The best introduction to the strand tangle model for physicists is the latest preprint. It shows how wave functions, quantum theory, fermions and bosons follow from strands.
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, all the observed elementary particles and all the observed interactions are deduced.
The paper also contains a note about the impossibility to solve the Clay millennium problem on Yang-Mills theory. In fact, it is not required to read the paper to see why. Whatever the complete theory of nature may be, that theory will explain that only the three observed gauge theories are possible in nature. However, the millennium problem asks to prove the existence of an infinity of gauge theories. This is in contrast with observation. The millennium problem also asks to define these quantum field theories with local operators (`point particles'). The existence of exact locality (below the Planck length) and of point particles (smaller than the Planck length) is also in contrast with observations. The impossibility of a solution of the millennium problem (that concerns nature) was known since the problem was posed.
For a physicist, working on the millennium problem - even reading about it - is a waste of time. The papers on this page and those on maximum force provide more details about why the millennium problem does not increase knowledge about quantum field theory.
The strand tangle model makes these arguments explicit. Strands show how the three gauge groups arise, show how the elementary particle spectrum and the three generations arise, and how the masses, mixing angles and coupling constants arise. All are coupled to the three-dimenionality of space and to its lack of continuity. In short, strands explain how quantum field theory arises. The strand explanation forbids other gauge groups, other particles, other dimensions, and even other values for coupling constants and masses.
In fact, the strand tangle model even suggests the lack of a finite mass gap for SU(3). The lack of glueballs is deduced in the preprint on QCD found later on this page. (Of course, this particular argument could contain an error.)
The strand conjecture about the complete description of nature
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 all of 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 tests is also found on the bet page, by clicking here.
The standard model of particle physics deduced from strands
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(w). Working out the details gives usual particle physics, with no additions, no modifications and no omissions.
C. Schiller, Testing a conjecture on the origin
of the standard model, European Physical Journal Plus
136 (2021) 79. Download it at
Read the published paper online for free
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, correct, hard to vary, and complete.
Gravitation and quantum gravity deduced from strands
C. Schiller, Testing a conjecture on
the origin of space, gravity and mass,
Indian Journal of Physics 96 (2022) 3047–3064. Read the published paper online for free at
Download the preprint here.
50 700 solar masses per second. Strands provide a microscopic model for space and horizons. This allows to derive the field equations of general relativity and a model for quantum gravity. Numerous tests of the strand conjecture in the domain of gravitation and quantum gravity are deduced, starting from a single principle. All tests agree with observations so far.
For example, strands confirm that gravitation – like nature itself – has a power or luminosity limit c5/4G, a momentum flow or force limit c4/4G, a mass flow limit c3/4G, and a mass to length limit c2/4G. The limits are given by one quarter Planck mass per Planck time, or 50 756 solar masses per second (times c-1, times c, or times c2). No observation ever exceeded these limits.
Many predictions about gravitons and quantum gravity are deduced, including a direct derivation of black hole entropy from strands. Above all, strands also explain the gravitational masses of elementary particles and provide upper and lower limits for the mass values. All predictions agree with data.
Strands seem to be the simplest quantum gravity proposal in the literature. Strands agree with and predict all observations: strands provide a microscopic model of space, black hole horizons and gravitons, explain mass, particles and black hole radiation, imply general relativity without modifications, prevent singularities and wormholes, reproduce cosmology, but predict the lack of elementary dark matter particles. Strands are also complete: no question of quantum gravity is unanswered.
A specific discussion of black hole quantum gravity
– to be published in 2022 – is
C. Schiller, Testing a microscopic model for black holes deduced from maximum force.
Any complete description of nature has to be strange. To satisfy this requirement for gravitation, the following animation, made by Jason Hise, shows how black hole rotation is modelled in the strand conjecture. (The flattening of the black and white horizon is not shown.) With a bit of imagination you can determine the location of the ergosphere.
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
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.
The spin of leptons. Tangles of strands reproduce
spin. Leptons consist of three strands. The animation by Jason Hise gives
The spinning electron tangle. Strands are not
observable, only crossing switches are. Every chiral crossing produces an
electric charge e/3. Jason Hise produced an animation for the spinning
electron (though neither the tangle nor the strands should be
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 lack 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 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.
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 made of unknown elementary particles does not exist; 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 to modified gravity and to the baryonic
Tully-Fisher relation is a challenge as well.
Maximum force and power. The strand model is based on a result that is older and unrelated to strands: the maximum force in nature with the value c4/4G. For details and publications, see the dedicated web page on maximum force and maximum power.
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 a number of black hole and singularity issues, implies gravitational waves, has no dark matter particles, has a naturally small cosmological constant, solves various problems about gauge theories, answers Hilbert's sixth problem, and explains the principle of least action.
Several of these and a number of related papers and preprints were supported with grants of the Klaus Tschira Foundation. (Eur Phys J Plus, Indian J Phys, J Geom Phys; QCD preprint, Dark energy preprint, 9 line preprint, Emergent quantum theory preprint.)
Images of the three conjectured neutrino tangles:
Note the similarity of the electron neutrino tangle with three loose strands. This is one reason for its low mass value.
Images of the conjectured tangles for the electron, the muon and the tau:
These tangles, together with the quark tangles and the elementary boson tangles, appear to reproduce all Feynman diagrams of the standard model. (Can you help producing 3d pictures that can be rotated by a html viewer?)
Blog. The blog on research about fundamental physics and tangles of strands tells more about general ideas, past mistakes, objections, encountered difficulties, and progress.
T-shirt. An important motivation has always been the support for the ailing physics T-shirt industry. Since decades, it has been desperate for new designs.
Volume VI of Motion Mountain
History. 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. The present edition has been updated with most results from the above preprints, and it also presents and corrects the errors of the past:
Here is a preview:
It can also be found at https://www.scribd.com/document/11598480.