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

●  Summary of strand quantum gravity
●  Testable predictions of strand quantum gravity
●  Interpretation of strand quantum gravity
●  The fascination of strand quantum gravity
●  Similar ideas by other authors
●  Bets and future tests
●  Bibliography

Summary of strand quantum gravity

Strands provide a microscopic model for space, black hole horizons and gravitons. This model is consistent, correct, and complete. Strands allow to derive, from a single principle, the field equations of general relativity and wave functions - as well as the standard model. In the domain of gravity, the model explains gravitational mass, particles 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 many conclusions and predictions. So far, all tests 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.


Testable predictions of strand quantum gravity

Many reviews on testable predictions of quantum gravity exist. No quantum gravity effect has been observed. Taken from the many reviews and books on quantum gravity (Kiefer, Giulini, Rovelli, Oriti, Burgess, Donoghue etc.), here is a list of issues – physical, mathematical, conceptual, philosophical – and of how strands solve them.

Strands describe every quantum effect with crossing switches. Every event, every observation and every process is a quantum effect.

Strands confirm and predict that gravitation – like nature itself – has a power or luminosity limit c5/4G, a momentum flow or force limit c4/4G, a mass flow limit c3/4G, and a mass to length limit c2/4G. 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). Indeed, no observation exceeding these limits has ever been made. A publication about the various tests of these predictions is Physical Review D 104 (2021) 124079.   Download the preprint here.pdf

Strands predict that the gravitational constant G does not run with energy (see Donoghue).

Strands predict that no trans-Planckian effects occur in any experiment or observation (corrected with 4G instead of G). Strands predict the lack of physical speeds above c, the lack of curvature values above the corrected Planck limit (corrected with 4G instead of G), and the lack of mass densities above the corrected Planck limit. Strands predict that all corrected Planck limits hold for elementary particles, including the corrected Planck acceleration, the corrected Planck jerk and many others. All physical quantities are bound from above.

Strands predict that there are no observable deviations from general relativity (and its Hilbert Lagrangian) of any kind, at any sub-galactic distance: this prediction contradicts doubly special relativity, deformed special relativity, and all alternative approaches to gravity, including conformal gravity, twistor approaches to gravity, Palatini gravity, Gauss-Bonnet gravity, models with torsion, or models with higher derivatives.

Strands imply that quantum gravity is an (effective) perturbative quantum field theory based on the Hilbert Lagrangian. It is valid for all measurable energies. Strands also imply that the Hilbert Lagrangian is the exact Lagrangian of perturbative quantum gravity. Perturbative calculations are possible. There are no additional terms, of any higher order of the Ricci scalar, of the Ricci tensor, or of the Riemann tensor. Strands thus realize and confirm the summary given by Burgess (and they disagree with Woodard). Strands also contradict asymptotically safe gravity, but only in its numerical predictions based on trans-Planckian energy behaviour.

Strands predict that gravitons exist, have no mass, have spin 2, but that they cannot be detected. However, this prediction is much older than the strand model. So far, every attempted observation failed. As calculated in doi:10.1016/0370-2693(75)90608-5, gravitons do not induce a measurable correction to g-2. As reviewed by Arif and Shiekh in, the classical gravitational potential only gets unmeasurably small corrections.

Strands imply that gravitational fields are emergent. At Planck scales, strands predict superposition of gravitational fields.

Strands predict all properties of black holes. Horizons are strand weaves. Strands predict that the mass and charge of a black hole is located at its horizon. Therefore, strands predict that black holes have a moment of inertia. Strands predict the usual charge limit for black holes, their angular momentum limit, their magnetic moment limit, the hoop conjecture, and the Penrose conjecture. Strands predict the lack of remnants after evaporation. Strand predict that black holes have no hair. Strands predict black hole entropy, the Bekenstein entropy bound, and a black hole g-factor of 2. Elementary particles are not black holes.

Strands explain the gravitational masses of elementary particles and provide upper and lower limits for the mass values.

Strands explain the particle and force spectrum of quantum field theory, and all the fundamental constants.

Strands predict that there are no deviations from the Unruh effect. Also usual black hole thermodynamics arises.

Strands predict that there are no measurable deviations from the equivalence principle.

Strands predict that the corrected Planck values are the smallest measurable length and time intervals. The size indeterminacy of a physical system cannot be smaller than the energy indeterminacy divided by the maximum force. Strands thus predict that, despite a smallest length, space is continuous in all observation, without discontinuities, without graininess or any other granular structure, without holography. There is no degradation of images, no space viscosity, no observable space-time noise, and space does not induced particle diffusion. There is no double relativity and no deformed relativity. Space has (almost) trivial topology – though with holes given by the black holes it contains. Space is stable against the formation of black holes.

Strands predict – because of the smallest length – that there are no singularities of any kind, and no exception to the hoop conjecture or to weak cosmic censorship. Strands also predict the lack of cosmic strings, different vacuum states and domain walls.

Strands describe space similarly to wave functions. Both are continuous because of shape fluctuations, but contain fluctuating discrete structures with a smallest length. Strands predict that, at small scales, space has no higher or lower dimensions, no Euclidean space-time structure, no supergravity, and no observable exceptions to translation or rotation invariance. Space is continuous and isotropic. Frame-dragging occurs. Causality holds without exception.

Strands predict a trivial topology of space, the lack of time-like loops, wormholes, geons, cosmic strings, cosmic domain walls, dilatons, torsion, negative energy regions, and particle masses that vary over space and time.

Strands imply that the gravitational memory effect is not a change in the structure of space (Gibbons 2017), but an effect on the relative position of bodies.

Strands provide a model for dark energy.

Strands predict that no new quantum gravity effects will ever be observed, such as the detection of single gravitons, the quantum interference of gravitational fields, microscopic black holes, fermionic coordinates, non-commutative spacetime, causal sets, spin networks, simplices, superstrings, ribbons, string nets, twistors, different vacua, positive results in the SpaceQUEST satellite experiment, quantum gravity effects in table-top experiments, or quantum gravity effects of the vacuum on distant galaxy images. Gravity does not violate CP symmetry. There are no inflatons, dilatons, and similar particles.

Strands predict that no new non-perturbative quantum gravity effects will ever be observed. Strands predict that all such effects (such as particle masses and related properties) are already known. Strands imply that the only non-perturbative effects are due to the tangling of strands, and thus that such effects occur only at the (corrected) Planck scale.

In cosmology, strands imply a cosmological horizon and an expanding universe. Strands predict the absence of inflation and of any unknown elementary dark matter particle. Strands also imply that the universe's integrated luminosity never was and never will be larger than c^5/4G.


Interpretation of strand quantum gravity

Strands are simple and consistent: All strand predictions are due to the fundamental principle and the implied lack of trans-Planckian effects. In particular, strands confirm that there is no observable conflict between general relativity, perturbative quantum gravity, and quantum theory. All follow 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 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'.


Similar ideas by other authors

"Fluctuating lines" were proposed by Carlip: "Space at a fixed time is thus threaded by rapidly fluctuating lines" says arXiv:1009.1136. Independently, similar ideas were published by Botta Cantcheff in "Spacetime Geometry as Statistic Ensemble of Strings", in arXiv:1105.3658.

"Tetrahedral atoms of space" are explored by Oriti, in arXiv:2112.02585. They are very similar to strand crossings.

These proposals for descriptions of the vacuum are equivalent to that with strands. However, they differ because the proposals have not continued yet to a description of matter and radiation particles. In fact, they even do not contain descriptions of the graviton.

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


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.

The proposed predictions and bets 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 deduced interesting connections between the two effects. This is a topic for the future. (See, e.g.,



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 – to be published in 2022 – is C. Schiller, Testing a microscopic model for black holes deduced from maximum force.pdf


The first publication 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