Pedagogical. For physicists, the best introduction to the strand tangle model is the preprint showing how wave functions, quantum theory, fermions and bosons, the three gauge interactions, the three elementary particle generations and unique elementary particle masses follow from strands. A longer introduction is found on this page.
Wave functions and interactions. A single principle is used to derive the Schrödinger equation, the Pauli equation and the Dirac equation. Spin 1/2, fermion behaviour, mass and, above all, the observed elementary particles and the observed gauge interactions are deduced - without any modification.
Complete. The strand tangle model explains why all measurements are electromagnetic, why only massive particles can have electric charge, why the spin-statistics theorem holds, and why the origin of gauge interactions settles the Yang-Mills millennium problem. (The latter topic is also explained here.) In short, it is shown that all "laws" of physics are uniquely defined, without any possible variation or alternative. There is only one possible universe.
From 9 lines to 1 line. In 2022, the strand tangle model, with its one line, explains about 8.2 lines of the 9 lines that describe all of physics and of nature. The strand tangle model also agrees with all experiments. The remaining constants of line 9 still have to be deduced. The task is not finished. But: no other theory in the literature has achieved this much. (In fact, two other approaches have similar results. The octonion model by Singh, arxiv.org/pdf/2206.06911.pdf, and Connes' non-commutative geometry, arxiv.org/pdf/1004.0464.pdf, both explain more than 8 lines, but both appear to predict additional unobserved particles. A more detailed evaluation is found here.)
Using strands, nature is summarized in just 1 line: General relativity and the standard model are due to fluctuating strands of Planck radius, for which each crossing switch yields a quantum of action.
Qubits. The strand tangle model also shows how to give concrete meaning to Zizzi’s expression “it from qubit”: qubits can be modelled with strands. So can entanglement and decoherence. And gravity.
Lepton tangles. Use your mouse to play with the 3d visualizations of the three simplest tangles (derived in the various papers) for the electron neutrino, the muon neutrino, and the tau neutrino:
and the simplest tangles for the electron, the
muon and the tau:
All these beautiful 3d visualizations were realized with Blender by Aleksandr, by Lucas and by Mitchell.
Step 5a: The strand tangle model for the standard model of particle physics
Beautiful. When we look at the starry sky, we admire the vast space, the coloured twinkling stars, and the deep blackness. The strand conjecture proposes an explanation for their origin, their properties and their motion. The foundations of what we find around us – particles, space, horizons and colours of everything we see – are explained.
C. Schiller, A conjecture on deducing general relativity and the standard model with its fundamental constants from rational tangles of strands, Physics of Particles and Nuclei 50 (2019) 259–299. Download the published paper at dx.doi.org/10.1134/S1063779619030055. Read the published paper online for free at rdcu.be/cdCK7. Download the preprint here, with films.
Testable. The paper argues that modern physics arises, directly and inevitably, from the Planck scale. Below, the more pedagogical papers and preprints deduce additional experimental predictions and tests. A detailed list of experimental tests is found on the bet page, by clicking here.
Simple. The strand conjecture starts with deducing Dirac’s equation from Dirac’s trick for tangles. Then, tangle classification yields the particle spectrum. Tangle deformations yield, via the Reidemeister moves, the particle gauge interactions groups U(1), SU(3) and broken SU(2). Working out the details gives usual particle physics, with no additions, modifications, or omissions. More details are found on this page.
A compact introduction for physicists and physics students is C. Schiller, On the relation between the three Reidemeister moves and the three gauge groups, preprint on Researchgate at https://www.researchgate.net/publication/369794894.
C. Schiller, Testing a conjecture on the origin of the standard model, European Physical Journal Plus 136 (2021) 79. Download it at doi.org/10.1140/epjp/s13360-020-01046-8. Read the published paper online for free at rdcu.be/cdwSI. Download the preprint here.
Elegant. It is regularly claimed that the standard model is complex, incomplete or even ugly. The strand conjecture argues the exact opposite: all of particle physics is due to tangled strands fluctuating at the Planck scale. A single fundamental process appears to explain the principle of least action, the Dirac equation, the observed interaction spectrum, the observed gauge symmetry groups, the observed elementary particle spectrum, and the fundamental constants (masses, mixing angles, and coupling constants) describing them. The Lagrangian of the standard model arises, without modifications. Over 100 additional tests and predictions about particle physics beyond the standard model are deduced. They agree with all experiments. So far, no other approach in the research literature appears to make (almost) any of these predictions. Indeed, it appears that the explanation of the standard model using tangled strands is consistent, complete, correct, hard to vary, and unique. Above all, it is beautifully simple.
Step 5b: Quantum electrodynamics deduced from strands
Colours and beauty. The strand conjecture shows how the tangle model leads to quantum electrodynamics, including electricity, magnetism and optics. Over 40 tests for the conjecture are given. So far, they are all positive. In particular, the strand conjecture appears to allow approaching two old challenges: how to calculate the fine structure constant and how to calculate the lepton masses – both from first principles. The preprint uses the tangle model of particles to deduce estimates. The fine structure constant with its measured value 1/137.036(1) and the lepton masses, in particular the electron mass, are the ingredients that determine all colours, tastes, smells, sounds and most shapes around us. In other words: it is argued that tangles of strands generate all beauty in nature.
Presently, tangles lead to a crude estimate of the fine structure
constant that is correct within 30%. This is not good; but so far,
it is one of just two attempts worldwide to explain the value ab initio,
using a unified description of particle physics and general relativity.
The spinning electron tangle.
Fabrice Neyret, inspired by Jason Hise, produced two animations
showing two options for the spinning electron. Use your mouse to change
point of view:
The radius of the strands is the Planck length. The green bar is only added for better visualization; it shows the orientation of the electron. The tangle tethers reproduce spin 1/2 and fermion behaviour under particle exchange. The wave function arises from the blurring of the tangle crossings. The tangle details determine electric charge (every chiral crossing produces an electric charge e/3), parities (behaviour under mirror reflection and rotation reversal), lepton number (results from the 3 strands), mass (not visible directly, via the average rotation speed), electromagnetic coupling and the fine structure constant (through the statistics of tangle shapes), and the behaviour in particle reactions (due to the topology of the rational tangle). Positrons are mirror tangles rotating in the opposite sense. More details are found in the published paper on quantum electrodynamics linked a few paragraphs higher up, and also in the pdf found at step 4. No other model of the electron achieves all these explanations.
Here is the photon, showing its rotating phase:
Here is a topologically equivalent version, also showing the photon and its rotatig phase, animated by Mitchell Wieringa and seen from two different directions:
Step 5c: Quantum chromodynamics deduced from strands
Quarks and nuclei. The strand conjecture shows how the tangle model leads to the strong interaction, the quark model, gluon flux tubes, confinement and asymptotic freedom. The existence (new in 2022) of glueballs is predicted. Many other tests for the tangle model are deduced, including the lack of new generations, the lack of CP violation and the lack of deviations from QCD. All consequences agree with the data. In particular, the strand conjecture allows estimating the strong coupling constant and the quark masses ab initio.
Indeed, the tangle model is peculiar – to say the least.
Step 6: Cosmology deduced from strands
The universe. This and a subsequent preprint on cosmology complete the topic of gravitation. In the strand conjecture, the universe consists of a single closed strand that forms the cosmological horizon and also the particles and the space inside it. Over time, this strand gets more and more tangled. (As one reader said: the universe plays cat's cradle.) This description reproduces usual cosmology and leads to numerous tests and predictions: the universe expands; nothing – no matter, no radiation and no space – exists beyond the cosmological horizon; inflation did not occur; there are no cosmic strings and no higher dimensions; there is no non-trivial topology; there is no bouncing universe; there is just one universe; the luminosity of the universe is always limited by c5/4G; dark matter is not made of unknown elementary particles; if dark matter exists at all, it is made of known matter or black holes or both; dark energy, or vacuum energy, does exist and is a natural consequence of strands; the density of vacuum energy, the cosmological constant, is small; baryogenesis appears to be due to non-perturbative effects.
The strand description of cosmology is promising. However, calculating
the vacuum energy density remains a challenge.
Therefore, clarifying the relation of strands to modified gravity and to the baryonic
Tully-Fisher relation remains a challenge as well.
Particle size. As the animation at the very top of this page shows, there is no way to define the size of an elementary particle. The wave function describes its average extension. The electric charge describes its interactions; but the charge is a consequence of Planck-sized crossings. Finally, every electron has tethers reaching the cosmological horizon. In short, an electron is at the same time wave-function sized, of Planck size, and of the size of the night sky.
The same is valid for all other elementary particles. Their size is always described by their wavelength, by the Planck length, and by the size of the universe. Everything in nature has three sizes. But not more. And not less.
Blog. The blog on research about fundamental physics and strand tangles tells more about general ideas, past mistakes, objections, encountered difficulties, and progress.
T-shirt. An important motivation for strand research has always been the support for the ailing physics T-shirt industry. For decades, it has been desperate for new designs. Now they are available.
History. The strand conjecture is a side result of the free Motion Mountain physics book series, in particular of Dirac's spin 1/2 demonstration, of the principle of maximum force, of the strand explanation of back hole entropy, and of the meditation time offered by the Munich subway. Strands reduce the 9 lines describing textbook physics to a single principle (that fits on a T-shirt), and make clear predictions for experiments and calculations. If you want to bet about the outcomes, to evaluate your chances, to comment, or if you want to help with animations similar to these, write to email@example.com.
Technicalities. The strand conjecture reproduces the Lagrangians of the standard model and general relativity, explains the number of generations and the particle spectrum, deduces all Feynman diagrams and propagators, explains the gauge groups U(1), SU(2) and SU(3), explains the fundamental constants ab initio, solves the hierarchy problem, explains neutrino masses without a see-saw mechanism, solves the strong CP problem, predicts the validity of the standard model and of general relativity up to the Planck scale without any intermediate energy scale, implies that the weak interaction violates parity maximally, explains the equality of proton and positron charge, has no problems with anomalies, predicts no issues with baryogenesis, has no grand unification, has no supersymmetry, has no additional spatial dimensions, has no inflation, no inflaton and no dilaton, solves black hole and singularity issues, implies gravitational waves, has no dark matter particles, has a naturally small cosmological constant, solves various problems with gauge theories, answers Hilbert's sixth problem, and explains the principle of least action.
Several of these articles were supported by grants from the Klaus Tschira Foundation: Eur Phys J Plus, Indian J Phys, J Geom Phys, IJGMMP, Z f Naturf, dark energy preprint, emergent quantum theory preprint, first Bronshtein cube preprint.
Volume VI of Motion Mountain
Older work. A more extensive, more passionate, but also older and less precise presentation is the original text on the strand model. It was written as a research volume that continues the adventure of the five textbook volumes.
Strands in other languages
A `strand' is best translated in Dutch as draad, in French as fil, in German as Faden, in Italian as filo and in Spanish as hilo. The mathematical concept of `tangle' is best translated in Dutch as wirwar, in French as enchevêtrement, in German as Gewirr, in Italian as groviglio and in Spanish as enredo. A `tether' is best translated in Dutch as lijn, in French as lien, in German as Leine, in Italian as nesso and in Spanish, for example, as vínculo.
On the Planck limits as foundations of the strand tangle model
U. Hohm and C. Schiller, Testing the Minimum System Entropy and the Quantum of Entropy, Entropy 25 (2023) 1511.
A. Kenath, C. Schiller and C. Sivaram, From maximum force to the field equations of general relativity – and implications, International Journal of Modern Physics D 31 (2022) 2242019. This paper received an honourable mention in the 2022 competition of the Gravity Research Foundation.
C. Schiller, From maximum force to physics in 9 lines and towards relativistic quantum gravity, Zeitschrift für Naturforschung A 78 (2022) 145–159.
C. Schiller, From maximum force via the hoop conjecture to inverse square gravity, Gravitation and Cosmology 28 (2022) 305–307.
C. Schiller, Tests for maximum force and maximum power, Physical Review D 104 (2021) 124079.
C. Schiller, Comment on "Maximum force and cosmic censorship", Physical Review D 104 (2021) 068501.
Older papers on the topic can be found via Google Scholar and via ResearchGate.
On deducing general relativity from strand tangles
C. Schiller, Testing a microscopic model for black holes deduced from maximum force, chapter in the book „A Guide to Black Holes“, Nova Science Publishers (January 2023).
C. Schiller, Testing a conjecture on the origin of space, gravity and mass, Indian Journal of Physics 96 (2022) 3047–3064.
On deducing the standard model from strand tangles
C. Schiller, On the relation between the three Reidemeister moves and the three gauge groups, International Journal of Geometric Methods in Modern Physics (2023).
C. Schiller, From points to fluctuating strands: advancing theoretical physics, online publication at Essentia foundation (2023).
C. Schiller, Testing a conjecture on quantum chromodynamics, International Journal of Geometric Methods in Modern Physics, 20 (2023) 2350095.
C. Schiller, Testing a conjecture on quantum electrodynamics, Journal of Geometry and Physics 178 (2022) 104551.
C. Schiller, Testing a conjecture on the origin of the standard model, European Physical Journal Plus 136 (2021) 79.
C. Schiller, A conjecture on deducing general relativity and the standard model with its fundamental constants from rational tangles of strands, Physics of Particles and Nuclei 50 (2019) 259–299.