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.

 
• The bet – in six parts – on the unification of fundamental physics
• 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
• Thinking about betting on the hardest problem of modern science?
 

The bet – in six parts – on the unification of fundamental physics

1. No deviation from the standard model of particle physics (with massive Dirac neutrinos) will be discovered.
2. No deviation from general relativity (at subgalactic distances) will be discovered.
3. No exception to any (corrected) Planck limit will be discovered.
4. All observations and all theories derive from the fundamental principle of the strand conjecture. Its assumptions are minimal, clear, and unmodifiable.
5. Calculating the fundamental constants of the standard model (masses of the electron and the other elementary particles, fine structure constant, nuclear coupling constants, and mixing angles) is possible.
6. Everything unexplained so far in fundamental particle physics is explained.

Papers and preprints explaining how the parts of the prediction arise are found here.

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Tests with particle experiments – of parts 1 and 3:

• Any deviation of any kind that is detected from quantum field theory, in particular from the standard model of particle physics and its Lagrangian (with massive Dirac neutrinos) – including 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 – implies that the prediction and the strand conjecture are wrong.

  In particular, the strand conjecture predicts the lack of results in the three research topics planned at the future circular collider – described in the CERN paper FCC Physics Opportunities, European Physical Journal C vol 74 (2019) p 474 (with 1363 authors) – namely (1) the search for unexpected phenomena around the Higgs and the electroweak gauge bosons, (2) the search for new elementary particles, such as dark matter, and (3) the search for tiny deviations from the standard model. If any such result arises, the prediction and the strand conjecture are wrong.

  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 prediction and the strand conjecture are wrong.

  The strand conjecture further predicts that the proposals for physics beyond the standard model collected by the Snowmass 2021 theory frontier group will not agree with future experiments. If one of them does, the prediction and the strand conjecture are wrong.

• 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 prediction and the strand conjecture are wrong.

  In particular, the strand conjecture predicts the lack of results in the research topics listed 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 prediction and the strand conjecture are wrong.

• 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 prediction and the strand conjecture are wrong.
• If any unknown fundamental interaction or interaction property is discovered – including but not limited to a fifth force, 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 prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• If half the quantum of action, hbar/2, is not the smallest action value measurable in nature, or if any deviation from quantum theory is observed, the prediction and the strand conjecture are wrong.
• If any measurement whatsoever is ever realized without electromagnetism – i.e., using the nuclear or the gravitational interaction – the prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong. Also if physical speeds above c or physical actions below ℏ are observed, the prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• If any future experiment helps to clarify the origin of the fundamental constants, the prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.

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Tests with gravity experiments – of parts 2 and 3:

• 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 – implies that the prediction and the strand conjecture are wrong.
• If any momentum flow or force larger than the corrected Planck limit c⁴/4G or any power/luminosity larger than the corrected Planck limit c⁵/4G is observed, the prediction and the strand conjecture are wrong. They correspond to about 50 000 solar masses per second. Also if any mass flow larger than c³/4G or any mass to length ratio above c²/4G is observed, the prediction and the strand conjecture are wrong. Also if physical speeds above c, singularities of any kind, curvature values above the Planck limit, or mass densities above the Planck limit are observed, the prediction and the strand conjecture are wrong.
• If the gravitational constant G changes with energy, or deviations from the Unruh effect or from the equivalence principle are observed, the prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• If any observed or observable property of any kind of black hole is in contrast with the strand conjecture, the prediction and the strand conjecture are wrong.
• If the 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 prediction and the strand conjecture are wrong.
• 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, or quantum gravity effects of the vacuum on distant galaxy images – is discovered, the prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.

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Theoretical tests – of parts 4, 5 and 6:

• 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, Planck-scale black holes, but also any other, future unification approach – then the prediction and the strand conjecture are wrong.
• If any other non-equivalent explanation for the mass hierarchy of elementary particles is found – i.e., one not due to tangle topology – the prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• If number fields other than the reals, complex numbers, quaternions or octonions are found to play a role in gauge interactions, then the prediction and the strand conjecture are wrong.
• If the Planck scale is ever found not to play a role in nature, then the prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong. 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 R⁴ 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 – i.e., that no axiomatic system for all of physics is possible, just a consistent description, but that axiomatic systems are possible for parts of physics – the prediction and the strand conjecture are wrong. See the Encyclopedia of Mathematics about the problem.
• If a background-free description of motion is ever achieved, the prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• If the existence of fundamental constants in the standard model – couplings, masses and mixings – is not due to strand fluctuations, the prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• 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 prediction and the strand conjecture are wrong.
• If any observation or question – such as the matter-antimatter ratio in the universe – remains unexplained or unanswered in the strand conjecture, the prediction and the strand conjecture are wrong. (However, see also the next section.)

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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.
• 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, and the lack of unknown elementary dark matter particles. However, strands did not yet yield definite predictions about (1) the nature, the value and the time-dependence of the cosmological constant and about (2) possible deviations from general relativity at galactic and cosmological distances due to the cosmological constant or to already known "dark matter" particles. These two issues are in work.

The aim remains to extend the list of tests and to reduce the limitations of the prediction, which was first formulated in 2009. More on the story behind the prediction is found in the blog on strand research. In principle, the prediction has no end in time. Due to finite lifetime of homo sapiens, an earlier date for a challenge would be more practical, such as 1 September 2030.

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Why you should bet against the strand conjecture

• A well-known historic argument:
  Es gibt viele Theorien,
  die sich jedem Test entziehen.
  Diese aber kann man checken,
  elend wird sie dann verrecken.
  Indeed, if only a single test of the above list of over 200 tests fails, the strand conjecture is wrong and the bet is lost.
• Everything – particles, space, horizons – is made of strands? That is crazy. (Yes.)
• The strand conjecture deduces general relativity and the standard model from a few lines. That is too simple to be true. (No. The lines represent the way the Planck units are realized in nature.)
• The conjecture has been published only once, in a Russian 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? (See below. Mistakes do happen.)
• The lack of deviations from present theories (part 1 and 2 of the prediction) and the existence of Planck limits (part 3 of the prediction) contradict each other, at least at first sight. (The contradiction is only apparent.)
• Strands predict the lack of physics beyond the standard model and general relativity. Apart from calculating the fundamental constants, nothing in nature, or at least not much, remains to be explored. Strands do not appear to empower other researchers to make many new discoveries. (Wrong; just find a formula for any of the 25 fundamental constants. And there is still a lot to be understood in other branches of physics.)
• Strands predict the lack of unknown fundamental physics – i.e., that we know already "everything" in this domain (part 1 and 2 of the prediction). As every physicist knows, in the past this prediction has always been utterly wrong. (True; but at present, in contrast to the past, the prediction agrees with data.)
• The tangle model is based on the statements that special relativity follows from an invariant speed limit c, that quantum theory follows from an invariant action limit ℏ, and general relativity follows from an invariant force limit c⁴/4G. More precisely, the tangle model is based on the idea that Lorentz covariance follow from the limit c, that the Dirac equation follows uniquely from the limits c and ℏ, and that the field equations of general relativity follow from the limit c⁴/4G. However, despite the existence of publications on each of these statements, this description of motion is too simplified to be acceptable in the eyes of most researchers.
• The tangle model for particles describes events, interactions, physical processes and the full standard model with simple pictures and almost no mathematical formulae. This possibility – due to the invariant Planck limits – goes against the convictions of many researchers. They find this possibility too simple to be true and dismiss it as unsound.
• 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 such attempts in the past, by numerous researchers in this domain.
• 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 tangle model for particles arises directly from Planck-scale physics, without any additional concept or mathematical structure; this possibility goes against the convictions of many researchers and is usually dismissed as impossible.
• The strand conjecture proposes a specific model for the microscopic details of space. The proposal differs from all the proposals that were explored by hundreds of researchers in the past.
• The strand conjecture proposes a specific model for black holes. The proposal differs from all the proposals that were explored by hundreds of researchers in the past &ndash in particular, from the proposals by general relativity, but also from firewalls and fuzzballs, though it resembles them.
• 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 and dreams of many researchers. For example, CERN is betting against the strand conjecture.
• The strand conjecture is not axiomatic. This goes against the aims of most researchers.
• The strand conjecture is not mainstream. Even in 2019, 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 parts 2 and 3 of the prediction and the strand conjecture is rare (arxiv.org/abs/1701.06343 is an example). And so far (2020), only a few physicists consider the strand conjecture (part 4, 5 and 6 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, it is unique (there is no multiverse), the universe is not made of strings, and the universe is not made of loops.
• Calculating the fundamental constants is a hard (but fascinating) mathematical problem. The final test of the conjecture is not yet possible.

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Why you should bet on the strand conjecture

1. So far, every consequence of the strand conjecture – every consequence and every prediction – agrees with all known experiments. Since the predictions were deduced in 2014 – in fact, almost all were deduced in 2009 – all checks are positive. And, besides, the strand conjecture agrees with all physics textbook theories: quantum theory, the standard model, and general relativity.
2. The strand conjecture is the first and so far the only conjecture that explains the elementary particles and all their properties. For example, strands explain why there are three particle generations and why protons have the same charge as positrons.
3. The strand conjecture is the first and so far the only conjecture that explains the four interactions and their properties. For example, strands explain quantum field theory, the gauge groups, the gauge interaction Lagrangians, the vanishing vacuum energy and the lack of a Landau pole; strands explain the field equations of general relativity, black hole entropy and the no-hair theorem.
4. The strand conjecture is the first and so far the only conjecture that estimates the fundamental constants ab initio. For example, 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.
5. 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, and all conventional "principles" of 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.
6. The strand conjecture gets no points on the Baez and the Caldwell crackpot indices, and it fits on a T-shirt.

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Thinking about betting on the hardest problem of modern science?

Unification is hard. Thousands of people have worked on it and thousands are still working on it. It is the hardest problem we know at present. It is harder than the Riemann conjecture, which itself is much harder than Fermat's last theorem. Do you want to bet about the best way to unification? Then write me at christoph@motionmountain.net. I will bet on the strand conjecture or on one of its predictions. This is a fascinating scientific wager.

A simple way to bet against the conjecture is to point out gaps in the preprints on the research page. A simple way to bet on the conjecture is to donate to our tiny non-profit, the Motion Mountain Physikverein. Donations that support research on strands will be mentioned – except if not desired – in future publications and on this website.

Are you a researcher from CERN or another institution? You can bet against the conjecture by finding a single effect beyond the standard model or beyond general relativity. You can bet on the conjecture by supporting strand research – with 10 ppm of your annual budget.

Do you want to place a long bet on the homonymous website? Let me know. (An example bet: "The tangle model and its predictions on particle physics and gravitational physics will not be falsified by any experiment at least until 1 September 2030.")

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 above predictions and tests fails, the received financial support for strand research will be refunded. In short: strand conjecture falsified, money back.

You want to support without being named? No problem.

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.

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