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Tangles of strands - a conjecture

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

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.

Abstract. It appears possible to deduce black holes, general relativity and the standard model of elementary particles from one-dimensional strands that fluctuate at the Planck scale. This appears possible as long as only switches of skew strand crossings are observable, but not the strands themselves. Woven fluctuating strands behave like horizons and imply black hole entropy, the field equations of general relativity, and cosmological observations. Tangled fluctuating strands in flat space imply Dirac’s equation. The possible families of unknotted rational tangles produce the spectrum of elementary particles. Fluctuating rational tangles also yield the gauge groups U(1), broken SU(2), and SU(3), produce all Feynman diagrams of the standard model, and exclude any unknown elementary particle, gauge group, and Feynman diagram. The conjecture agrees with all known experimental data. Predictions for experiments arise, and the fundamental constants of the standard model can be calculated. Objections are discussed. Predictions and calculations allow testing the conjecture. As an example, an ab initio estimate of the fine structure constant is outlined.


This shorter preprint will make you enjoy the standard model.

Free pdf of alphacalcA conjecture on the origin of the standard model, the fine structure constant and the other constants. 18 pages, 2 MB.

Abstract. The conjecture that particles are tangles of fluctuating strands appears to explain Dirac’s equation, the observed particle spectrum, the observed gauge interactions, the observed Feynman diagrams, and the full Lagrangian of the standard model. No modifications to the standard model appear to arise and no alternatives to be possible. The fundamental Planck-scale principle at the basis of the strand conjecture appears to enable an ab initio calculation of the coupling constants and of the other fundamental constants. An approximate calculation of the fine structure constant arises, as well as ways to improve it.


From beauty to elegance. It is sometimes claimed that the standard model is 'ugly'. In contrast, the strand conjecture argues that the standard model is incredibly 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 consistent and surprisingly hard to vary. That is not just beauty; it's elegance.


Nature. 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, including the colours of everything we see - are explained.


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 appears to be a complete description of motion. The expression in italics is much to be preferred to the more sensational terms that are used in other fields. The term 'theory of everything' is reserved for unsuccessful esoteric healing practices, 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 fascinating, but also older presentation (the tangle assignments for the gluons and leptons appear to be wrong, in retrospect) is the original text given here:

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:

By the way, Lubos Motl, the funny string theory blogger, explained in an email to me that this research was based, I quote, on "stealing ideas". Of course, this not the case. But probably this is the best compliment that a string theory fan can ever make.

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