Skip to main content

A Conjecture on Deducing General Relativity and the Standard Model with Its Fundamental Constants from Rational Tangles of Strands


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 is a preview of subscription content, access via your institution.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.
Fig. 15.
Fig. 16.
Fig. 17.
Fig. 18.
Fig. 19.
Fig. 20.
Fig. 21.
Fig. 22.
Fig. 23.
Fig. 24.
Fig. 25.
Fig. 26.
Fig. 27.
Fig. 28.
Fig. 29.
Fig. 30.
Fig. 31.
Fig. 32.
Fig. 33.
Fig. 34.
Fig. 35.
Fig. 36.
Fig. 37.
Fig. 38.


  1. 1

    V. de Sabbata and C. Sivaram, “On limiting field strengths in gravitation,” Found. Phys. Lett. 6, 561–570 (1993).

    Article  Google Scholar 

  2. 2

    T. Jacobson, “Thermodynamics of spacetime: The Einstein equation of state,” Phys. Rev. Lett. 75, 1260–1263 (1995).

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. 3

    G. W. Gibbons, “The maximum tension principle in general relativity,” Found. Phys. 32, 1891–1901 (2002).

    MathSciNet  Article  Google Scholar 

  4. 4

    C. Schiller, “General relativity and cosmology derived from principle of maximum power or force,” Int. J. Theor. Phys. 44, 1629–1647 (2005).

    Article  MATH  Google Scholar 

  5. 5

    S. Carlip, “Dimension and dimensional reduction in quantum gravity,” Classical Quantum Gravity 34, 193001 (2017).

    ADS  MathSciNet  Article  MATH  Google Scholar 

  6. 6

    C. Schiller, The Strand Model—A Speculation on Unification, The Adventure of Physics—Vol. VI (Motion Mountain, 2009);

  7. 7

    R. P. Feynman, QED—the Strange Theory of Light and Matter (Princeton University Press, 1988).

    Google Scholar 

  8. 8

    E. Battey-Pratt and T. Racey, “Geometric model for fundamental particles,” Int. J. Theor. Phys. 19, 437–475 (1980).

    MathSciNet  Article  Google Scholar 

  9. 9

    J. Hise, Several animations visualizing the belt trick with multiple belts.

  10. 10

    A. Martos, Animation visualizing the fermion exchange behaviour of two tethered cores. 62143283.

  11. 11

    L. H. Kauffman and S. Lambropoulou, “On the classification of rational tangles,” Adv. Appl. Math. 33, 199–237 (2004).

    MathSciNet  Article  MATH  Google Scholar 

  12. 12

    K. Reidemeister, Elementare Begründung der Knotentheorie, in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Hamburg, 1926), Vol. 5, pp. 24–32.

  13. 13

    J. A. Heras, “Can Maxwell’s equations be obtained from the continuity equation?,” Am. J. Phys. 75, 652–657 (2007).

    ADS  MathSciNet  Article  MATH  Google Scholar 

  14. 14

    G. Egan, Two animations of the belt trick.

  15. 15

    L. H. Kauffman, Knots and Physics (World Sci., Singapore, 1991).

    Book  MATH  Google Scholar 

Download references


The author thanks Sergei Fadeev for his suggestion to avoid knotted tangles in the strand conjecture. The author thanks Jason Hise, Eric Rawdon, Tyler Spaeth, Jason Cantarella, Marcus Platzer, Antonio Martos, Ralf Metzler, Greg Egan, Andrzej Stasiak, Franz Aichinger, Thomas Racey, Peter Battey-Pratt, Klaus Tschira, and Louis Kauffman for support and suggestions. Above all, the author thanks his wife Britta, for everything. The author declares that he has no conflict of interest.

Author information



Corresponding author

Correspondence to Christoph Schiller.

Additional information

The article is published in the original.



Two animations show that tethered particles have spin 1/2, can rotate forever, and are fermions. These properties, intrinsically linked to the three-dimensionality of space, are important for the appearance of Dirac’s equation in the case of tethered tangles. The animations, cited in the paper, are included here with permission.

Tethering in three-dimensional space implies the equivalence of no rotation and rotation by \(4\pi \)—but not \(2\pi \). Tethering thus yields spin 1/2 behaviour and the possibility of tethered rotation to go on forever. The number of tethers is unlimited, as is easily checked. (Animation by Jason Hise [9]).

Tethering in three-dimensional space implies the equivalence of no particle exchange with double particle exchange—but not of simple particle exchange. Tethering thus yields fermion behaviour. The number of tethers is again unlimited, as is easily checked. (Animation by Antonio Martos [10]).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Christoph Schiller A Conjecture on Deducing General Relativity and the Standard Model with Its Fundamental Constants from Rational Tangles of Strands. Phys. Part. Nuclei 50, 259–299 (2019).

Download citation


  • strand conjecture
  • tangle model
  • quantum gravity
  • standard model constants
  • coupling constants
  • fine structure constant