Test and prediction score: 100% correct since
2014.

Even the faintest whisper about the unification of physics must stand up to experiment with new tests and new predictions. This page lists those high-precision predictions and tests that were deduced from the strand conjecture, or strand tangle model, by Christoph Schiller. The positive and negative aspects of strands are also evaluated. Donors who support strand research can get a money-back guarantee.

● Tests with
particle experiments – of part 1

● Tests with
gravity experiments – of part 2

● Theoretical tests – of parts
3 and 4

● Present limitations and timeline of the
predictions

● What speaks
**against** the strand conjecture

● What speaks
**in favour** of the strand conjecture

● **Support – with a money back guarantee for
donors and sponsors**

### Predictions about fundamental physics – in four short parts

**1. No deviation from the standard model of particle
physics** (with massive Dirac neutrinos and PMNS mixing) will ever
be observed. Thus also no exception to the invariant local limits c, ℏ and ℏ/c. (Part 1, based on
results
from
1973 that were simplified over time, agrees with all data.)

**2. No deviation from general relativity** (at
sub-galactic distances) will ever be observed. Thus also no exception to
the invariant local limits c, c^{5}/4G, c^{4}/4G,
c^{3}/4G and c^{2}/4G. (Part 2, based on results from
1915, 1973 and
corrected c. 2002, agrees with all data.)

**3. Every observation in elementary particle physics is
explained** by the fundamental Planck-scale principle of the strand
conjecture, i.e., by Dirac's trick at the Planck scale. No other,
inequivalent approach will achieve this completeness of explanation. The
assumptions are minimal, clear and unmodifiable. (Part 3, formulated
c. 2014, agrees with all data.)

**4. Calculating the fundamental constants of the standard
model** – the mass of the electron and of the other elementary
particles, the fine structure constant and the nuclear coupling constants,
and all mixing angles and CP phases – is possible with strands. No
other, inequivalent approach will achieve this calculation. (Part 4 was
formulated c. 2014 and agrees with all data – though one other
approach, by Tejinder Singh, is also trying hard.)

The research page lists papers and preprints explaining how these rather daring predictions arise from the fundamental principle. The rest of this page shows how to test and falsify both the predictions and the strand conjecture itself.

### Tests with particle experiments – of part 1:

- 1.1/2.1 If
*any*deviation from the 9 lines summarizing physics is ever discovered, the strand conjecture is falsified. - 1.2 If
*any*deviation of any kind is detected from the standard model of particle physics and its Lagrangian (with massive Dirac neutrinos and PMNS mixing) – such as a triple-Z or a triple photon vertex, neutrinoless double-beta decay, non-unitary scattering of W or Z bosons, non-unitary mixing matrices of quarks or leptons, or any deviation from quantum electrodynamics – the strand conjecture is falsified.In particular, the strand conjecture predicts the lack of results in the three research topics planned at the future circular collider – see the CERN paper

*FCC Physics Opportunities*, European Physical Journal C 74 (2019) 474 (with 1363 authors) – namely the search for unexpected phenomena around the Higgs and the electroweak gauge bosons, the search for new elementary particles, such as dark matter, and the search for tiny deviations from the standard model. If any such result arises, the strand conjecture is falsified.The strand conjecture also disagrees with the CERN report CERN-ESU-014 on the

*European Strategy for Particle Physics*(with over 70 authors): if it is indeed found that neutrino masses are a sign of new physics, or if new discoveries at higher energy are indeed made, the strand conjecture is falsified.The strand conjecture further predicts that all 43 proposals for physics beyond the standard model collected by the Snowmass 2021 theory frontier group (by over 100 authors) will disagree with future experiments (see also https://arxiv.org/abs/2301.06581). If any one of the proposals agrees with future data, the strand conjecture is falsified.

- 1.3 If
*any*unknown elementary particle is observed – including but not limited to a fourth generation lepton or quark, any unknown dark matter elementary particle, an additional elementary gauge boson, an additional Higgs boson, a supersymmetric partner, a sterile neutrino, an inflaton, a dilaton, a leptoquark, a magnetic monopole, a dyon, an anyon, a WIMP, or an axion – the strand conjecture is falsified. (New in November 2022: glueballs are predicted by strands.)In particular, the strand conjecture predicts the lack of results in the research topics listed by 33 authors in the CERN report arxiv.org/abs/1901.09966 on

*physics beyond the standard model:*if a dark photon, a light dark matter particle, a millicharged particle, a Higgs-mixed scalar, a heavy neutral lepton, or an axion-like particle is discovered, the strand conjecture is falsified. - 1.4 If
*any*deviation from the quark model or from QCD is observed – including scalar mesons not made of quarks, CP violation in additional hadrons, additional quark generations, incorrect hadron form factors, or wrong glueball quantum numbers or masses (new in 2022) – the strand conjecture is falsified. - 1.5 If
*any*unknown fundamental interaction or interaction property is discovered – including but not limited to a fifth force, any kind of grand unification, a new gauge group, CP-violation in the strong interaction, technicolor, supersymmetry, a new charge, a new conservation law, a new quantum number, additional spatial dimensions, the breaking of established symmetries, or any non-conservation in contrast with the standard model – the strand conjecture is falsified. - 1.6 If
*any*new fundamental constant is discovered in particle physics – thus in addition to the known masses, mixings and couplings – or if coupling constants, particle masses or mixing angles vary across the universe, the strand conjecture is falsified. - 1.7 If
*any*new energy scale in high energy physics is discovered – and thus the so-called energy desert is disproven, e.g., with a composite Higgs, a see-saw mechanism, or a GUT scale – the strand conjecture is falsified. - 1.8 If
*any*measurement whatsoever is ever realized without electromagnetism – i.e., using the nuclear or the gravitational interaction – the strand conjecture is falsified. - 1.9 If
*any*physical effect from quantities beyond the (corrected) Planck limits is observed – including but not limited to electromagnetic field values or speeds or accelerations larger than the (corrected) Planck limits, effects from singularities, effects of action values, length or time intervals smaller than the (corrected) Planck limits – the strand conjecture is falsified.Also if any physical speed above c, any physical action below ℏ, or any deviation from quantum theory is observed, the strand conjecture is falsified.

- 1.10 If
*any*elementary particle with energy larger than the (corrected) Planck energy is observed, or if the force limit is exceeded by strong fields or weak fields in neutron stars or quark stars or anywhere else, the strand conjecture is falsified. - 1.11 If
*any*future experiment helps to clarify the origin of the fundamental constants, the strand conjecture is falsified. - 1.12 If the tangle model of elementary particles is contradicted by future
observations in
*any*way – such as fundamental constants varying in space or time across the universe, large electric dipole moments, anomalous magnetic moments (such as that of the muon) that contradict quantum field theory or any of the additional tests mentioned in the papers and preprints found here – the strand conjecture is falsified. - 1.13 If instead of tangles of strands
*any other*(non-equivalent) substructure is discovered in elementary particles – such as preons, prequarks, knots, ribbons, rishons, Möbius bands, tori, vortices or any other localised or extended constituents – the strand conjecture is falsified.

### Tests with gravity experiments – of part 2:

- 2.1/1.1 If
*any*deviation from the 9 lines summarizing physics is ever found, the strand conjecture is falsified. - 2.2 If
*any*deviation of any kind is observed from general relativity (and its Hilbert Lagrangian) at sub-galactic distances – including doubly special relativity, deformed special relativity, different vacua, twistors, or conformal gravity – the strand conjecture is falsified. - 2.3 If
*any*local momentum flow or force larger than the corrected Planck limit c^{4}/4G or*any*local power/luminosity larger than the corrected Planck limit c^{5}/4G is observed, the strand conjecture is falsified. They correspond to about 50 700 solar masses per second. Also if*any*local mass flow larger than c^{3}/4G or*any*mass to length ratio above c^{2}/4G is observed, the strand conjecture is falsified. Also if physical speeds above c, singularities of any kind, curvature values above the corrected Planck limit, or mass densities above the corrected Planck limit are observed, the strand conjecture is falsified. - 2.4 If the gravitational constant G changes with energy, or deviations from the Unruh effect or from the equivalence principle are observed, the strand conjecture is falsified.
- 2.5 If the charge limit for black holes, their angular momentum limit, their magnetic moment limit, the hoop conjecture, or the Penrose conjecture is violated, the strand conjecture is falsified.
- 2.6 If any observed or observable property of any kind of black hole is in contrast with the strand conjecture, the strand conjecture is falsified.
- 2.7 If the corrected Planck values are not the smallest measurable length and time intervals, or if the size indeterminacy of a physical system can be smaller than the energy indeterminacy divided by the maximum force, the strand conjecture is falsified.
- 2.8 If
*any*new quantum gravity effect – such as the detection of single gravitons, the quantum interference of gravitational fields, microscopic black holes, fermionic coordinates, non-commutative spacetime, different vacua, positive results in the SpaceQUEST satellite experiment, or quantum gravity effects of the vacuum on distant galaxy images – is discovered, the strand conjecture is falsified. - 2.9 If the strand conjecture about gravitation is contradicted by future
observations in
*any*way – such as a non-trivial topology of space, time-like loops, wormholes, geons, cosmic strings, cosmic domain walls, dilatons, torsion, a number of dimensions different from three, negative energy regions, particle masses that vary over space and time, or any of the additional tests mentioned in the publication on the topic or on the dedicated web page on quantum gravity – then the strand conjecture is falsified. - 2.10 In cosmology, if inflation is confirmed, if any new elementary dark matter
particle is discovered (however, see the limitations below), or if the
universe's integrated luminosity is or ever was above c
^{5}/4G, the strand conjecture is falsified.

### Theoretical tests – of parts 3 and 4:

- 3.1 If
*any other*non-equivalent approach for unification ever agrees with experiment – including additional or grand unified gauge groups, technicolor, supersymmetry, preons, additional dimensions, see-saw mechanisms, supergravity, string theory, loop quantum gravity, M theory, membranes, ribbon models for elementary particles, causal dynamical triangulations, quantum foam, amplituhedrons, torsion, multiverse, knot models for elementary particles, micro-wormholes, non-commutative space-time, causal fermion systems, sedenions, Planck-scale black holes, but also any other, future unification approach – the strand conjecture is falsified. - 3.2 If
*any other*non-equivalent explanation for the mass hierarchy of elementary particles is found – i.e., one not due to tangle topology and shape – the strand conjecture is falsified. - 3.3 If the validity in nature of the principle of least action is
ever explained in
*any*way that differs from the strand conjecture – i.e., that differs from minimizing crossing switch number – the strand conjecture is falsified. - 3.4 If the elementary particle spectrum (with all quantum numbers) or the
elementary particle interactions (with their gauge groups and all other
properties) are
*not*determined by specific tangle families, their topological properties and their deformations, but by*any other, inequivalent structure*, the strand conjecture is falsified. - 3.5 If
*any concept*used in fundamental physics – from wave functions to spatial curvature – is ever explained in a way that differs from the strand conjecture, the strand conjecture is falsified. - 3.6 If the Planck scale is ever found
*not*to play a role in nature, then the strand conjecture is falsified. - 3.7 If the Clay Millennium Prize problem about the existence of
Yang-Mills theories and mass-gaps is ever solved in any way that
*differs*from the strand conjecture – as described here – the strand conjecture is falsified. See the official problem description and, for example, the Encyclopedia of Mathematics on the axioms of quantum field theory. The strand conjecture predicts that*no*non-trivial Yang-Mills theory on R^{4}other than the two known ones is possible (in nature and, most probably, even in mathematics). This is in contrast with the statement of the problem. The strand conjecture also appears to imply that SU(3) yields glueballs (new in 2022) and thus a finite mass gap. - 3.8 If Hilbert's sixth problem about the axiomatic formulation of
physics is solved in any way that
*differs*from the strand conjecture – which states that no axiomatic system for all of physics is possible, just a consistent description, and that axiomatic systems are only possible for parts of physics – the strand conjecture is falsified. See the Encyclopedia of Mathematics about the problem. - 3.9 If a
*background-free*description of motion is ever achieved, the strand conjecture is falsified. (Background-free means observer-free.) - 3.10 If the strand conjecture – i.e., the tangle model of elementary
particles, the strand model of space, or the weave model of horizons
– is found to be incomplete, inconsistent, modifiable, easy to vary,
a special case of a more general theory, not unified, in disagreement with
observations, or otherwise
*not final*, the strand conjecture is falsified. - 3.11 If the
*existence*of fundamental constants in the standard model – couplings, masses and mixings – is*not*due to fluctuating strands, the strand conjecture is falsified. - 3.12 If the
*values*of the fundamental constants of the standard model – fine structure constant, nuclear couplings, masses and mixings – which are calculated from strand fluctuations*disagree*with experiments, the strand conjecture is falsified. - 3.13 If the number of spatial dimensions is ever explained in
a
*different*way than by strands – tangling of strands is not possible in other dimensions – the strand conjecture is falsified. (The argument was made by many researchers independently of strands.) - 3.14 If
*any*equation of motion or Lagrangian for the fundamental degrees of freedom, any unified equation of motion, or any unified Lagrangian - containing both general relativity and the standard model, but differing from them - is ever found to describe nature, the strand conjecture is falsified. (Arguments in this article.) - 3.15 If
*any*observation or question – such as the matter-antimatter ratio in the universe – remains unexplained or unanswered in the strand conjecture, the strand conjecture is falsified. (However, see also the next section.)

### Present limitations and timeline of the predictions

- The strand conjecture does not yet include specific values for the
fundamental constants, only upper and lower limits. As the preprints explain, the mathematical
challenge involves statistical tangle geometry and is
*tough*.

In particular, the approximation for the fine structure constant needs improvements.

Also, as the preprint on QED explains, strands predict massive Dirac neutrinos with very low mass. However, only rough estimates for the upper and lower limits are possible so far. - The tangle–particle assignments could still be wrong, especially those for the leptons and the W boson.
- Strands reproduce cosmology: strands predict the existence of an expanding cosmological horizon, the correct matter density, the lack of inflation, the equality of inertial and gravitational mass in cosmology, the existence of dark energy, and the lack of unknown elementary dark matter particles. However, strands did not yet yield definite predictions about (1) the time dependence of the cosmological constant and (2) possible deviations from general relativity at galactic and cosmological distances. These two issues are in work.

The predictions have no end in time. The aim remains to extend the list of tests in cosmology and to improve the calculations of the fundamental constants.

### What speaks against the strand conjecture

- Everything – particles, space, horizons – is made of strands? That is crazy. (Yes.)
- The strand conjecture maintains that the standard model and general relativity can be unified without changing either theory. There are literally thousands of texts stating the opposite. (Yes.)
- A well-known historic argument states:

Es gibt viele Theorien,

die sich jedem Test entziehen.

Diese aber kann man checken,

elend wird sie dann verrecken.

(Indeed, strands will die if only a*single*one of the above list of tests fails.) - Strands deduce general relativity and the standard model from a few lines. That is too simple to be true. (No. The lines represent the way the (corrected) Planck units are realized in nature and are deduced from the 9 lines explaining everything in textbook physics.)
- Strands are too simple. The tangle model is based on the statements
that special relativity and Lorentz covariance follow from the local limit
c, that the Dirac equation follows from the limits c and
ℏ, and that
the field equations of general relativity follow from the local limit
c
^{4}/4G. (True. Despite publications about each of these statements, this simple description of motion is not accepted by many researchers. But it agrees with all experiments.) - The tangle model for particles describes events, interactions, physical processes and the full standard model with simple pictures, directly at the Planck scale, and with almost no mathematical formulae or mathematical structures. This possibility – due to the invariant Planck limits – appears unsound or too simple to be true to most. (Yes.)
- The strand conjecture uses almost no mathematics and provides no equation(s) of motion or Lagrangian. (True. And it explains why.)
- The strand conjecture and the ideas leading to it have been published only in a handful of papers. (True. More will come.)
- Christoph Schiller has made a wrong prediction in the past, due to wrong particle tangle assignments. Why should he be right this time? (Why not? Mistakes occur. Science advances by mistakes.)
- The lack of deviations from present theories (parts 1 and 2 of the prediction) and the existence of Planck limits contradict each other, at least at first sight. (The contradiction is only apparent.)
- Strands predict that space is quantum and at the same time predict that no deviation from general relativity will be observed. (Indeed, this is what strands imply.)
- Strands are demotivating. They predict the lack of physics beyond
the standard model and general relativity. (Wrong! Experiments show the
lack of new physics for 50 years, strands just confirm this.
Strands are
*motivating:*just find a formula for any of the 25 fundamental constants. So far, there was no way to search for such a formula. Also, a new way to calculate in QCD, QED and the weak interaction is predicted. Entanglement and quantum theory get a new description. Quantum gravity gets a new description. Knot theory gets a boost. Dark matter research and MOND will profit.) - Strands predict that we know already "everything" in fundamental physics (parts 1 and 2 of the prediction). As every physicist knows, in the past this prediction has always been utterly wrong. (True; but in contrast to the past, the prediction now agrees with data - since 50 years.)
- The strand conjecture is counter-intuitive: it requires getting used to the idea that every particle in nature is tethered. This old proposal by Dirac is usually dismissed as a mere analogy with no deeper significance. (True.)
- The strand conjecture proposes a microscopic model for quantum theory that agrees with decoherence, despite the failure, without exception, of all such attempts in the past. (True.)
- The ideas of Battey-Pratt and Racey on the Dirac equation have not been taken up by many other researchers. Several who did, such as Jean-Pierre Vigier, have passed away. (True.)
- The strand conjecture proposes a specific model for the microscopic details of space. The proposal differs from all the proposals that were and are explored in the past. (True.)
- The strand conjecture proposes a specific model for black holes. The proposal differs from all the proposals that were explored in the past – including those of classical general relativity, firewalls and fuzzballs. (True.)
- The strand conjecture describes quantum theory as a consequence of a minimal action – as Bohr did – and general relativity as a consequence of a maximum force – as several researchers did in the past. This view is not shared by the majority of physicists. (True.)
- The strand conjecture predicts the lack of new quantum gravity effects, of new discoveries in particle physics, and of new discoveries in fundamental physics. This goes against the hopes, wishes or even requirements of many researchers. All of CERN is betting against the strand conjecture. CERN even wants to build a new collider. (True.)
- The strand conjecture is not axiomatic. This goes against the aims of most researchers. (True. This wish cannot be realized.)
- There are many physics researchers, publications and books disagreeing with each prediction, including the lack of trans-Planckian effects. (True. Strands prevent trans-Planckian effects of any kind, but most other approaches include them.)
- The strand conjecture unifies quantum field theory and general relativity, but Christoph Schiller does not work at a university, worked mainly alone, and is not young. (True.)
- The strand conjecture goes against fashions and avoids hype. Even though there is a relation to qubits, there is none to quantum computing. The universe is not a computer. The universe is not made of strings nor loops, but of strands. There are no higher dimensions, no supersymmetry, and no multiverse. Strands also contradict almost all other approaches to physics beyond the standard model found in the media. (True. And they explain why.)
- The strand conjecture states that the unified theory cannot be based on points, neither discrete nor in manifolds. The strand conjecture states that the unified theory cannot have equations - at all. The strand conjecture states that the unified theory cannot have additional symmetries - only U(1), broken SU(2), and SU(3). The strand conjecture states that the unified theory predicts no new effects and no new energy scales. The strand conjecture states that the unified theory is completely different from all attempts so far. The strand conjecture states that the unified theory is not something earth-moving, not a holy grail, not something revolutionary, but the last piece in a puzzle. (True.)
- The strand conjecture is not mainstream. Even in 2021, only a small percentage of theoretical physicists are known to believe part 1 of the prediction on the completeness of the standard model (arxiv.org/abs/2001.09088 by Shaposhnikov, Shkerin, and Zell is an unrelated example). Agreement with part 2 of the prediction, correctness of general relativity and of maximum force, was rare for many years but is now increasing (arxiv.org/abs/1701.06343 by Barrow and Gibbons is an example). But almost no physicist considers the strand conjecture (parts 3 and 4 of the prediction) to be of interest. (True.)
- Above all, calculating the fundamental constants is a hard mathematical problem. The final check of the conjecture, which includes the calculation of coupling constants and neutrino masses, has not yet been performed. (True. But predictions are the first part of the tests of any theory. The calculations are a fascinating mathematical challenge that combines knot and tangle theory, the geometry of ideal tangle and knot shapes, and statistics.)

### What speaks in favour of the strand conjecture

- So far, every consequence of the strand conjecture –
as well as every prediction and every test –
**agrees with all known experiments.**Starting in 2019, the predictions were listed on this page and published in physics journals. So far, all checks are positive. (More precisely, the lack of deviations from general relativity was predicted in 2000, whereas most strand predictions are from 2009 and were included in volume VI of the Motion Mountain series. The remaining strand predictions are from 2014.) - The strand conjecture is
**based on Planck limits**, including a discovery in fundamental physics that is experiencing growing interest: maximum force. This limit principle, combined with the ideas of Dirac and of Battey-Pratt and Racey, led to the fundamental principle of the strand conjecture. (If preferred, one can also take any other classical black hole property as an equivalent limit principle.) - The strand conjecture is the first and only conjecture
that
**explains the elementary particles**and all their observed properties, and does not add unobserved ones. Strands explain why there are three particle generations and why protons have the same charge as positrons. - The strand conjecture is the first and only conjecture
that
**explains the four interactions**and their observed properties, and does not add unobserved ones. Strands explain quantum field theory, the gauge groups, the gauge interaction Lagrangians, the full standard model Lagrangian, the vanishing vacuum energy and the lack of a Landau pole; strands explain the field equations of general relativity, the Hilbert Lagrangian, black hole entropy and the no-hair theorem. - The strand conjecture is the first conjecture (of only two)
that
**estimates the fundamental constants**ab initio. Strands predict the normal neutrino mass sequence and a rough value for the weak mixing angle, ab initio; and by explaining the fine structure constant and the mass of the electron more precisely – and ab initio – strands will explain all colours in nature. - The strand conjecture is the first and only conjecture
that
**explains fundamental physics from a single principle**. It explains the principle of least action, the dimensionality of space, all conventional "principles", and all Lagrangians used in physics. All consequences of the strand conjecture – all explanations and all predictions – derive from a single principle at the Planck scale. There is no way to modify the strand conjecture. There is no way (except by changing tangle–particle assignments) to change the predictions of the conjecture. No question in fundamental physics is left unanswered. - Finally, the strand conjecture
**fits on a T-shirt**, as often required. The T-shirt contains and agrees with all of textbook physics. And of course, the strand conjecture is based only on professional physics books, papers and journals and is published only in such books and journals. And of course, the strand conjecture gets no points on the various crackpot indices. Above all, the strand conjecture agrees with all available experimental data - but remains falsifiable. As required by science, the numerous high-precision predictions on this page, in the publications and in the preprints – and the many people working on those topics – make falsification easy in principle, as is demanded by any candidate theory in physics.

### Support – with a money back guarantee for donors and sponsors

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You can contribute to efforts towards *falsifying* the strand
conjecture by finding an effect or by funding an experiment that detects
physics beyond general relativity or beyond the standard model with massive
Dirac neutrinos. Or you can contribute *towards* the strand
conjecture and **support strand research with 0.001% (10 ppm)**
**of your or your organisation's annual budget.** You will get
an entry on the sponsor page. If donor
anonymity is desired, it will be respected.

Are you a donor or a sponsor thinking about a *medium-sized*
contribution? Given the promising results so far, the Motion Mountain
Physikverein and Christoph Schiller make an unusual offer (since 2020): if
desired, in the case that just one of the hundreds of experimental
predictions and tests given above fails, the received financial support for
strand research will be refunded. In short, **strand conjecture
falsified, money back.**

Are you a donor or a sponsor thinking about a *large*
contribution? In this case, the Motion Mountain Physikverein and Christoph
Schiller make an additional offer (also since 2020): if another,
inequivalent conjecture about the unification of physics arises –
explaining particles and forces, estimating fundamental constants, and
explaining least action and the number of dimensions – then the
received financial support for strand research will also be refunded. Even
if the strand conjecture is *not* falsified. In short, **strand
conjecture not unique, money back.**

Private bets about the best path to unification are a fun pastime. In the past, christoph@motionmountain.net has proposed private bets on one or several predictions of the strand conjecture. All predictions above have withstood the test of time. For various years he also offers a free dinner to anybody providing a new and good argument (even if incorrect) against or in favour of the strand tangle model. This includes the first person telling him about a specific counterexample to any prediction listed above.