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Tangles of strands - a conjecture

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This paper will make you enjoy physics and nature. All of it.

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 motion and their properties. The foundations of what we find around us - space, particles, horizons and colours of everything we see - are explained.

Free pdf of paperA conjecture on deducing general relativity and the standard model with its fundamental constants from rational tangles of strands. 59 pages, 8 MB. Published in Physics of Particles and Nuclei, vol. 50 (2019) pages 259-299.


Extension 1. This shorter preprint will make you enjoy the standard model of particle physics.

Free pdf of alphacalcA conjecture on the origin of the standard model and its constants. 24 pages, 1 MB.

Abstract. It is argued that a specific Planck-scale model of nature allows deducing the entire standard model of particle physics. First, it is shown how an idea by Dirac leads to a conjectured model for elementary particles. Then it is summarized how the conjectured model explains Dirac's equation, the observed particle spectrum of bosons and fermions, and the three observed gauge interactions. The specific models for the elementary particles appear to determine spin, quantum numbers, particle masses and mixing angles. The conjecture appears to imply the observed propagators, the observed Feynman diagrams and all terms of the full Lagrangian of the standard model. Modifications or extensions of the standard model appear to be excluded. Predictions deduced from the conjecture are listed. They agree with all observations performed so far. The particle models imply specific processes at the interaction vertices. The vertex processes in turn suggest ways to perform ab initio calculations of the coupling constants. An approximate calculation of the fine structure constant arises, as well as ways to improve it.


Simplicity, beauty, elegance. It is sometimes claimed that the standard model is 'ugly'. In contrast, the strand conjecture argues that the standard model is simple, unique, without alternative, and complete: the full, unmodified standard model is due to tangled strands fluctuating at the Planck scale. A single fundamental process appears to explain the observed interactions and their symmetry groups, the observed elementary particle spectrum, and the constants describing them. The explanation of the standard model is almost incredibly simple, consistent in all its aspects, and surprisingly hard to vary. That is not only beauty; it's elegance.


Extension 2. The following preprint tells how gravitation arises from strands.

Free pdf on strand gravitationA conjecture on the microscopic details of space and gravity. 25 pages, 1 MB.

Abstract. It is argued that a specific Planck-scale model for the microscopic degrees of freedom of space allows deducing the properties of black holes, the field equations of general relativity, and the masses of elementary particles. First, the conjectured Planck-scale model is shown to derive naturally from similar concepts that are known since a long time in quantum theory and black hole physics. Then it is shown that the conjectured model allows to derive black hole entropy, black hole energy, black hole temperature and black hole radiation. All other known black hole properties are derived. Using established arguments, the field equations of general relativity are derived. It is shown that no additions or modifications arise at subgalactic scales. An extensive list of experimental consequences is derived. All agree with data. The conjectured model also implies a maximum mass flow c^3/4G, a maximum momentum flow c^4/4G, and a maximum luminosity c^5/4G in all processes in nature. These limits, corresponding to about 50 000 solar masses per second, respectively times c and times c^2, are not exceeded by any known physical or astrophysical process. The conjectured model also allows visualizing quantum gravity effects, reformulating mathematical problems of general relativity, and deriving limits for elementary particle masses. No contradictions with observations arise.


Tests. Numerous experimental predictions - about electric dipole moments, graviton detection options, parity violation, additional elementary particles, new forces, supersymmetry, anomalous magnetic moments, glueballs, scalar mesons, and many more - provide tests of the tangle conjecture.


Objections. Feel free to contribute issues, criticisms or suggestions to the wiki found at


Naming. The tangle model promises to be a complete description of motion. The expression in italics is preferable to the more sensational terms that are used in other fields. The term 'theory of everything' is reserved for unsuccessful esoteric healing attempts, the term 'final theory' is reserved for titles of bad books and films, and the term 'world formula' is reserved for calculating the optimal way to park a car backwards.


Motivation. Some thoughts are found on my blog on fundamental physics and tangles and on my blog on teaching. Past discussions about the strand model can be found on this page. An important motivation has always been the support for the ailing T-shirt industry.


History. A more extensive, more passionate, but also older and less precise presentation (the tangle assignments for the gluons and leptons appear to be wrong, in retrospect, as are some statements on cosmology) is the original text on the strand model:

Free pdf of vol. 6 of Motion
The quest for a final theory leads to a proposal with testable predictions, to estimates of the W/Z and Higgs/Z boson mass ratios, and to a new approximation for the fine structure constant and the other fundamental constants. 480 pages, 36 MB.

The preview:


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. DOI: 10.1134/S1063779619030055

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.

C. Schiller, General relativity and cosmology derived from principle of maximum power or force, International Journal of Theoretical Physics 44 (2005) 1629-1647.

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