Welcome to Motion Mountain Research. The grey-coloured pages propose a complete description of fundamental physics, called the strand conjecture, and compare its consequences and predictions with experiments.

Talk pdfTalk slides with an introduction to the strand conjecture, a complete description of motion. With five animations and experimental predictions. The slides explain the origin of the fine structure constant, of the electron mass and of all colours.

For an introduction to strands in 12 simple steps, see here.
For the comparison with experiment, click here.
For commented scientific papers and preprints on strands, read further.

• Summary
• The strand conjecture about the complete description of nature
• The standard model deduced from strands
• Gravitation and quantum gravity deduced from strands
• Quantum electrodynamics deduced from strands
• Cosmology deduced from strands
• Physics background
• Volume VI of Motion Mountain


1. It appears that all observations and all equations of fundamental physics follow from Dirac's trick at the Planck scale. The complete Lagrangian of the standard model – with Dirac's equation, Maxwell's equations, the nuclear interactions, their gauge groups, and the particle spectrum – as well as Einstein's field equations of general relativity with their Hilbert Lagrangian can be deduced. And they agree with all data.
2. All fundamental constants – coupling constants, particle masses and mixing angles – follow from Dirac's trick at the Planck scale. Nothing remains unexplained in fundamental physics.


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. Feel free to write, also if you want to bet about the experimental predictions. Click here for an evaluation of your chances. If you want to help with animations similar to those included here, write to christoph@motionmountain.net.


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 it at dx.doi.org/10.1134/S1063779619030055. Read it online for free at rdcu.be/cdCK7. Download the manuscript pdf here, with films.

Testable. The paper argues that all of modern physics arises, directly and inevitably, from the Planck scale. Below, the more pedagogical paper and preprints deduce even more experimental predictions and tests. A detailed list of tests is also found on the bet page, by clicking here.


The standard model 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. The Reidemeister moves yield the particle interactions. Working out the details gives 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 it online for free at rdcu.be/cdwSI. Download the manuscript pdf 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

pdfTesting a conjecture on the origin of space, gravity and mass (short version, to appear in 2021).

pdfTesting a conjecture on the origin of space, gravitation and mass (long version, preprint).

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 made. 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.

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 is not shown.) With a bit of imagination you can determine the location of the ergosphere.



Quantum electrodynamics deduced from strands

pdfTesting a conjecture on quantum electrodynamics.

Colours and beauty. The strand conjecture shows how the tangle model leads to quantum electrodynamics. 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 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):
Electron tangle 


Cosmology deduced from strands

A preprint on cosmology will appear here in the future, to complete the topic. 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 a reader said, the universe plays cat's cradle.) This description reproduces usual cosmology and leads to numerous tests and predictions. A few ones beforehand: the universe expands; nothing – no matter, no radiation and no space – exists beyond the cosmological horizon; the luminosity of the universe is always limited by c5/4G; dark matter made of unknown particles does not exist: if it exists at all, it is made of known matter or black holes or both; dark energy, or vacuum energy, does exist; the density of vacuum energy is positive and small; inflation did not occur; there are no cosmic strings, no higher dimensions and no non-trivial topology; there is no bouncing universe; there is just one universe.


Physics background

On gravitation, ideas from the following paper were used: C. Schiller, General relativity and cosmology derived from principle of maximum power or force, International Journal of Theoretical Physics 44 (2005) 1629–1647. Download it at doi.org/10.1007/s10773-005-4835-2. Read it online for free at rdcu.be/cdG3C.

The paper explains how the force limit F≤c⁴/4G implies general relativity. As a result, it became possible to state that the speed limit v≤c yields special relativity, the action limit W≥ yields quantum theory, and the force limit F≤c⁴/4G yields general relativity.

See also C. Schiller, Comment on "Maximum force and cosmic censorship", Physical Review D 104 (2021) 068501, 10.1103/PhysRevD.104.068501, free preprint at arxiv.org/abs/2109.07700.


On Planck limits, see: C. Schiller, Simple derivation of minimum length, minimum dipole moment and lack of space–time continuity, International Journal of Theoretical Physics 45 (2006) 213–227. Download it at doi.org/10.1007/s10773-005-9018-7. Read it online for free at rdcu.be/cdG3E.


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:
N1 N2 N3
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:

The quest for a complete, unified theory leads to a proposal with testable predictions, to ab-initio estimates of the W/Z and Higgs/Z boson mass ratios, and to a new ab-initio approximation for the fine structure constant and the other fundamental constants. 500 pages, 40 MB.

Here is a preview:

It can also be found at https://www.scribd.com/document/11598480.