Even the faintest whisper about the unification of physics must stand up to experiment with new explanations, tests and predictions. The following ones were deduced by Christoph Schiller from the strand conjecture, i.e. from the statement: The Dirac trick at the Planck scale describes motion and nature completely.

In simple words, strands predict: the search for physics beyond the standard model or beyond general relativity will be as successful as the search for energy speeds faster than light.

• Tests with
particle experiments

• Tests with
gravity experiments

• Theoretical tests

• Present limitations and timeline of the
prediction

• Why you should bet
**against** the strand conjecture

• Why you should bet
**on** the strand conjecture

• Do you want to bet about this
fascinating issue of modern science?

### The predictions and proposed bet about fundamental physics – in four 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 and
ℏ.

**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.

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

**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 – is possible with strands.
No other, inequivalent approach will achieve this calculation.

The research page lists papers and preprints explaining how the predictions arise. The rest of this page shows how to test and falsify both the predictions and the strand conjecture.

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

- If
*any*deviation of any kind is detected from the standard model of particle physics and its Lagrangian (with massive Dirac neutrinos) – 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. If any one of them agrees, the strand conjecture is falsified.

- 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, a glueball, an inflaton, a dilaton, a leptoquark, a magnetic monopole, a dyon, an anyon, a WIMP, or an axion – the strand conjecture is falsified.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. - 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 knotted glueballs – the strand conjecture is falsified. - 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. - 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. - 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. - If
*any*measurement whatsoever is ever realized without electromagnetism – i.e., using the nuclear or the gravitational interaction – the strand conjecture is falsified. - 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 that 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.

- 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. - If
*any*future experiment helps to clarify the origin of the fundamental constants, the strand conjecture is falsified. - 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 preprints found here – the strand conjecture is falsified. - If instead of tangles of strands
*any other*(non-equivalent) substructure is discovered in elementary particles – such as preons, prequarks, knots, ribbons, rishons, MÃ¶bius bands, tori, vortices or any other localised or extended constituents – the strand conjecture is falsified.

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

- If
*any*deviation of any kind that 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. - 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 50 000 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. - 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.
- 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.
- If any observed or observable property of any kind of black hole is in contrast with the strand conjecture, the strand conjecture is falsified.
- 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.
- 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. - 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 preprint on gravitation – the strand conjecture is falsified. - In cosmology, if inflation is confirmed, if any new dark matter particle is discovered, or if the universe's integrated luminosity is above c^5/4G, the strand conjecture is falsified.

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

- 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. - If
*any other*non-equivalent explanation for the mass hierarchy of elementary particles is found – i.e., one not due to tangle topology – the strand conjecture is falsified. - 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., by minimizing crossing switch number – the strand conjecture is falsified. - 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 way*, the strand conjecture is falsified. - 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. - If the Planck scale is ever found
*not*to play a role in nature, then the strand conjecture is falsified. - 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, 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) has no glueballs and thus an infinite mass gap, as explained in volume VI. - 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 ony possible for parts of physics – the strand conjecture is falsified. See the Encyclopedia of Mathematics about the problem. - If a
*background-free*description of motion is ever achieved, the strand conjecture is falsified. - 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. - 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. - If the
*values*of the fundamental constants of the standard model – fine structure constant, nuclear couplings, masses and mixings – that are calculated from strand fluctuations*disagree*with experiments, the strand conjecture is falsified. - 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. - 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 prediction

- 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 for the leptons and the W.
- 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 about (2) possible deviations from general relativity at galactic and cosmological distances. These two issues are in work.

The aim remains to extend the list of tests in cosmology and to improve the calculations of the fundamental constants. In principle, the predictions, made in the years between 2009 and 2018, have no end in time. Due to finite lifetime of homo sapiens, an earlier date for a challenge is more practical, such as 1 September 2030.

### Why you should bet 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.

(Maybe. If only a*single*one of this list of tests fails, the strand conjecture is falsified and the bet is lost.) - 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.)
- The conjecture has been published only twice, in a Russian and in a Western European journal. (True. Russian physics has often been faster.)
- 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.)
- The lack of deviations from present theories (part 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 are demotivating. They predict the lack of physics beyond the standard model and general relativity. (Wrong; just find a formula for any of the 25 fundamental constants. And much remains to be understood in other branches of physics and science.)
- Strands predict that we know already "everything" in fundamental physics (part 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.)
- 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. Despite of the publications about each of these statements, this simple description of motion is not accepted by many researchers. - The tangle model for particles describes events, interactions, physical processes and the full standard model with simple pictures, directly from Planck-scale and with almost no mathematical formulae or mathematical structures. This possibility – due to the invariant Planck limits – appears too simple to be true and unsound to most.
- The strand conjecture is counter-intuitive: it requires to get 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.
- The strand conjecture proposes a microscopic model for quantum theory that agrees with decoherence, despite the failure, without exception, of all attempts in the past.
- 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.
- The strand conjecture proposes a specific model for the microscopic details of space. The proposal differs from all the proposals that were explored in the past.
- The strand conjecture proposes a specific model for black holes. The proposal differs from all the proposals that were explored in the past &ndash including those of classical general relativity, firewalls and fuzzballs.
- The strand conjecture describes quantum theory as consequence of a minimal action – as Bohr did – and general relativity as consequence of a maximum force – as several researchers did in the past. This view is not shared by the majority of physicists.
- 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 of many researchers. All of CERN is betting against the strand conjecture.
- The strand conjecture is not axiomatic. This goes against the aims of most researchers.
- There are many physics researchers, publications and books disagreeing with each of the statements in the proposed bet.
- The strand conjecture is not mainstream. Even in 2021, only a small number of theoretical physicists are known to believe part 1 of the prediction (arxiv.org/abs/2001.09088 is an unrelated example). Agreement with part 2 of the prediction is rare (arxiv.org/abs/1701.06343 is an example). Only a few physicists consider the strand conjecture (part 3 and 4 of the prediction) to be of interest.
- The strand conjecture goes against fashions. 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. There is no multiverse.
- Above all, calculating the fundamental constants is a hard (but fascinating) mathematical problem. The final test of the conjecture is not yet possible.

### Why you should bet on the strand conjecture

- So far, every consequence of the strand conjecture –
and every prediction –
**agrees with all known experiments.**Since the predictions listed on this page were published 2019 (in fact, most are from 2009) all checks are positive. - The strand conjecture is the first and so far the only conjecture
that
**explains the elementary particles**and all their properties. Strands explain why there are three particle generations and why protons have the same charge as positrons. - The strand conjecture is the first and so far the only conjecture
that
**explains the four interactions**and their properties. 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 and so far the only conjecture
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 so far the only conjecture
that
**explains everything**ab initio in fundamental physics. It explains the principle of least action, the dimensionality of space, all conventional "principles" and 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. And no issues in fundamental physics are left unexplained. - A few remarks about form and quality: The strand conjecture
**fits on a T-shirt**, as often required. The T-shirt contains and agrees with all textbook physics. The strand conjecture is based only on professional papers and journals. The strand conjecture gets no points on the Baez and the Caldwell crackpot indices. The strand conjecture agrees with data but is falsifiable; in fact, the numerous predictions on this page and in the preprints – and the many people working on them – make falsification possible for everyone, as required by any candidate theory in physics.

### Do you want to bet about this fascinating issue of modern science?

Thousands have worked and are still working on unification,
one of the most captivating
problems in science. Do you want to bet about the best path to
unification? Then write me at christoph@motionmountain.net.
I will bet *on* one or several predictions
of the strand conjecture,
privately or publicly, even on the long bets
website. The central aspect of this scientific wager is: Is
unification as simple as strands suggest?

Are you a researcher from a university, CERN, another research
institution or a funding organisation? You can bet *against* the
conjecture by finding (or funding) a single effect (or experiment) showing
physics beyond the standard model or beyond general relativity. Or you can
bet *on* the conjecture and **support strand research with 10
ppm of your annual budget.**

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

An easy way to bet *against* the conjecture:
point out errors in the preprints on the
research page. An easy way to bet *on* the conjecture:
donate to our tiny non-profit research organization, the Motion Mountain
Physikverein. Sizeable donations that support research on strands will be
mentioned – except if anonymity is preferred – in future
publications and on this website.

Are you a donor or a sponsor thinking about a *large* bet or
contribution? In this case, the Motion Mountain Physikverein makes an
additional offer: 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.**