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

Nature is made of strands with Planck radius. Thus, they are unobservable. Only switches of strand crossings are observable and define Planck's quantum of action. Therefore, a black hole horizon is a spherical weave of strands:

 
 

 
● Summary of strand quantum gravity
● Testable predictions of strand quantum gravity
● The fascination of strand quantum gravity
● Evaluation of strand quantum gravity
● Bets and dinner invitations
● Similar ideas by other authors
● Strand cosmology
● 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.
 

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Testable predictions of strand quantum gravity

Despite many attempts, no relativistic quantum gravity effect – defined as an effect that includes G, ħ and c – has ever been observed. The following 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.

• 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 C. Schiller, Tests for maximum force and maximum power, Physical Review D 104 (2021) 124079. Download the preprint here.  
• 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 the smallest length, space is continuous in all observations, without discontinuities, without graininess or any other granular structure, and without holography. There is no degradation of images, no space viscosity, and no observable space-time noise. Space does not induce particle diffusion. There is no double relativity and no deformed relativity. Space, when it is defined, has trivial topology – except for the black holes it contains. Space is stable against the formation of black holes.
• Strands imply and reproduce universal, inverse square gravity.
• Strands imply that gravitational fields are emergent. At Planck scales, strands predict gravitational fields for quantum superpositions. They have no special or surprising properties.
  
• Strands imply that gravitons exist and are made of two linked strands, and that they have spin 2 and vanishing mass. The strand model for the graviton implies and confirms that both black holes and curved space can be said to consist of (soft) gravitons, as told by Dvali in arXiv:1112.3359 and in "Occam’s Razor for Black Holes".
• Strands imply that gravitons cannot be counted or detected one by one. So far, every attempt to count gravitons failed. As reviewed by Arif and Shiekh in https://www.researchgate.net/publication/26510077, the classical gravitational potential only gets unmeasurably small corrections. As calculated by Berends in doi:10.1016/0370-2693(75)90608-5, gravitons do not induce a measurable correction to g-2.
• Strands imply and reproduce black hole physics, including black hole thermodynamics.
• Strands predict that the gravitational constant G does not run with energy (see Donoghue).
• Strands describe every quantum effect with crossing switches that each produces a quantum of action ħ. Every event, every observation, and every process is a quantum effect.
• Strands predict a minimum length and a minimum time interval in nature, given by twice the Planck values.
• 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 energy, the corrected Planck acceleration, the corrected Planck jerk and many others. All physical quantities are predicted to be bound by a Planck limit. All experiments so far agree.
• 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 in the Lagrangian, 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 https://link.springer.com/article/10.12942/lrr-2004-5 (and they disagree with Woodard). Strands also contradict asymptotically safe gravity, because strands state the non-existence of trans-Planckian energy values.
• Strands predict all usual properties of black holes. Horizons are strand weaves. Strands predict that the mass and charge of a black hole are located at its horizon. Therefore, strands predict that black holes have a moment of inertia. In particular, strands predict that the moment of inertia is MR^2, and thus differs from that of a thin mass shell. Strands also 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 that black holes have tethers but no hair. Strands predict the lack of black hole remnants after evaporation (apart from particles). Strands predict black hole entropy, the Bekenstein entropy bound, and a black hole g-factor of 2. Strands also predict that elementary fermions are not black holes, though similar to them.
• Strands predict that there are no deviations from the Unruh effect. Also, usual black hole thermodynamics arises.
• Strands explain the existence of gravitational mass of elementary particles as a consequence of virtual gravitons surrounding them and provide upper and lower limits for the mass values.
• Strands predict that there are no measurable deviations from the equivalence principle because, at the Planck scale, inertial and gravitational mass occur through the same mechanism: both mass values are due to Dirac's trick.
• Strands explain the particle and force spectrum of quantum field theory, and all the fundamental constants.
• Strands predict – because of the smallest length – that there are no singularities of any kind, no exception to the hoop conjecture and no exception 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; both are due to fluctuating discrete structures with the 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 as long as space and time are defined.
• 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 potentially provide a model for dark energy. More precise investigations show that it is unmeasurably small.
• Strands predict that no additional 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, or 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 that, therefore, such effects occur only at the (corrected) Planck scale in three dimensions.
• 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.
• Strands imply that spinor wave functions of elementary particles are due to the two or three fluctuating strands in fermion tangles. Wave functions are oriented crossing densities.
• Strands imply the standard model of elementary particle physics with massive neutrinos. Strands predict the lack of additional particles, forces, energy scales, symmetries, effects or any other modification. Strands imply that the fundamental constants – elementary particle masses, coupling constants, and mixings angles – are quantum gravity effects. Particle physics is an effect of quantum gravity.
• Strands imply that the only effects of quantum gravity are general relativity and the standard model with massive mixing Dirac neutrinos. Strands predict the lack of unknown physics laws or effects.
• In other words, the only measurable effects of quantum gravity are spatial curvature in three dimensions and elementary particles – with their masses, wave functions, properties, interactions, and Planck limits. In contrast, many researchers hope to find additional effects. If you ever find a new quantum gravity effect, the strand tangle model is falsified, and I'll invite you to dinner.
• In short, everyday colours – which depend on the fine structure constant and the electron mass – are effects of relativistic quantum gravity. But no additional effects of relativistic quantum gravity will be found.

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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 tangle model. (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 with massive Dirac neutrinos, without any modification.
 

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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. Strands suggest that MOND is not correct, that dark energy vanishes.

Strands are unique: no alternative 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 results or effects.
 

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Bets and dinner invitations

In science, every statement must be continuously tested. The detailed strand predictions and proposed bets listed on this dedicated web page are quite general. Strands predict that the only experimental consequences of quantum gravity are general relativity and the standard model of particle physics. Finding a single observation falsifying a single prediction of the strand tangle model, or finding any alternative, correct and inequivalent description of quantum gravity – or of nature – wins the bet. I also offer a money-back guarantee for donors.

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 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.105.086001)

Sweeping statements like "strands explain quantum gravity" or "strands describe nature" must be checked with particular care. If you have a counterargument or notice a missing issue, I'd like to hear about it. For any interesting argument, whether true or false, I'll invite you to dinner.
 

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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 under investigation since around 2016 by M. Headrick and several university groups to describe entanglement entropy and holography.

All these proposals for descriptions of the vacuum are subsets of the strand tangle model. (Therefore, strands can still be called the "only" road to quantum gravity.) However, the proposals differ because they have not yet continued 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 https://arxiv.org/abs/1702.00319. The strand tangle model agrees.

In https://arxiv.org/abs/2211.09902, John Donoghue gives a modern summary of quantum gravity. Strands agree.
 

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Strand cosmology

A quick summary of the history and present state of the universe is given in the figure.
 

 

More details can be found in the preprint C Schiller, Testing a conjecture on cosmology and dark energy. It suggests that dark energy does not exist. Given that strands also exclude elementary dark matter, strands support the timescape model by Wiltshire and collaborators and agree with the experimental results of Sarkar and collaborators.
 

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Strands vs superstrings

Both strands and superstrings imply gravity. The strand model is three-dimensional and simpler: strands imply that there are no anomalies, no higher dimensions, no string tension, no supersymmetry, no larger gauge groups, no fundamental Lagrangian or action, no landscape, no moduli, no membranes, no compactifications, no swampland, and no dualities. Compared to superstrings, strands have different definitions of wave functions, of elementary particles, of gauge interactions, and of empty space-time. Strands are featureless, whereas superstrings carry fields and have tension. In the strand model, particles are tangles of several strands in three dimensions. In superstring theory, particles are oscillating superstrings or supermembranes in higher dimensions.

Nevertheless, there is a way to reconcile strands and superstrings. It is presented in the appendix on strings of this pedagogical text.

The single fundamental principle of strand model yields testable experimental predictions, specifically, on the number of gauge interactions and their gauge groups, on the elementary particle generations and their particle spectrum, on neutrino masses and the fundamental constants, and on the observation of new physics.

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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 rdcu.be/czpom.   Download the preprint here.

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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.

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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 dx.doi.org/10.1134/S1063779619030055. Read the published paper online for free at rdcu.be/cdCK7. Download the preprint here, with films.

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

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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.

Strands are special: The uniqueness of the unified description of motion with strands is shown in even more detail in this preprint.

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