### What happens beyond the standard model?

Welcome to Motion Mountain Research. The
grey-coloured pages propose a unified description of motion
– and of
fundamental physics – called the *strand conjecture* or the
*strand tangle model*, and compare its
consequences and predictions with experiments.
The strand conjecture describes all of nature with a single sentence:
**General relativity and the standard model are due to fluctuating strands of
Planck radius, for which each crossing switch yields a quantum of
action.**
So far, there are no disagreements from experiment, and a number of new explanations: the origin
of the elementary particles, the origin of the gauge interactions,
the origin of the fundamental constants - thus the origin of both
Lagrangians - and the origin
of the principle of least action are explained.

For an introduction to strands in 12 simple steps, see here.

For the comparison of the strand conjecture with experiment, click here.

For the textbooks on conventional physics (green pages), go here.

For commented scientific publications and preprints about strands, read further.

● The strand conjecture about
quantum mechanics

● The strand conjecture about the complete
description of nature

● The standard model of particle
physics deduced from strands

● Gravitation and
quantum gravity deduced from strands

● Quantum electrodynamics deduced from strands

● Quantum chromodynamics deduced from strands

● Cosmology deduced from strands

● Physics background

● Acknowledgements

### Summary: what happens beyond the standard model?

1. **All observations and all equations of fundamental
physics** follow from fluctuating strands with Planck radius that reach the
cosmological horizon.

Particles are rational tangles of strands, wave functions are blurred strand crossing densities, black hole horizons are blurred weaves of strands, space is made of blurred criss-crossing strands, and the three gauge interactions are due to the three Reidemeister moves of strands.

Assuming that each strand crossing switch produces a quantum of action ℏ, the complete
standard model of particle physics and full general relativity can be
deduced.
This includes deducing spinor wave functions, Dirac's equation, electromagnetic fields,
Maxwell's equations, the nuclear
interactions, the gauge groups U(1), SU(3) and broken SU(2),
the particle spectrum, the Higgs mechanism, CP violation, the full standard model Lagrangian (with Dirac neutrino
masses and PMNS mixing), curvature, the metric, Einstein's field equations, the Hilbert Lagrangian, and
cosmology. All deduced consequences agree with all data.
Strands predict – like textbook physics does
and like Bronshtein's physics cube does
– that there is *no physics* beyond the standard model and beyond
general relativity. Detailed experimental predictions are found on the dedicated page. They agree with all experiments so far.

2. **All fundamental constants** – number of dimensions, coupling constants, particle masses
and mixing angles – appear to follow from the strand tangle model and can be calculated.
No observation remains unexplained in fundamental physics.

### The strand conjecture about quantum mechanics

**Pedagogical.**
For physicists, the best introduction to the strand tangle model is the
latest preprint. It shows how wave functions, quantum theory, fermions and
bosons, the three gauge interactions, the elementary particle generations
and elementary particle masses follow from strands.

**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 in not
finished. But: no other theory in the literature has achieved this much.
(There are two approaches with similar results. The *octonion model*
by Singh (https://arxiv.org/pdf/2206.06911.pdf) explains more than 8 lines,
but appears to predict various unobserved particles. Connes'
*non-commutative geometry* (https://arxiv.org/pdf/1004.0464.pdf) also
explains about 8 lines in total, but it is not fully clear on lines 6 and
7, predicts the unobserved see-saw mechanism in line 8 and possibly
additional unobserved particles, and appears to predict the unobserved
unification of coupings in line 9. See here.)

### 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(2). 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
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, correct, hard to vary, and complete.

### Gravitation and quantum gravity deduced from strands

See also the page dedicated to quantum gravity.

**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
rdcu.be/czpom.

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 c^{5}/4G,
a momentum flow or force limit c^{4}/4G,
a mass flow limit c^{3}/4G,
and a mass to length limit c^{2}/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 c^{2}). 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 as a book chapter in early 2023 – 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 horizon at the poles is not shown.) With a bit
of imagination you can determine the location of the ergosphere.

### Quantum electrodynamics deduced from strands

**C. Schiller, Testing a conjecture on quantum
electrodynamics**,
*Journal of
Geometry and Physics* 178 (2022) 104551. Download the preprint
here.

**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
an impression:

**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
flattened):

### Quantum chromodynamics deduced from strands

**C. Schiller, Testing a conjecture on quantum
chromodynamics** (to appear).

**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 data. In particular, the strand
conjecture allows estimating the strong coupling
constant and the quark masses ab initio.

**The spinning motion of the simplest tangle of
the down quark.** Jason Hise also produced the animation for this
case:

Indeed, the tangle model is peculiar – to say the least.

### Cosmology deduced from strands

**C. Schiller, Testing a conjecture on cosmology and
dark energy** (preprint).

**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 c^{5}/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.

### Physics background

**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 c^{4}/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.

*

**Particle tangles.**
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.

*

**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, and of the strand explanation of back hole
entropy. 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 (click here for an evaluation
of your chances), to comment, or if you want to help with animations similar to these, write to christoph@motionmountain.net.

### Acknowledgements

Several of these articles and a number of related ones were supported by grants of the Klaus Tschira Foundation. (Eur Phys J Plus, Indian J Phys, J Geom Phys; QCD preprint - to appear, 9 line preprint - to appear, dark energy preprint, emergent quantum theory preprint, Bronshtein cube preprint.)

### 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.