The strand conjecture provides a simple, correct and complete model of relativistic quantum gravity.

pdf This simple introduction argues that strands are the only road to quantum gravity: C. Schiller, From the Bronshtein cube of limits to the degrees of freedom of relativistic quantum gravity.

pdfStrands are special: Uniqueness of the unified description of motion.

In the strand model, only switches of strand crossings are observable. Therefore, a black hole horizon is a thin spherical cloud:

strings vs strands

●  Summary of strand quantum gravity
●  Testable predictions of strand quantum gravity
●  Evaluation of strand quantum gravity
●  The fascination of strand quantum gravity
●  Bets and future tests
●  Similar ideas by other authors
●  Strand cosmology
●  Simple strands vs superstrings
●  Publications on strand quantum gravity

Summary of strand quantum gravity

Strands provide a microscopic model for space, black hole horizons, gravitons, and all other particles. Fluctuating strands of Planck radius allow deriving, from a single principle, the field equations of general relativity, wave functions, and the standard model. In the domain of gravity, the model explains gravitational mass, particles, gravitons and black hole radiation, prevents singularities, quantum foam and wormholes, reproduces cosmology, predicts the lack of elementary dark matter particles, and predicts the absence of new observable quantum gravity effects. Strands imply that the only experimental effects of relativistic quantum gravity are general relativity and the standard model of particle physics. So far, all predictions and tests of the strand tangle model agree with observations. All questions about quantum gravity at short scales are answered. Almost all questions about quantum gravity at large scales appear to be answered. Modifications of the strand model are not possible. As a result, the strand model is consistent, correct, complete and unique.


Testable predictions of strand quantum gravity

Despite reviews on testable predictions of relativistic quantum gravity, no relativistic quantum gravity effect – defined as an effect that includes G, ℏ and c – has been observed. Here is a list of issues taken from the many reviews and books on quantum gravity (Kiefer, Giulini, Rovelli, Oriti, Burgess, Donoghue etc.) – physical, mathematical, conceptual, philosophical – and how strands solve them.


Evaluation of strand quantum gravity

Strands are simple: All strand predictions are due to the fundamental principle and the implied lack of trans-Planckian effects.

Strands are consistent: strands confirm that there is no observable conflict between general relativity, perturbative quantum gravity, and quantum field theory. All of modern physics follows from strands.

Strands are correct: All strand predictions agree with data so far. All the predictions even have associated bets.

Strands are complete: no question of quantum gravity is unanswered. Well, two at lowest energy still are: Is MOND correct? Is dark energy constant in time? Both questions should be solved soon.

Strands are unique: no alernative to quantum gravity exists. No other model explains general relativity and the standard model.

If space were classical – i.e., continuous and without a minimum length – the standard model would not arise. Particles are defects of space. The defects can be classified.

Strands are boring: All theoretical and experimental predictions about quantum gravity are as expected. There is no room for science fiction. The research field does not promise any surprising result or effect.


The fascination of strand quantum gravity

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, drawn in black and white, is not shown.) With a bit of imagination, you can determine the location of the ergosphere.


Strands imply that everything is connected with everything else.

Strands imply that `every thing' is made of  `everything'.

Strands confirm that every spinor wave function is due to a few degrees of freedom of quantum gravity. An electron wave function is due to three blurred gravity quanta.

Strands confirm that elementary particles are defects in space.

Strands imply the standard model, without any modification.


Bets and future tests

In science, every statement must be checked continuously, again and again. This is ongoing. A sweeping statement like "strands explain quantum gravity" must be checked with particular care. If you have a counterargument or notice a missing issue, just send a note.

Strands predict that the only experimental consequences of quantum gravity are general relativity and the standard model of particle physics.

The proposed detailed predictions and bets on this dedicated web page are quite general. Finding any single observation falsifying the strand conjecture, or finding any alternative, correct and inequivalent description of quantum gravity – or of nature – wins the bet.

It might well be that the similarities between strand gravity and strand particle entanglement can be used to deduce connections between the two effects. This is a topic for the future. (See, e.g., Danielson, Satishchandran and Wald


Similar ideas by other authors

"Fluctuating lines" were proposed by Carlip. He writes "space at a fixed time is thus threaded by rapidly fluctuating lines" in arXiv:1009.1136.

Independently, similar ideas were published by Botta Cantcheff in "Spacetime Geometry as Statistic Ensemble of Strings", arXiv:1105.3658.

"Tetrahedral atoms of space" are explored by Oriti in arXiv:2112.02585. They are similar to (skew) strand crossings.

Asselmeyer-Maluga explored the motion of space between strands, instead of the strands themselves.

"Bit threads" of Planck size are being investigated since around 2016 by M. Headrick and several university groups to describe entanglement, entropy and holography.

These proposals for descriptions of the vacuum are equivalent to that with strands. (Therefore, strands can still be called the "only" road to quantum gravity.) However, the proposals differ because they have not continued yet to a description of matter and radiation particles. For example, none of these proposals contains a description of the graviton.

Donoghue, Ivanov and Shkerin argue that quantum gravity is possible. See The strand tangle model agrees.

In, John Donoghue gives a modern summary of quantum gravity. Strands agree.


Strand cosmology

A quick summary of the history and present state of the universe is given in the next two figures.

Strand unverse


Everything is made of strands

Everything strands

More details can be found in the preprint C Schiller, Testing a conjecture on cosmology and dark energy.


Simple strands vs superstrings

Both strands and superstrings imply gravity. The strand model differs from superstring theory in many ways. The strand model implies that there are no higher dimensions, no supersymmetry, no string tension, no E8 or SO(32) gauge groups, no GUT, no string action(s), no fundamental Lagrangian, no landscape, no moduli, no membranes, no compactifications, no dualities and no trans-Planckain effects. In the strand model, nature is neither continuous nor discrete. Compared to superstrings, strands have different definitions of wave functions, of Planck units, and of space-time. In the strand model, particles are tangles of several strands in three dimensions; in superstring theory, particles are oscillating superstrings or membranes in 10 or 11 dimensions. There are no anomalies in the strand model, so there is no need to add higher dimensions to get rid of them. Strands are featureless; superstrings carry fields and have tension. Particles and the vacuum state differ in the two approaches.

Superstring theory has no known basic principle(s). The strand model is based on a single fundamental principle. This principle explicitly contradicts superstring theory.

The strand model makes many testable experimental predictions, also on neutrino masses and the fundamental constants. Superstring theory makes almost none.

However, there is a way to reconcile strands and superstrings! See the appendix of this pedagogical text. Talk pdf


Publications on strand quantum gravity

The basis of strand quantum gravity was published in C. Schiller, Testing a conjecture on the origin of space, gravity and mass, Indian Journal of Physics 96 (2022) 3047–3064. Read the published paper online for free at   Download the preprint here.pdf


A dedicated discussion of black hole quantum gravity – published as a book chapter in 2023 – is C. Schiller, Testing a microscopic model for black holes deduced from maximum force.pdf


The first publication on strands was 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 the published paper at Read the published paper online for free at Download the preprint here, with films.pdf


Click here to learn how strands deduce both the standard model and general relativity.


*         *         *