The above animation by ronwnor is an example and a slight extension of Dirac’s trick. Dirac used the trick in his lectures, but never published anything about it. Imagine the strands to have Planck radius. Such strands thus are just thin enough to be unobservable in practice but thick enough to still be physical.

To be precise, Dirac’s trick shows a ħ/2 particle (or spin 1/2 particle for short), where ħ is Planck’s quantum of action. The quantum of action ħ is due to a crossing switch of strands, as this the only difference between the unrotated structure and one rotated by one turn. (Such structures are called tangles.) This was deduced by Kauffman in 1987.

The animation uses Dirac’s trick to realize and visualise spin 1/2. The rotating structure is a spinning fermion. Why? First, the structure comes back to the original state every two rotations. This is the definition of spin 1/2. Then, if you take two such structures and exchange their positions, the whole sets comes back to the original state only after two such exchanges (try it at home with two paper stripes!). This is the definition of a fermion.

This video was made by Antonio Martos. It is also found at at motionmountain.net/videos.html#fermion. Instead of a strip, you can substitute each edge by a strand, so that each strip is changed into two strands.

The animations are also interesting for a second reason: this is the only way to visualize a spin 1/2 particle. There is no other way - across the scientific literature. There are various attempts, but none succeeds in visualizing locality, spin 1/2, fermion behaviour, and particle countability. Of course, must always recall that the tethers are invisible, and that the fluctuating central structure is observable as a cloud, i.e., as a wave function.

In other words, spin 1/2 implies that particles are tethered - even though we do not see such tethers in everyday life. Spin is rotation, particles are tangles.

But the wonders go on. In Dirac’s trick, the little central triangle is chiral. So the structure represents a chiral fermion. Now imagine that the spinning particle is surrounded by a heap of untangled strands. (They represent the vacuum.) The chiral core will act like a screw or a maple seed, and advance. This visualizes a chiral fermion moving through vacuum.

If we imagine a little arrow attached to the central triangle, while advancing, the arrow will trace out a helix. The wavelength of that helix is the wavelength of a quantum particle. Dirac’s trick thus implies the wave-particle duality.

A particle with high momentum has many rotations per length. Every rotation of the arrow corresponds to a Planck quantum of action ħ. Dirac’s trick thus yields de Broglie’s wavelength! The energy E of such a particle then is the angular frequency 𝜔 times the Planck quantum of action ħ. This is Planck’s relation!

Now let us take Dirac’s trick and not forget the random shape fluctuations. We then only get and see a fuzzy cloud. The oriented crossing density of that cloud is what is usually called the wave function. If instead, we imagine the strands to be infinitely thin and the chiral rotating region to be as small as a point, recalling that the strands are unobservable, we get Feynman’s path integral description: we get an advancing point with a rotating arrow.

In both cases, combining the wave properties with the relations for energy and momentum E=p²/2m yields Schrödinger’s equation. But even more follows from Dirac’s trick.

The relation for energy and momentum allow defining an effective inertial mass value of the chiral fermion. Mass describes how frequently and how rapidly Dirac’s trick takes place when a particle moves. When the strands fluctuate, the motion of the animation at the top is in fact quite unlikely. The rotations is thus slow. Therefore, the tangle structure has an effective mass that is much smaller than the Planck mass. Dirac’s trick thus solves the mass hierarchy problem, the question why elementary particles have such tiny mass values. But there is more.

The curved regions in Dirac’s trick are, as a deeper investigation shows, the virtual gravitons surrounding the central mass. Dirac’s trick thus describes both inertial mass and gravitational mass. Therefore, the two are equal. This is the equivalence principle that Galileo and Einstein made popular. It forms the basis of general relativity.

And yes, the fermion can also advance by rotating through curved space. And yes, it follows geodesics. (Empty space is itself made of strands as well, but in contrast to particles, the strands are untangled.)

All this follows from Dirac’s trick. In simple words, Dirac’s trick implies quantum theory and general relativity. For strands of Planck radius, the specific structure in the animation above, with the chiral central triangle, is well known. It is usually called an electron. And yes, every electron in our body is connected to the border of space with unobservable strands. This is the strand tangle model - the tiny theory of physics.

In simple words, if you take seriously the ideas of Dirac and Kauffman, Dirac’s trick contains the main wonders of nature and of physics: both quantum physics and general relativity follow - from topology. Nature is a topologist’s dream.

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A popular introduction to the mentioned dream, the tiny theory of physics, is available here.
A short technical preprint is researchgate.net/publication/397264142.
A long technical preprint is researchgate.net/publication/361866270.
The preprints show that Dirac’s trick also implies the Dirac equation, the electric charge of the electron, and black hole rotation. Mathematically speaking, Dirac’s trick visualises the double cover of SO(3) by SU(2) and the behaviour of the unit quaternions.

AI systems are good at summarizing known facts and ideas, at providing references, and at being kind. They do not make fun of simple questions, they rarely mix politics into questions about science, and they react like a teacher with empathy, patience and a vast knowledge. Thus, AI systems are useful for learning topics quickly and efficiently. For young people, they are really helpful to catch up.

But what about research, especially research in fundamental physics? You might have seen videos of AI experts claiming that AI will soon “solve physics” - whatever that may mean - or that AI systems will “find quantum gravity”.

It appears that such hopes are premature. Just ask Gemini “Are you able to solve physics as a whole?” and it will answer negatively. But it will also mix hard facts and blabla.

Gemini writes about Gödel’s incompleteness theorem and makes other statements that have no relevance to physics. Above all, Gemini does not list the most important problems in modern physics: the origin of the coupling constants - including the famous fine-structure constant 1/137.0359991(1) - the particle masses, and the mixing angles.

Instead, Gemini lists an AI-generated paper on unification and a few approaches that have not brought any progress. Grok does not differ much.

In other words, AI is directing people to work on the same topics on which everybody is already working now. AI is thus reinforcing the mainstream, independently of whether it is successful or not. From a business perspective, this is OK. But from a research perspective, this is not helpful at all.

As an example, ask your favorite AI system: “Is the Planck length the smallest possible length?”. Grok will say “No.” Gemini will say something like “Probably no.” This is indeed the consensus of the last 127 years. However, the consensus is wrong, as explained on the web page motionmountain.net/minimumlength.html. When you ask Grok or Gemini about the issue, they claim that things that cannot be measured can still exist. Even though this might be the consensus, it is a deeply unscientific attitude. AI systems suggest the multiverse as useful, falsely suggest that quantum gravity is not renormalizable, and falsely suggest that there is not enough experimental data.

As another example, ask your favorite AI system to evaluate the strand tangle model or the latest text about it researchgate.net/publication/397264142. You will get an mixture of more or less incorrect arguments, all boiling down to the fact that the approach is not mainstream.

In short, the arguments provided by AI systems about research in fundamental physics are misguided, unscientific, and often wrong. But they reflect the consensus. As a result, AI systems direct the user into the same thinking habits that have been responsible for the lack of unification for the last 50 years. AI systems will neither “find quantum gravity” nor “solve physics”.

On the one hand, AI is useful for discovering literature references. On the other hand, AI does not help at all to think clearly or to advance into unchartered territory. AI systems, all trained on the consensus, are not innovative. AI is short for absent innovation. Only a good teacher, a good friend, and above all, yourself can encourage you to be innovative. As Kant put it: sapere aude!

Testing the uniqueness of a fundamental principle by comparing it with observations, excluding alternatives, and estimating elementary particle masses.

The text argues that the strand tangle model is indeed the only possible approach that unified general relativity and the standard model of particle physics with massive neutrinos.

The text summarizes how strands follow from nature’s limits for speed, action, entropy, and force. It is summarized how the two present theories arise. In almost all arguments, it it worked out that alternative constituents, alternative numbers of dimensions, alternative descriptions of quantum effects and wave functions, alternative gauge groups, alternative elementary particles, alternative Feynman vertices, alternative values of the constants of nature, alternative theories of gravitation, and alternative Lagrangians contradict nature’s limits.

But the text also shows that strands allow estimating particle masses, possibly the first such derivation from first principles.

Furthermore, the text also shows that only filiform constituents derive the principle of least action, again possibly for the first time.

Thus, only strands deduce general relativity and the standard model with massive neutrinos, and only strands solve the mass hierarchy problem - all this while agreeing with all observations.

Also for the first time, strands appeal to describe all observations, all laws, and all of nature, with full precision, using a single principle:

Enjoy.