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*Physics of Particles and Nuclei,*vol. 50 (2019) pages 259-299. The conjecture predicts the lack of effects beyond the standard model. It describes particles as rational tangles.

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In summary, the strand model is a recent conjecture that combines the standard model and general relativity. It predicts the lack of effects beyond the standard model and describes particles as rational tangles. The strand conjecture has been published in the Physics of Particles and Nuclei journal, but some skepticism has been raised due to the journal's low impact factor. However, the journal has a history of reputable editors and is affiliated with the Joint Institute for Nuclear Physics. The strand model also makes testable predictions, including the impossibility to exceed the Planck limits and the lack of undiscovered particles or symmetries. However, there are still some concerns and criticisms about the theory, such as the lack of clear mathematical explanations and its ability to

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Physics of Particles and Nuclei is a pretty low quality journal, with an impact factor of less than 0.8. I would be fairly skeptical of anything that is only published in this journal.cschiller said:the reference isPhysics of Particles and Nuclei,vol. 50 (2019) pages 259-299.

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Intense skepticism should be the reaction to any proposal that claims to combine the standard model and general relativity. To make the skepticism even more intense, the testable predictions of the strand conjecture are now listed in detail on motionmountain.net/bet.html .

The specific predictions include the*impossibility* to exceed the Planck limits c^4/4G and c, to observe effects below the Planck length and the Planck time, to exceed the maximum electric field c^4/4Ge, but also the *lack* of undiscovered energy scales below the Planck scale, of undiscovered particles and particle generations, of undiscovered symmetries or larger gauge symmetries, of undiscovered interactions, of any deviation from the standard model with massive neutrinos, the *lack* of dark matter particles, of additional dimensions, of detectable new quantum gravity effects, of singularities, of non-trivial topology of space, and of any deviation from general relativity at sub-galactic scales. Many additional predictions are listed.

So far, the predictions and the retrodictions from the Planck scale - including the Planck limits for physical observables, the emergence of space and all physical observables, all black hole properties, the observed unbroken and broken gauge symmetries U(1), SU(2) and SU(3) from the Reidemeister moves, and all particle quantum numbers - appear to agree with all experiments. Various additional experimental and theoretical tests, checks and ways to falsify the strand conjecture are proposed.

The only*new* aspect of the strand conjecture appears to be the possibility to calculate particle masses, couplings and mixings from the rational tangles of elementary particles.

Finally, the page also lists reasons to continue to be intensely skeptical, including the one from the previous comment, and many others. Additions to the lists on the page are welcome.

The specific predictions include the

So far, the predictions and the retrodictions from the Planck scale - including the Planck limits for physical observables, the emergence of space and all physical observables, all black hole properties, the observed unbroken and broken gauge symmetries U(1), SU(2) and SU(3) from the Reidemeister moves, and all particle quantum numbers - appear to agree with all experiments. Various additional experimental and theoretical tests, checks and ways to falsify the strand conjecture are proposed.

The only

Finally, the page also lists reasons to continue to be intensely skeptical, including the one from the previous comment, and many others. Additions to the lists on the page are welcome.

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Of course, having testable predictions is itself a very good thing. Something testable might be wrong, but at least it has gone beyond the “not even wrong” stage.cschiller said:To make the skepticism even more intense, the testable predictions of the strand conjecture are now listed in detail on motionmountain.net/bet.html .

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Alas, the *experimental* predictions of strand conjecture given on motionmountain.net/bet.html are *not* *unusual*.

The lesser known maximum force c^4/4G, maximum power c^5/4G, maximum electric field c^4/4Ge, maximum magnetic field c^3/4Ge, and similar (corrected) Planck limits are indeed not achieved in any microscopic, macroscopic, astrophysical or cosmological setting. But these limits can hardly be called unusual.

Strands mainly predict the complete lack of new physics. Most speculations of the past 40 years are predicted to be wrong. Therefore, any discovery of new physics would falsify the strand conjecture. The only unusual aspect is that strands*imply* that nothing unusual can occur. Before the strand conjecture, it was not possible to derive this prediction from first principles.

The lesser known maximum force c^4/4G, maximum power c^5/4G, maximum electric field c^4/4Ge, maximum magnetic field c^3/4Ge, and similar (corrected) Planck limits are indeed not achieved in any microscopic, macroscopic, astrophysical or cosmological setting. But these limits can hardly be called unusual.

Strands mainly predict the complete lack of new physics. Most speculations of the past 40 years are predicted to be wrong. Therefore, any discovery of new physics would falsify the strand conjecture. The only unusual aspect is that strands

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Dale said:Physics of Particles and Nuclei is a pretty low quality journal, with an impact factor of less than 0.8. I would be fairly skeptical of anything that is only published in this journal.

I share some of your skepticism. But the journal does appear to have an interesting pedigree.

From the current abstracts it appears to be what I'd call a bread-and-butter physics journal: usually nothing exciting or controversial. In it's 50 years, the journal seems to have had three heavy-weight Russian nuclear physicists as Editors-in-Chief for most of existence. All three were directors of the Joint Institute for Nuclear Physics, a large and prestigous Russian organization. Condensed-matter physicists might recognize it's founding editor N.N. Bogolyubov of Bogolyubov particles fame. I suspect that the journal might be a much like a house journal for the JINP.

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How?cschiller said:possibility to calculate particle masses, couplings and mixings from the rational tangles of elementary particles.

What are the strand made of?

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What are strings made of?ftr said:How?

What are the strand made of?

What points are made of?

We assume in every mathematical theory some building blocks which are aren't defined, like in set theory, category theory etc.

What is a set made of? of other sets...

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MathematicalPhysicist said:What are strings made of?

What points are made of?

We assume in every mathematical theory some building blocks which are aren't defined, like in set theory, category theory etc.

What is a set made of? of other sets...

Here we are not talking pure math. We are taking about physics and anything in the system that has reality we like to measure it. My question was in what way the strands represent anything real or it is just another by the way of wavefunction as an abstract object. In physics we have different types of concepts, like energy and mass we can measure and the those notorious "virtual particle ", and then the "wavefunction". So my question was in what sense are the strands.

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To save everyone time, here are some other issues last time he promoted this.

- For a theory starting with strands, one might think each different knot would be a different particle. It is not. This is never clearly explained. It's one of those "it can only be interpreted by the author" crackpot theories.

- As a specific example, the photon is an unknot.

- There was no math behind the theory explaining how the strands moved. He just claimed all motions that didn't cause strands to cross each other were allowed. This causes several problems.

* First, we do not even have a theory we can really calculate from.

* Second, why doesn't this predict all particles move like brownian motion? How is momentum conserved?

* Third, he claims to derive space-time from the arrangement of the strands, therefore space-time is discrete and his theory needs to do something to suppress Lorentz violating terms.

* Fourth, given that the photon is the unknot, photons can just decay into nothing.

- How can two unknots interact to form two knots? (two photons -> pair of particles) As far as he could explain back then, the knots came in from infinity really fast to make it happen or something.

In short, back then, this was firmly in the "not even wrong" state. Considering how little he was able to even admit to himself these short comings, or have a mathematical discussion about any of them, I have trouble believing he will ever be able to make this into a real theory. If someone wants to waste their time reading the 40 pages he wrote to this journal, let me know if it got better. But I've previously read his similarly published "proof" that he can derive general relativity, and it is just straight hand waving.

Furthermore, reading his self published books, it is clear that while he is very passionate about the subjects, he does not really understand quantum mechanics and general relativity. I am not as well versed in thermodynamics, but I've heard from others that this chapter has issues as well.

In short, please do not encourage this individual. Last time showed it will just suck a bunch of people's time.

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Definition:

0. Strands have Planck radius (negligible at usual energy scales) and fluctuate in 3d (background/tangent space); only crossing switches are observable, not the strands themselves, and they define h-bar, c, G and k.

Consequences:

1. The tangle model describes matter particles as rational (i.e. unknotted) tangles - not as knots - that fluctuate. (Knots indeed do not describe particle interactions.)

2. Fermions (i.e., rational tangles) move via the belt trick, which makes the phase rotate and the tangle core advance. Particles are observed to be "clouds".

3. Using the results of Battey-Pratt and Racey from 1980, this implies the free Dirac equation, thus the Dirac Lagrangian and the propagator. (Dirac's equation conserves momentum. And indeed, a localized wave function of a particle spreads out over time.)

4. If one classifies all tangle topologies, one gets tangles for all known elementary particles - not more, not less. (All quantum numbers arise. The lack of specific dark matter particles is thus predicted.)

5. The Higgs particle (a braid) leads to Yukawa terms for tangles of two or of three strands only (of quarks or of leptons, W, Z, Higgs).

6. Deformations of tangles yield, via the three Reidemeister moves, the three known gauge groups and the expected coupling structure - not more, not less. (So the lack of other gauge groups or GUTs is predicted.)

7. Rational tangles can split and recombine. If one explores all possibilities for such splittings, one gets the vertices of the standard model - not more, not less.

8. Thus, the exact Lagrangian of the standard model arises (with massive Dirac neutrinos) - without additions or modifications, at all measurable energies. (So the lack of unknown energy scales and of additional dimensions is predicted. The interaction vertices conserve momentum, automatically.)

9. Photons are twisted strands; they have spin 1; being untangled, they have no mass and move with the maximum speed c. (They cannot decay for the same reasons that they do not decay in the standard model.)

10. Fundamental constants are due to tangle geometry and can be calculated. Predictions are made for particle physics (e.g. normal neutrino mass ordering, mass hierarchy explanation) and tests are formulated (nothing beyond the standard model will be seen).

11. Due to strand fluctuations, empty space (a network of strands) is continuous and Lorentz invariant, despite having a smallest observable length (the diameter of the strands).

12. The microscopic model for space and particles also describes horizons (weaves of strands) and black holes, including their energy and entropy.

13. General relativity and its field equations (at sub-galactic scales) emerge from the microscopic structure of space and black hole horizons using the usual arguments.

14. Predictions and tests are formulated about gravity (inertial mass equal to gravitational mass and no deviations from general relativity at sub-galactic distances, no unknown quantum gravity effects).

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Can you please answer our specific questions. Thanks.

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See:HBrown said:At the time, he claimed that if the higgs boson was found, it would disprove his theory. Guess what, it was found, and his theory (which he claimed could not be modified) ... was ... you guessed it ... modified to no longer make that claim.

cschiller said:The strand model also has a clear experimental signature, namely a "desert" up o Planck energy, including a lack of Higgs bosons. Let's see what the LHC and the other experiments will bring us.

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How [to calculate]? What are the strand made of?

--

In the tangle model, only the known particles arise. In the tangle model (like in quantum theory),**mass** is the quantity that connects phase rotation and translation. In the tangle model, the belt trick is responsible for this connection. Estimating the probability for the belt trick for each tangle allows to estimate the mass value. See the preprint on QED for an estimate. As a consequence, masses are predicted to be constant over time and space, positive, equal for particles and antiparticles, equal to the gravitational mass, running with energy, and much smaller than the Planck mass.

In the tangle model, only three coupling constants arise. In the tangle model,**coupling constants** describe the average phase jump due the emission or absorption of a gauge boson. In the tangle model, the average phase jump is given by exchange of Reidemeister moves (gauge bosons), itself due to the geometry of tangles. Depending on the geometric details of a gauge boson, the phase of a fermion is changed more or less. See the preprint on QED for an estimate. As a consequence, the values for the coupling constants are unique, constant over time and space, running with energy, equal for all particles with the same charge, and smaller than one.

In the tangle model,**mixing angles** are due to the probability with which one tangle changes, through strand fluctuations, into another tangle of a related fermion. This is natural for rational tangles. In the tangle model, for topological reasons, this arises only among leptons or among quarks. In the tangle model, the probability depends on the tangle geometry. See the website (long pdf) for estimates. As a consequence, mixing matrices are unitary and the values for the mixing angles are, in general, larger for neighbouring generations than for distant generations.

Generally speaking, quantum numbers are topological properties of tangles, whereas the fundamental constants are due to average geometric properties of tangles.

The**"old** strand model" based (partially) on open knots, not on rational tangles, led to **wrong** predictions. It has been **falsified**, as mentioned several times. The "**new** tangle model", based on rational tangles (only), does not appear to have this problem. Also the Higgs and the Yukawa terms are reproduced: all Feynman vertices arise. The new tangle model predicts the lack of measurable deviations from the standard model.

Strands are not observable and cannot be cut, so one cannot say that they are "made of" something. In the strand conjecture, nature is made of one single strand. If you follow (in thought) one strand segment, you would arrive to the cosmological horizon, then go along the horizon, then come back to the interior of the universe somewhere else, continue to the horizon again, etc. In a sense, a strand segment is thus a part of everything. But strands/the strand have no parts.

--

Today is the first of April.

Imagine strands as fluctuating, scaled-down, uncuttable, massless, endless, knot-free, cooked spaghetti.

--

In the tangle model, only the known particles arise. In the tangle model (like in quantum theory),

In the tangle model, only three coupling constants arise. In the tangle model,

In the tangle model,

Generally speaking, quantum numbers are topological properties of tangles, whereas the fundamental constants are due to average geometric properties of tangles.

The

Strands are not observable and cannot be cut, so one cannot say that they are "made of" something. In the strand conjecture, nature is made of one single strand. If you follow (in thought) one strand segment, you would arrive to the cosmological horizon, then go along the horizon, then come back to the interior of the universe somewhere else, continue to the horizon again, etc. In a sense, a strand segment is thus a part of everything. But strands/the strand have no parts.

--

Today is the first of April.

Imagine strands as fluctuating, scaled-down, uncuttable, massless, endless, knot-free, cooked spaghetti.

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I imagine them as Loacker's vanilla and milk cookies!cschiller said:Today is the first of April.

Imagine strands as fluctuating, scaled-down, uncuttable, massless, endless, knot-free, cooked spaghetti.

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If all particles are unknots, can you show us an example configuration of strands that represents a chunk of 3D vacuum?

Is it something like this? (made with mathematica, 3x3 lines parallel to each axis, not intersecting)

Can you place your new paper on arxiv?

Now that particles are not knots, are strands allowed to move through each other?

Do they move deterministically (but we can just never know their detailed positions because they themselves are unobservable), or do they move stochastically?

Either way, what are the equations describing how the strands move, or if stochastic, what probability for each motion?

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http://www.motionmountain.net/Schiller-StandardModel-Constants.pdfHBrown said:Can you place your new paper on arxiv?

Not much math as you said. Very hard to make any sense of it.

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In the strand conjecture, particles are not unknots. Particles are rational tangles, i.e. tangles that can be undone by moving the tethers around in space, as illustrated e.g. in https://www.encyclopediaofmath.org/index.php/Rational_tangles. The motion of tethers also leads to interactions and to mixing. Strands cannot move through each other.

The vacuum picture is roughly right, but the (unobservable) "distance between strands" is*much larger* by *many *(over 30) orders of magnitude and they are continuously fluctuating in shape. Strands' (unobservable) "motion" is stochastic.

Because you asked, the most recent details are here: http://www.motionmountain.net/Strands-QED.pdf and http://www.motionmountain.net/Strands-Gravitation.pdf

The virus is starting to make trouble. See you afterwards.

The vacuum picture is roughly right, but the (unobservable) "distance between strands" is

Because you asked, the most recent details are here: http://www.motionmountain.net/Strands-QED.pdf and http://www.motionmountain.net/Strands-Gravitation.pdf

The virus is starting to make trouble. See you afterwards.

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cschiller said:The vacuum picture is roughly right

Can you walk us through your thought process for deciding there are no particles in that configuration?

More specifically, can you please define how one can _systematically_ take a strand configuration and extract what particles are represented. For example if someone made a computer simulation, we cannot just constantly turn to you and say "what is the total electric charge in this configuration?", "what is the total angular momentum in this configuration?", etc.

The assignment of particles and properties may make sense to you, but until it is clear and systematic so everyone can do it, it is not really well defined enough.

cschiller said:Strands' (unobservable) "motion" is stochastic.

Thank you. But that was only part of the question.

What are the equations describing how the strands move?

Based on what you have described so far, the following motion is allowed.

Is that correct?

cschiller said:particles are not unknots. Particles are rational tangles

I struggle for the correct word here, because it appears that what you point to as different particles are sometimes equivalent rational tangles. For example, the electron and W-boson assignment.

Or any of the W-bosons above the electro-weak symmetry breaking transition.

So calling them rational tangles is not sufficient. Because you are distinguishing things that are topologically equivalent. This needs to be better explained.

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Tonight I can only give a few answers.

Flat vacuum, as depicted, contains no matter, because there are no localized rational tangles, i.e., no regions where strands are tangled, i.e., there are no regions where strands are "forced to stay near each other if the tails are imagined to be ropes and pulled straight toward the outside". I think that this might make the point clearer.

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

Total angular momentum = orbital angular momentum + spin, as usual. Orbital angular momentum comes from the linear or circular motion of the tangle core. Spin magnitude is 1/2 for matter tangles, because they obey the belt trick: tethers are*tangled up* after rotation of the core by 2 pi; fermion tangles are not the same after a rotation of the core by 2 pi. Spin direction depends on rotation axis and rotation sense of tangle core.

Elementary fermions are rational tangles. Gauge bosons (unbroken) indeed are*not* rational tangles; unbroken gauge bosons are all *trivial* tangles. (I guess that is what you named "unknots".)

Flat vacuum, as depicted, also contains no radiation, because there are no radiation tangles, i.e., no regions that contain gauge bosons - thus no regions with untangled strands (trivial tangles) that are*curved* on average, over time.

The red motion is only allowed if the spin (the rotating crossing) of the red strand is transferred to some blue strand. If strands that are not straight on average (like the red strand on the left), they carry linear momentum and angular momentum, and thus energy. (The old image of a photon as a localised corkscrew on a strand that advances and rotates is rather good. But it can also jump to another strand.) Indeed, all this is hard to imagine and badly explained.

Spin magnitude is 1 for gauge bosons, because the tangle stays*the same* after a rotation by 2 pi of the curved region of the strand (in contrast to fermions). This is valid for photons, gluons, and the W_i bosons before SU(2) breaking. After symmetry breaking, the W differs from the electron: it is "flat at spatial infinity (i.e., 2d, all strands in the paper plane)", the electron is not. I will write more about the W and Z in the coming days - if the Coronavirus allows.

Flat vacuum, as depicted, contains no matter, because there are no localized rational tangles, i.e., no regions where strands are tangled, i.e., there are no regions where strands are "forced to stay near each other if the tails are imagined to be ropes and pulled straight toward the outside". I think that this might make the point clearer.

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

Total angular momentum = orbital angular momentum + spin, as usual. Orbital angular momentum comes from the linear or circular motion of the tangle core. Spin magnitude is 1/2 for matter tangles, because they obey the belt trick: tethers are

Elementary fermions are rational tangles. Gauge bosons (unbroken) indeed are

Flat vacuum, as depicted, also contains no radiation, because there are no radiation tangles, i.e., no regions that contain gauge bosons - thus no regions with untangled strands (trivial tangles) that are

The red motion is only allowed if the spin (the rotating crossing) of the red strand is transferred to some blue strand. If strands that are not straight on average (like the red strand on the left), they carry linear momentum and angular momentum, and thus energy. (The old image of a photon as a localised corkscrew on a strand that advances and rotates is rather good. But it can also jump to another strand.) Indeed, all this is hard to imagine and badly explained.

Spin magnitude is 1 for gauge bosons, because the tangle stays

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Then please define it clearly enough that we could program it in a computer then.cschiller said:Electric charge: 1/3 for each topologically chiral crossing (in minimal crossing projection) in a matter/fermion tangle. Charge can be determined by computer.

It currently seems to have no rhyme or reason to it, and you include no equations to make your ideas precise.

Here are three "rational tangles"

They look very similar, yet you assign them different charges, different spins, and wildly different masses.

Please write down explicitly some equations or computer code so that it would be possible for anyone to unambiguously determine these values themselves.

By your definition there, all three above should be fermions. But you assigned them otherwise.cschiller said:Spin magnitude is 1/2 for matter tangles, because they obey the belt trick: tethers aretangled upafter rotation of the core by 2 pi; fermion tangles are not the same after a rotation of the core by 2 pi.

...

Spin magnitude is 1 for gauge bosons, because the tangle staysthe sameafter a rotation by 2 pi of the curved region of the strand (in contrast to fermions).

Let's look at a concrete example.

Here is another diagram made with mathematica. In some sense it is the "mirror" of one of those tangles above, because the sequence of over/under crossings are the opposite. Does this make it the anti-particle of one the above "tangles"? Which one? What spin, and charge would you assign this?

What is forbidding this?cschiller said:The red motion is only allowed if the spin (the rotating crossing) of the red strand is transferred to some blue strand.

Can you at least agree that since this motion occurs without strands moving through each other, that you cannot derive all your consequences without positing some rules for how the strands move?

Then please just give us the equations describing how the strands move, so that we could try deriving consequences ourselves.cschiller said:Indeed, all this is hard to imagine and badly explained.

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Please be aware that although your blog may contain your most recent work it is not on topic here. The discussion on PF must focus exclusively on your peer reviewed publications. If you cannot answer a question from that material then you should not attempt to answer it here.cschiller said:Because you asked, the most recent details are here: http://www.motionmountain.net/Strands-QED.pdf and http://www.motionmountain.net/Strands-Gravitation.pdf

The virus is starting to make trouble. See you afterwards.

This thread was temporarily closed and is at risk of permanent closure if it cannot stay within the rules.

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The

The

The

Short definitions:

You wrote: "Can you at least agree that since this motion occurs without strands moving through each other, that you cannot derive all your consequences without positing some rules for how the strands move?"

There are rules on how (

Motion of curved strands cores that produce crossings through the flat vacuum is easiest to picture. Attach a phase arrow to it; then the core advances in a straight line and the end of the phase arrow produces a helical motion. This is like described, e.g., by arXiv:1910.11085 by Hestenes for fermions (see also his earlier papers). But all this is what the Dirac equation also says, already since almost a hundred years. So it is not new. And there is a similar imagery of a rotating advancing arrow also for photons.

One more remark about your previous question about the vacuum. Fluctuations can indeed tangle up and untangle the vacuum strands that you drew with Mathematica. The temporary tangle-antitangle pairs that arise through such fluctuations correspond to virtual particle-antiparticle pairs.

*

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In the abstract of https://dx.doi.org/10.1134/S1063779619030055 , the statement is about woven strands forming black hole horizons. This is an old idea found scattered in the literature. In fact, many people have stated already decades ago that the surface dependence of black hole entropy is explained by extended constituents. That these entities are "woven" just derives from the idea that (crossings and) crossing switches are the physical observables.

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Let's start at the foundations.

It is trivial to see that all three of those tangles can be made to look locally the same, and then straight segments going off to infinity. Indeed you admitted the difference between the electron and W is "at spatial infinity".

My point though is that all THREE can be made to look locally the same where the "tangle" is localized, and then straight segments going off to infinity.

This causes two problems:

1) we cannot locally determine if something has charge

2) we cannot locally determine if something is a fermion or boson

You may call something an electron, but its strands curve differently off beyond our galaxy, making it actually a boson, or a neutrino.

If you feel we are misunderstanding. Again, I implore you, provide your meaning clearly in math so that _anyone_ can play with your ideas and test out predictions themselves.

Let us try to elevate this discussion to the precision of math.

Can we describe your setup in the following way?

We start with a flat unobservable background spacetime. For some finite spherical region of space, but "macroscopic" (i.e. R >> Planck scale) there are N strands which we can define with parametric equations, strand_i : (s,t) -> (x,y,z). Where i indexes/labels the strands 1 to N, the variable s is some parameterization along the strand (say length), and t,x,y,z are coordinates in the background space-time. It is a requirement of your theory that each strand_i terminates on the spherical surface.

A rough overview as I understand it.

Your belief is that given such a configuration at time t_0,

1) you can describe the particle content at that time

2) you can point out all the crossings

and that moving forward in time

3) the motion of the strands is stochastic (besides "do not cross each other", these details appear unknown)

4) you can point out all the crossing switches

5) only these switches are observable

-- even larger leap you seem to not acknowledge --

without even knowing how to describe the motion of the strands, you claim you can derive how these strand motions lead to the following

6) somehow the observable switches give rise to a derived space-time which is observable

7) somehow all the of GR is derived

8) somehow all of standard model is derived

It is too much to do all at once, so let's focus on #1 first, so no need to discuss kinematics at the moment.

You state confidently that you have systematically characterized all possible particles. But there are plenty of more tangles possible. So can you describe _mathematically_ how your characterization works? For instance, why are you confident that there are no particles with 237 strands cores?

Let's break this down even further:

If I give you all the parameterized strand_i for some time t, can you describe _mathematically_ how to calculate the charge in this volume?

Since your particle assignment seems to need no more than three strands, is it possible to break this up into:

total charge Q = sum_{all possible choices of three strands, i<j<k} charge_of(strand_i, strand_j, strand_k)

that is

Q = sum q_ijk

where q_ijk is the charge assigned to the configurations of the strands i,j,k ?

Is so, then you only need to state how to calculate q_ijk.

If you can provide this, it would be the first step in making your particle assignments rigorous.

This is exactly why you need to start responding in math instead of making up new terms you do not clearly define.cschiller said:Theleftone (electron neutrino) is almost massless: it is localized, but a straight strand can be "pulled away". The tangle is chiral, but nottopologicallychiral.

A) It is not clear what is meant by "a strand can be pulled away", as the three diagrams are so similar any interpretation of this appears to be true for the others.

B) It is unclear what you mean by "chiral, but not

If how "localized" the tangle is affects its mass, it is unclear how any of those tangles are more localized than the others ... and definitely not orders or magnitude more "localized".

It appears what you are saying doesn't fit together.

This makes no sense. Why do you demand the whole core (all three strands) rotate for the others, but here suddenly only require rotating one of the stands.cschiller said:Therightone (W) ... It has spin 1, because you can put rotate its core (curved region, just one strand needs to be rotated) by pi and return to the original tangle. This is not possible with the previous 2 tangles.

If I rotate the diagram 2pi, I will need to rotate another 2pi before the belt trick can be used.

Yes, those strands are straight.cschiller said:If the strands are straight in your Mathematica drawing, it is an electron neutrino or antineutrino, depending on chirality.

And now I KNOW you are completely making it up as you go.

Because those three strands are three from what you previously called vacuum.

Your definition of a particle is so vague it is completely unclear to me how you can have a vacuum.

What you previously called empty, you are now claiming is actually filled with neutrinos.

If this doesn't make it clear to you why you need to be more systematic and precise in your definitions, I'm not sure what will.

- #27

1. Quantum numbers are *topological* properties of tangles. In mathematical terms, they are topological invariants.

2. Mass, coupling strengths and mixings are *geometrical* properties of tangles. They depend on 3d shape.

1. Quantum numbers are given by the tangle core topology. (Not by the tethers at the end of the galaxy.) To get electric charge, for each particle tangle, count the topologically chiral tangle crossings (in their minimal crossing projection, as always intended in knot theory) and divide by three. (This is as in usual physics: count particles and determine the charge of each particle.) Chiral means "different from its mirror"; topologically chiral means "cannot be deformed into its mirror". Defining topological invariants with analytical formulae from the strand shapes is a research field in itself; it is not helpful for understanding, because the shape must be specified, and the topological invariant is (by definition) independent of the shape. In knot theory, topological invariants are always defined in the way done here: by counting specific features.

2. The paper does not mention mass value calculation. But your intuition for mass values is not correct. Mass values are given by the number of crossing switches per time induced by fluctuations. It is easy to check that this value varies extremely, depending on the tangle topology and on the tangle geometry.

--

General remark: please take three ropes and play with them. You will notice a strong difference between the electron tangle and the electron neutrino tangle - even though their 2d projections look the same.

--

About the electron neutrino tangle (simplest version) and a portion of the vacuum. Yes, they are equal, as you wrote. But there still is a small difference, to higher order. And indeed, the similarity between vacuum tangle and electron neutrino tangle is one reason for the low mass of the electron neutrino.

About the charge of the neutrino: If you take three ropes, you will note that the neutrino tangle is not topologically chiral. You can find a projection in which it has only two crossings. And in that projection, the electron neutrino tangle is not topologically chiral.

About the W tangle: The explanation was not good. More to follow. Thanks for pointing it out.

Classification and number of strands in elementary particle tangles. In 3d, rational tangles with large numbers of strands *decompose* into simpler rational tangles of 1, 2 or 3 strands. One gets a good intuition for this by playing with ropes.

*

2. Mass, coupling strengths and mixings are *geometrical* properties of tangles. They depend on 3d shape.

1. Quantum numbers are given by the tangle core topology. (Not by the tethers at the end of the galaxy.) To get electric charge, for each particle tangle, count the topologically chiral tangle crossings (in their minimal crossing projection, as always intended in knot theory) and divide by three. (This is as in usual physics: count particles and determine the charge of each particle.) Chiral means "different from its mirror"; topologically chiral means "cannot be deformed into its mirror". Defining topological invariants with analytical formulae from the strand shapes is a research field in itself; it is not helpful for understanding, because the shape must be specified, and the topological invariant is (by definition) independent of the shape. In knot theory, topological invariants are always defined in the way done here: by counting specific features.

2. The paper does not mention mass value calculation. But your intuition for mass values is not correct. Mass values are given by the number of crossing switches per time induced by fluctuations. It is easy to check that this value varies extremely, depending on the tangle topology and on the tangle geometry.

--

General remark: please take three ropes and play with them. You will notice a strong difference between the electron tangle and the electron neutrino tangle - even though their 2d projections look the same.

--

About the electron neutrino tangle (simplest version) and a portion of the vacuum. Yes, they are equal, as you wrote. But there still is a small difference, to higher order. And indeed, the similarity between vacuum tangle and electron neutrino tangle is one reason for the low mass of the electron neutrino.

About the charge of the neutrino: If you take three ropes, you will note that the neutrino tangle is not topologically chiral. You can find a projection in which it has only two crossings. And in that projection, the electron neutrino tangle is not topologically chiral.

About the W tangle: The explanation was not good. More to follow. Thanks for pointing it out.

Classification and number of strands in elementary particle tangles. In 3d, rational tangles with large numbers of strands *decompose* into simpler rational tangles of 1, 2 or 3 strands. One gets a good intuition for this by playing with ropes.

*

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- #28

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This in no way addresses the issue I pointed out.cschiller said:1. Quantum numbers are *topological* properties of tangles. In mathematical terms, they are topological invariants.

The electron, neutrino, and W tangles can be squished onto a plane just like your W tangle diagram, for as long as you want ... all the way out to the edge of the universe if you want, and then straight lines from there to infinity.

This means you cannot LOCALLY distinguish the tangle as boson or fermions, charged or uncharged.

Consider four strands (like on the edge of a square) going over under around the perimeter ... these do not decompose to any three strand core. Why is this not a particle?cschiller said:Classification and number of strands in elementary particle tangles. In 3d, rational tangles with large numbers of strands *decompose* into simpler rational tangles of 1, 2 or 3 strands. One gets a good intuition for this by playing with ropes.

Or consider weaving states with 4 strands, why are those not distinct particles?

If you want to say you can decompose these weavings into simpler weavings, then why can't I say the higgs is decomposed into multiple gluons, as the gluons are simpler 3-weaves than the higgs 3-weave?

Let's start smaller, can you show me exactly what the following look like:

W-

W+

electron-neutrino

anti-electron-neutrino

electron

positron

Do you have different tangles for right-chiral electron and left-chiral electron?

Define "core topology".cschiller said:1. Quantum numbers are given by the tangle core topology. (Not by the tethers at the end of the galaxy.)

Because as I explained the core tangles of e, w, neutrino can be made to look the same in a local region, and then just straight lines out to infinity. Does that not mean they have the same "tangle core topology"?

At the very least, the differ ONLY by how the strands go off to infinity. So that is the only thing you can use to distinguish them topologically.

That is what I took those terms to mean, but assumed you meant something else, because how you are using them does not make sense.cschiller said:To get electric charge, for each particle tangle, count the topologically chiral tangle crossings (in their minimal crossing projection, as always intended in knot theory) and divide by three. (This is as in usual physics: count particles and determine the charge of each particle.) Chiral means "different from its mirror"; topologically chiral means "cannot be deformed into its mirror".

You say the neutrino tangle is not "topologically chiral".

Here is are three strands in a neutrino geometry, and the parity transformed geometry.

Are you telling me these are topologically equivalent?

I see no way you can consider these topologically equivalent without thinking the electrons are topologically equivalent to their mirrors or positrons.

Then why do you not count the neutrino as having the same charge as the electron?cschiller said:In knot theory, topological invariants are always defined in the way done here: by counting specific features.

YOU were the one that mentioned mass calculation, and said it had to do with how localized the tangle core was.cschiller said:2. The paper does not mention mass value calculation. But your intuition for mass values is not correct.

By choosing different grouping of three strands, we could say space is filled with electrons and negative charge.cschiller said:About the electron neutrino tangle (simplest version) and a portion of the vacuum. Yes, they are equal, as you wrote. But there still is a small difference, to higher order. And indeed, the similarity between vacuum tangle and electron neutrino tangle is one reason for the low mass of the electron neutrino.

None of this is making sense. Adding extra ad-hoc explanations as you go is making it worse.

- #29

To make it even clearer to you: yes, the two drawings are topologically the same. You can find projections where they look the same. (Just try.) But you

Your statement "you cannot LOCALLY distinguish the tangle as boson or fermions, charged or uncharged" is not correct. This is unfortunate, as simply playing with three ropes would tell you that it is not correct. We can continue the discussion when you did.

- #30

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Sure, here is a viewpoint showing two crossingscschiller said:The images of the neutrino tangle that you show are *not* in the minimal crossing projection. Their minimal projection hastwocrossings, that of the electron tanglethree. This is a big difference.

But since two of the electron stands could be straight and meet your above/below paper requirements, then I can do the same for the electron as well.

As I said: I see no way you can consider these topologically equivalent without thinking the electrons are topologically equivalent to their mirrors or positrons.

Okay, I see, maybe I am taking your drawings too literally there. Is that the problem? If so, I think I am starting to understand better.

But that seems to make other things worse. Because a neutrino can also look like:

And so it appears impossible to have vacuum not appear as full of neutrinos.

And a photon can have zero crossings.

You say you want to use "topological invariants", but then you label things in a way inconsistent with this.

Why isn't the muon charge -2, since it is the electron + 3 more crossings? No matter how you assign +/-(1/3) to those crossings, they will not add to zero.

---

Furthermore, this is still ignoring the bigger issue.

The electron, neutrino, and W tangles can be squished onto a plane just like your W tangle diagram, for as long as you want ... all the way out to the edge of the MilkyWay if you want, and then straight lines from there to infinity.

This means you cannot LOCALLY distinguish the tangle as boson or fermions, charged or uncharged.

Simply playing with three ropes would tell you that what I am saying is correct. (Try it.)

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- #31

Now the next step. That is the

There is

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

Just to be clear:

- #32

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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.cschiller said:So now we finally agree thatelectron neutrinotangles are chiral butnottopologically chiral and that thus assigning zero electric charge makes sense. Phew, that took quite some time!

Now the next step. That is theelectrontangle. Please draw it in Mathematica or make one with ropes.

There isnoprojection that has only two crossings.

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

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

That does not sound like consistent characterization of particles to me. If it was consistent, then you would call that vacuum, not a photon.cschiller said:Another topic you brought up: Aphotontangle 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.

It looks like it is not possible to distinguish vacuum from photons and neutrinos everywhere.

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 ?cschiller said:Just to be clear:Crossing numberis 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 thechiral 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.

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?

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- #33

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.

The simplest case is the

The more complex case are

Let us start with the

But the

For the

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

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- #34

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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.

- #35

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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?

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.

So let's try to agree on some basics.

In John Conway's definition, ann-tangleis a proper embedding of the disjoint union ofnarcs into a 3-ball; the embedding must send the endpoints of the arcs to 2nmarked 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 )

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:

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