiral" was. This you did answer (thank you):

Chiral means "different from its mirror"; topologically chiral means "cannot be deformed into its mirror".

But this did not resolve anything as it still means your neutrino tangles are charged according to that definition, unless there is some way to smoothly deform the neutrino tangle into its mirror. That appears impossible, and so it still appears your definitions lead to charged neutrinos.

You still disagree, but refuse to show us how that one embedding can be deformed into the other.

Maybe there is still a terminology issue.
I'm taking the time to provide definitions here to hopefully speed this up. I would very much appreciate it if you could agree, or provide your own definitions, so that we can build up a foundation.

Question 1. Can we agree on this definition of a tangle from wikipedia?

"In John Conway's definition, an n-tangle is a proper embedding of the disjoint union of n arcs into a 3-ball; the embedding must send the endpoints of the arcs to 2n marked points on the ball's boundary."

Question 2. Can we agree on this definition of topological equivalence between two tangles?

Two tangles are topologically equivalent if and only if there is a smooth deformation from one to the other which holds the boundary fixed, but allows the strands to move in the interior of the ball subject to the constraint that strands do not pass through each other.If we agree please give a quick yes, if not then please provide alternative definitions.

 

[physics8553]

For future reference, here is a complete list of predictions, as specific as possible, made by the strand model.

1. Maximum force c^4/4G and maximum power c^5/4G will never be exceeded,
2. No physics beyond the standard model with massive neutrinos will ever be found,
3. No deviation from general relativity at sub-galactic scales will ever be found,
4. No conjecture differing from the tangle model will ever explain the masses, the mixing angles and the coupling constants of elementary particles.

The reason that point 3 mentions 'sub-galactic' scales is that the effective dark energy density might change over cosmological time scales in the strand model. This is still subject of research.

Time will show how these predictions will score against future experiments and future theory.

 

[physics8553]

Just for entertainment, here is an animation of the spinning electron in the tangle model:

https://www.motionmountain.net/research.html#et

 

[sysprog]

Shouldn't each of those 'strand model' claims be, before general acceptance, justified one by one (i.e. one claim at a time)?

 

[physics8553]

It is possible to insert animated gifs after all. Here is the animation of a spinning electron in the strand conjecture, programmed by Jason Hise.

Indeed, the strand conjecture makes many claims. There will be a paper for each claim of the prediction made 2 postings ago. The starting paper for all claims is the one cited at the beginning of this thread. More papers will follow.

This animation relates to a few sub-claims (in total over 100 sub-claims) of prediction 2, namely that the standard model is all there is in high energy physics. For example, the animation visualizes the unit charge of electrons, visualizes that only massive particles can have electric charge, and visualizes that electrons are fermions with spin 1/2. The paper and the new preprints on the motion mountain research page cited 2 postings before this one show more details, including why such a "crazy" conjecture implies that electrons obey the Dirac equation (a discovery by Battey-Pratt and Racey), that strands thus yield the Dirac propagator, and why strands yield minimal coupling to the electromagnetic field. Together with the one-stranded model for the photon, all of QED arises - including Lagrangian and perturbation expansions. In fact, the animation also visualizes why the electromagnetic coupling is the same for all particles with the same electric charge (such as positrons and protons, for example), why the g-factor is larger than 2, and why the mass of an electron is much smaller than the Planck mass. The last three consequences are non-trivial.

 

[PeterDonis]

There will be a paper for each claim of the prediction made 2 postings ago.

Then when those papers are published, they can be used as a basis for PF discussion. But not until then.

Thread closed.