These research texts are about enjoying 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 properties and their motion. The foundations of what we find around us – particles, space, horizons and colours of everything we see – are explained.

pdfA conjecture on deducing general relativity and the standard model with its fundamental constants from rational tangles of strands. 59 pages.

Unification. The paper argues that all of modern physics arises, directly and inevitably, from the Planck scale. It was published in Physics of Particles and Nuclei, volume 50 (2019) pages 259-299,
At present, the clearest introduction to the strand conjecture might well be the preprint "Extension 3" on QED that is found below.


Tests. The paper and the following preprints about the strand conjecture provide numerous experimental predictions about electric dipole moments, Planck limits, parity violation, additional elementary particles, graviton detection, torsion, new forces, supersymmetry, grand unification, anomalous magnetic moments, glueballs, scalar mesons, neutrino masses, effects beyond the standard model, and dark matter. A longer list is given here.


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

pdfA conjecture on the origin of the standard model and its constants. 25 pages.

Simplicity, unity, elegance. It is sometimes claimed that the standard model is complex, incomplete or even ugly. In contrast, the strand conjecture argues the full, unmodified standard model is due to tangled strands fluctuating at the Planck scale. A single fundamental process appears to explain the principle of least action, the observed interactions and their symmetry groups, the observed elementary particle spectrum, and the constants describing them. This explanation agrees with all experiments. The explanation of the standard model using strands is almost incredibly simple, complete, surprisingly hard to vary, and truly elegant.


Extension 2, revised. This preprint tells how strands induce gravity – with predictions and experimental tests.

pdfA conjecture on gravitation. 35 pages.

50 000 solar masses per second. Strands provide a microscopic model for space and horizons. This allows to derive the field equations of general relativity. Many tests are listed. And strands confirm that gravitation – like nature itself – has a mass to length limit c2/4G, a mass flow limit c3/4G, a momentum flow limit c4/4G and a power limit c5/4G. 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 reached these limits. The momentum flow limit is usually called the maximum force.


Extension 3, revised. This preprint tells how strands induce electricity, magnetism and optics.

pdfA conjecture on quantum electrodynamics. 34 pages.

Colours and beauty. The strand conjecture shows how the tangle model leads to quantum electrodynamics. Numerous tests for the conjecture are given. In addition, 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 deduces rough estimates from the tangle model of particle physics. The approximations are still (early 2020) in progress. Coupling constants, in particular the fine structure constant 1/137.036(1), and lepton masses, in particular the electron mass, are the ingredients that determine colours, but also shapes, tastes, smells, sounds and rhythms around us. In other words: strands generate all beauty in nature.


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, 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, if not vanishing cosmological constant, solves various problems about gauge theories, answers Hilbert's sixth problem, and explains the principle of least action.


Betting. The description with strands is called a conjecture throughout. But in fact, it is more than that: the strand conjecture is a bet on the correct description of nature. The precise formulation of the bet is given here. "Bets" that support our non-profit will be considered.


Objections. It is hard to get accustomed to the idea that every particle has tethers. Feel free to contribute issues, criticisms or suggestions to the wiki found at or send them via email to


Background. The blog on research about fundamental physics and tangles of strands tells more about general ideas, past mistakes, encountered difficulties, and more. An important motivation has always been the support for the ailing T-shirt industry.


On gravitation, see also this paper: C. Schiller, General relativity and cosmology derived from principle of maximum power or force, International Journal of Theoretical Physics, vol. 44 (2005) pp. 1629-1647.


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 first tangle assignments for the Higgs, for the gluons and for leptons appear to have been wrong. The present edition has been updated with the results from the above preprints, but also mentions the errors of the past:

The quest for a complete, unified 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. 500 pages, 40 MB.

Here is a preview of the research text:


Dante on nature, topology and beauty:

Nel suo profondo vidi che s’interna,
legato con amore in un volume,
ciò che per l’universo si squaderna:

sustanze e accidenti e lor costume
quasi conflati insieme, per tal modo
che ciò ch’i’ dico è un semplice lume.

La forma universal di questo nodo
credo ch’i’ vidi, perché più di largo,
dicendo questo, mi sento ch’i’ godo.

Paradiso 33, 85-93.


The translation by Laurence Binyon (but remember: traduttore, traditore):

I beheld the leaves within the unfathomed blaze
Into one volume bound by love, the same
That the universe holds scattered through its maze.

Substance and accidents, and their modes became
As if together fused, all in such wise
That what I speak of is one single flame.

Verily I think I saw with my own eyes
The form that knits the whole world, since I taste,
In telling of it, more abounding bliss.

The translation by Henry W. Longfellow:

I saw that in its depth far down is lying
Bound up with love together in one volume,
What through the universe in leaves is scattered;

Substance, and accident, and their operations,
All interfused together in such wise
That what I speak of is one simple light.

The universal fashion of this knot
Methinks I saw, since more abundantly
In saying this I feel that I rejoice.