The following musings explore the structure and the unification of physics. Various sections explain how to get from maximum force to physics in 9 lines and to the existence of strands. Other sections explain how to get from strands to general relativity and to the standard model.

Papers and manuscripts are found at

For the author of this site, science is as defined in the enlightenment: only ideas and concepts that agree with experiments are presented. Some of the musings are also posted on social media sites.


Surprise: glueballs do exist

The paper on QCD led to a discovery: glueballs are possible in the strand model. This surprising result is based on a possible tangle structure made from two gluon tangles. It is explained in the new version of the QCD paper. Also the quantum numbers match.


The aim of fundamental physics

Let me exagerate and simplify a bit:

The aim of fundmantal physics is not to unify quantum theory and gravity.

The aim of fundmantal physics is to explain the number 1/137.0359992(1).

Focussing on the wrong aim blocks progress.

Following the correct aim will put you among crackpots.


What does the minimum length of nature imply?


Even though both general relativity and quantum theory use continuous space, their combination yields a minimum length.

General relativity is not valid at lengths below the minimum length.

Quantum theory is not valid at lengths below the minimum length.

There is only one testable theory beyond general relativity: quantum theory/the standard model. And vice versa.

There are no contradictions between general relativity and quantum theory - as long as the minimum length is always respected and taken into account.

There are no singularities in nature.

There are no points in space or time.

There is no discrete space or time. There is no spatial lattice.

There are no additional dimensions, no other gauge groups, no twistors, no fermionic coordinates, no supersymmetry, no conformal symmetry, no higher derivatives, no holography, no space-time foam.

There are no observations beyond general relativity and the standard model.

There are no equations of motion beyond general relativity and the standard model.

A lot has to be thought differently.


Even though both general relativity and quantum theory use continuous space, their combination yields a minimum length.

The black hole horizon implies that there are fundamental constituents of space and particles.

Space and particles imply that the fundamental constituents are both extended and of Planck size at the same time.

The fundamental constituents are filiform.

The fundamental constituents fluctuate.

The fundamental constituents are described statistically.

The fundamental constituents yield a minimal length and finite black hole entropy.

The fundamental constituents yield wave functions, countable particles and extended space.

The rest follows.


What do researchers think about strands and maximum force? On encouragement

Strands describe nature. Their predictions match experiments. The same holds for maximum force and for the 9 lines that summarize physics.

Whether something is true depends on experiments, not on what other people think or say. Never, ever, get discouraged by what other people think, say or write. Follow experiments. Even if researchers tell you otherwise!

Even in the 2020s, there are numerous researchers who discourage students to think about the Planck scale. They are wrong - unfortunately. Sapere aude. Dare to know. And above all: dare to think!

The basis of the relativistic quantum gravity and of the strand model, as described in C. Schiller, From maximum force to physics in 9 lines and towards relativistic quantum gravity, pdf could have been deduced from the 1970s onwards, by any student, anywhere, if he or she had been encouraged to think about the Planck scale.


Lessons from decades of quantum gravity

1. Quantum gravity is defined by the smallest length, which is of the order of the Planck length.

2. The smallest length is the greatest challenge to the habits of thought in fundamental physics.

3. Gravity and quantum theory do not contradict each other - because there are no lengths smaller than the Planck length. All so-called contradictions usually discussed (singularities, big bang, etc.) make use of lengths smaller than the smallest length. Since such lengths do not occur, contradictions do not occur.

4. Quantum gravity requires us to find the common constituents of space and particles.


Space is only approximately continuous

There is a smallest length in nature, of the order of the Planck length. The result is known since over 50 years. The length is so small that in practice, it plays no role.

Measuring smaller length values is made impossible by quantum theory and by general relativity.

A detailed investigation shows that length is continuous for all values larger than the smallest value.

The smallest length has important implications. It contradicts a lot of research. Therefore, the existence of a smallest length should only be whispered, and only with care.

One cannot blame anybody for believing that space is continuous.

The smallest length is the greatest challenge to the habits of thought in fundamental physics.


The meaning of maximum force c4/4G

Nature limits force to c4/4G, a value of about 3 * 1043 N.

How can this be? Jupiter contains more than 1053 hydrogen atoms. Inside each atom, the force between the proton and the electron is about 10-7 N. The total force is thus higher than the maximum force. Besides, there are many more hydrogen atoms in the universe...

Maximum force can also be exceeded without quantum theory. Just take the force on a small mass near a black hole horizon. Then take a sufficient number of copies of this small mass, and place them arouns a horizon. (Typically just a handful are enough.) The total force will be larger than the maximum force.

Speed can help to understand the issue. Nature limits speed to c, a value of about 3 * 108 m/s.

How can this be? Just add all speeds of the atoms in the air of the room you are sitting in. The total value is higher than c. Besides, there are many more atoms in the universe...

Like maximum speed c, the maximum force c4/4G is the maximum value at a single point. In fact, like maximum speed, maximum force even applies to a sufficiently small region of space.

The maximum force c4/4G is equivalent to the maximum mass to length ratio c2/4G (the "hoop conjecture"): the maximum force simply states that there is no way to compress matter or energy to less than a black hole.

Exceeding maximum force implies being able to act across a horizon. Exceeding maximum force implies being able to avoid creation of a black hole when compressing matter to less than the Schwarzschild radius. Exceeding maximum force implies counterexamples the Einstein's field equations. All this contradicts observation.

It is easy to construct systems with speed values larger than the maximum speed. But they do not contradict the local maximum speed value. It is easy to construct systems with force values larger than the maximum force. But they do not contradict the local maximum force value. Local maximum speed agrees with all observations. Local maximum force agrees with all observations.

Sometimes, scholars believe in additional statements. In particular, believing that (local) force is unlimited implies believing that singularities exist, and in particular, that naked singularities exist. All this contradicts observation. In fact, due to experimental errors, an unlimited value of anything is unobservable in principle.


Relativistic quantum gravity - the unified theory of physics - has no evolution equation

The maximum speed c determines special relativity. It is realized by light and appears in its evolution equation x=ct.

The maximum force c4/4G - or any limit c5/4G or c3/4G or c2/4G - determines general relativity. Any of these limits is realized by black holes and appears in Einstein's field equations for the space-time metric.

The smallest action ℏ determines quantum theory. It is realized by electrons and appears in their evolution equation.

Likewise, the smallest length (4Gℏ/c3)1/2 determines relativistic quantum gravity. But this length limit is not realized by any physical system. Therefore it does not and cannot appear in any evolution equation.

This has the following unexpected implication. Even though the length limit (4Gℏ/c3)1/2 determines relativistic quantum gravity, there is no corresponding evolution equation.

In fact, there are several arguments telling why there is no evolution equation for relativistic quantum gravity.

(1) No known physical system is described by the smallest length - except black holes and similar systems, where the smallest length appears in the entropy and the temperature.

(2) No known single moving physical system is described by any other relativistic quantum gravity limit - thus by any limit containing c, ℏ and G, but without the Boltzmann constant k.

(3) Single gravitons are not detectable.

(4) Any evolution equation requires space and time, but these quantities are emergent from the microscopic degrees of freedom that make up space-time.

As a result, there is no way - and there cannot by any way - to define an evolution equation for relativistic quantum gravity. There is no evolution equation for the microscopic degrees of freedom of nature. There is no evolution equation for the final theory. There is no Lagrangian for the final theory. There is no complex mathematics for the final theory. The only math remaining are the inequalities involving the fundamental limits c, ℏ, 4G and k, as well as their combinations.

The only known equations where the Planck length limit appears are the relation between entropy and area of a black hole, or the expression for black hole temperature. But these equations only describe systems with large numbers of degrees of freedom.

In short, there is no evolution equation for relativistic quantum gravity - except for the case of large numbers of microscopic degrees of freedom. Only statistical or thermodynamic evolution can be described in relativistic quantum gravity.

Or again: there is no "world formula".

Or, for the media: there is no "god equation". The emptiness of this expression has always been obvious to every scholar of the field. The above argument sequence is just the last nail in its coffin.

The lack of an evolution equation does not imply the lack of a unified theory. The result just implies that the unified theory of relativistic quantum gravity is not described by an evolution equation for some microscopic degrees of freedom. Instead, the result implies that the unified theory, relativistic quantum gravity, is described by inequalities and limits only. In fact, limits that contain the limits c, ℏ and 4G are sufficient. An example is twice the Planck length: it limits length measurements.

In other terms: There is no evolution equation for relativstic quantum gravity. Relativstic quantum gravity only produces statistical effects.

Relativstic quantum gravity explains continuous gravitational waves with huge number of gravitons; it describes continuous space, flat and curved, as due to huge numbers of microscopic degrees of freedom; it describes continuous fields as due to huge numbers of virtual gauge bosons; it describes wave functions as due to huge numbers of microscopic degrees of freedom.

This reasoning can be extended. Relativistic quantum gravity is needed to explain the last open questions about nature: the interaction spectrum, the elementary particle spectrum and the fundamental constants.

Therefore, the interaction spectrum and the elementary particle spectrum must be statistical effects. For the same reason, particle masses, mixing angles and coupling constants must be statistical effects. Also the cosmological constant and the dimensionality of space must be statistical effects.

In summary, there is no evolution equation in relativstic quantum gravity, i.e., there is no evolution equation in the unified/final theory. Relativistic quantum gravity is determined by the Planck limits that contain c, ℏ and G. However, in relativistic quantum gravity, only statistical results can be deduced.

Together with the result that the microscopic degrees of freedom must be fluctuating and filiform (as argued in this article), the arguments just given provide a clear guidance on how to search for the unified theory of relativistic quantum gravity: the microscopic degrees of freedom are filiform, fluctuating, unobservable, of Planck radius, and yield only statistical effects.


Fundamental physics: from boring to fascinating

Since 50 years, there are no measurable deviations from general relativity or from the standard model of particle physics.

Any unified description will confirm this. Therefore, any unified description is inherently boring.

Any unified description remains testable: one can calculate the fundamental constants, such as particle masses, coupling constants and mixing angles.

Nevertheless, any unified description will be boring. It will have no news for the newspapers. It will not generate new business. It will now allow new weapons. It will not cure cancer. It will not solve hunger. It will not solve poverty. It will not change the world. It will not even improve the world.

Any unified description will simply allow us to understand the world better. Many will be disappointed. Instead, they should be optimistic. The beauty of nature will strike us more than ever. Our awe for nature will increase.

And physics, freed from the burden to understand the foundations, will change to a science that shows how to improve the world, using technology to diagnose, to heal, to feed, to communicate, and to help humans in more ways.


Wikipedia's "Physics Beyond the Standard Model"

Wikipedia states: "Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the inability to explain the fundamental parameters of the standard model, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy. Another problem lies within the mathematical framework of the Standard Model itself: the Standard Model is inconsistent with that of general relativity, and one or both theories break down under certain conditions, such as spacetime singularities like the Big Bang and black hole event horizons."

This text is a deeply misleading summary of the standard model and of 50 years of research on its details.

- There is no experimental evidence for any physical effect beyond the standard model, since over 50 years.
- The fundamental parameters/constants of the standard model do need explanation - including the strong CP problem, neutrino oscillations and matter–antimatter asymmetry that follow from these parameters.
- The nature of dark matter, like the nature of pink flying elephants, is not an issue nor a problem of the standard model, but of measurements: dark matter particles, like pink flying elephants, have never been detected.
- The nature of dark energy is described by the cosmological constant in all experiments. This is not an issue nor a problem of the standard model.
- There is no experimental evidence that the standard model or general relativity break down or are inconsistent in any situation. This is not an issue nor a problem of the standard model.
- There is no experimental evidence that singularities, or purple flying elephants, arise in nature. This is not an issue nor a problem of the standard model.

In short, there is no evidence for measurable effects beyond the standard model, and this since it was formulated 50 years ago. The only deficiency of the standard model is the lack of explanations for the fundamental parameters/constants and - missing in wikipedia - for the gauge interactions and the elementary particles.


To complete the argument, the strand tangle model shows and confirms that the problems of the standard model can indeed be solved without new physics:

- The fundamental parameters of the standard model can be calculated.
- The strong CP problem is solved: the parameter can be calculated.
- Neutrino oscillations are explained: the parameters can be calculated.
- Matter–antimatter asymmetry is explained: the parameter can be calculated.
- Dark matter does not consist of unknown elementary particles, but of a mixture of known matter, of black holes and other effects.
- The nature of dark energy is explained and is described by the cosmological constant.
- The mathematical framework of the standard model is not inconsistent with that of general relativity in any measured or measurable situation.
- Neither theory breaks down in any measured or measurable situation.
- Singularities cannot exist in nature.
- There are no measurable effects beyond the standard model.

In short, the strand tangle models explains all the open issues given by Wikipedia, and also explains the interaction spectrum and the elementary particle spectrum, without any new physics.


Correct statements about nature that are unusual but do not sell books

The unified theory will have no effects on technology, because it will not change the known laws of physics, but only explain the values of 27 numbers appearing in the standard model and in general relativity. See

There was nothing before the big bang - this was knwown already to Augustinus.

There is nothing behind a horizon.

There is no time travel.

There are no wormholes.

There are no higher dimensions.

Physics is great. See

The unified theory has no evolution equation, and cannot have one. No evolution equation describes the motion of the microscopic degrees of freedom that make up nature. There is no "god equation" and no "world formula". See


Modern anti-science

Whoever thinks, says or states that physical quantities can have values beyond the limits of nature, or that such values "exist" even though they cannot be measured, is not doing science. He is making statements that cannot be verified nor be falsified. He is making statements that have no relation to experiments. He is not talking about nature, but talking science fiction.

It is astonishing how many people are living with this anti-science mindset. The enlightenment finished over 200 years ago. Nevertheless, it did not reach everybody.


Some past tweets: statements about nature that are true but unusual

The standard model of particle physics is not ugly, but simple and beautiful. It derives uniquely, in all its details, without possible modifications, from just one principle: Dirac's trick at the Planck scale:

Deriving the standard model from strands, uniquely, without modification, ( means that there is no "multiverse", of any type. Strands describe everything - the universe - but not more than everything.

My little 3-page paper deducing inverse square gravity from maximum force c4/4G has appeared online: It also confirms the hoop conjecture and suggests the lack of gravitational physics beyond general relativity. Possible loopholes are discussed.

The LHC near Geneva has ben confirming every day that the standard model of particle physics is complete. This is a lot of concrete evidence for the unified theory of physics. Thus, 9 lines, 50 years old, summarize all of physics - and show us the way.

There is a length limit in nature: twice the Planck length. It defines relativistic quantum gravity. But in contrast to the previous cases, no system realizes it. Thus we cannot write an evolution equation. Thus there is no world formula, and no unified equation.

Dirac's trick at the Planck scale implies both quantum theory and general relativity. Dirac's trick unifies physics. Dirac's trick makes quantum theory easy to visualize.

Both the Lagrangian of the standard model of particle physics and the Hilbert Lagrangian of general relativity follow from Dirac's string trick at the Planck scale.

This is my newest version of Bronshtein's physics cube. It has a limit at every corner (except the lowest). Each limit defines a theory of physics. The topmost limit defines the final theory: relativistic quantum gravity. More details at

Extreme physics is fun. Every physical quantity has two limits: a (corrected) Planck limit and a cosmological limit. Nature's book of records, and how she realizes them, is found at Find an excpetion to any record and get famous.

Fundamental physics - the standard model and general relativity - can be summed up in 9 lines: 5 principles and 4 lines of choices: The choices are the main unknowns.


Gravitons and spin

In the strand model, single gravitons cannot be detected because they almost only rotate particles.

High numbers of gravitons deform space. But single gravitons mainly rotate a particle.

Such a rotation cannot be detected.

Gravitons mainly couple to spin. Their coupling to displacement is too weak.

The cross section of gravitons is small: it is related to the Planck length and/or the ratio between particle mass and Planck mass.

This topic needs more exploration.

See also the paper arXiv:gr-qc/0601043.


Maurice Materlinck

L’humanité nous a désignés pour accueillir ce qui s’élève à l’horizon. Elle nous a donné une consigne qu’il ne nous appartient pas de discuter. Elle répartit ses forces comme bon lui semble. A tous les carrefours de la route qui mène à l’avenir, elle a mis, contre chacun de nous, dix mille hommes qui gardent le passé; ne craignons donc point que les plus belles tours d’autrefois ne soient pas suffisamment défendues.

L'intelligence des fleurs,


Evidence-based physics

What percentage of papers in hep-th would disappear if only evidence-based ones were kept?

Is the strand tangle model evidence-based?


The Clay Millennium Problem about Yang-Mills theory was known to have no solution

The Clay Mathematics Institute offered a prize they will never have to pay out - and at least some people knew this when they published it.

The main part of the problem is stated as follows on their site:

Yang–Mills Existence and Mass Gap. Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on R4 and has a mass gap ∆ > 0. Existence includes establishing axiomatic properties at least as strong as those cited in [45, 35].

As stated, the problem has no solution. There are numerous arguments, physical and mathematical.

Physics. In nature, a solution is impossible. Whatever the complete theory of nature may be, that theory will explain that only the three observed gauge theories are possible in nature. (There are only three gauge interactions in nature: electromagnetism, the weak interaction and the strong interaction.) However, the millennium problem asks to prove the existence of an infinity of gauge theories. This is in contrast with observation.

The millennium problem also asks to define these quantum field theories with local operators (`point particles'). The existence of exact locality (below twice the Planck length) and of point particles (smaller than twice the Planck length) is also in contrast with observations. In nature, nothing is infinitely small, as Hilbert already said in 1935. Indeed, the double Planck length is a lower limit for length. A smaller length does not arise in nature. This is a consequence of the largest speed, the quantum of action and the the maximum force. For a summary of this story, see for example C. Schiller, Tests for maximum force and maximum power, Physical Review D 104 (2021) 124079, 10.1103/PhysRevD.104.124079, or the text C. Schiller, From maximum force to physics in 9 lines and relativistic quantum gravity. A minimum length prevents locality.

The millennium problem also starts with R4. But space-time is described by 4 dimensions only approximately, again because in nature there is a smallest distance given by twice the Planck length. Again, the existence of a smallest length and the non-applicability of continuous R4 in nature has been known for a long time, and was known already before the statement of the Yang-Mills problem was formulated.

In short, the impossibility of a solution of the millennium problem in nature was known since the problem was posed.

For a physicist, working on the millennium problem - even reading about it - is a waste of time.

The strand tangle model makes these arguments explicit. Strands show how the three gauge groups arise, show how the elementary particle spectrum and the three generations arise, and how the masses, mixing angles and coupling constants arise. All are coupled to the three-dimensionality of space and to its lack of continuity. In short, strands explain how quantum field theory arises. The strand explanation forbids other gauge groups, other particles, and other dimensions. Above all, the strand tangle model also forbids other values for coupling constants and particle masses.

The reason has been published in 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; See also the subsequent papers listed here. (The most pedagogical text is the recent preprint C. Schiller, Testing a model for wave functions and for emergent quantum theory, found at Researchgate as

All those publications show that in nature, there are no additional non-Abelian gauge groups apart from (broken) SU(2) and SU(3). The reason is the classification of tangle (and knot) deformations by Kurt Reidemeister, which only allow U(1) for twists, SU(2) for pokes, and SU(3) for slides. In fact, the publication also shows that nature does not even admit SU(3) or broken SU(2) with coupling constants or with particle masses that differ from the observed values. The paper effectively argues that there is only one possible quantum field theory in nature: the standard model. More specifically, the paper implies that no unbroken Yang–Mills theory apart from SU(3) with the observed particle spectrum and with the observed coupling constant can exist in nature.

The publications show that the non-continuity of space and the lack of higher gauge groups are related: strands explain three-dimensionality, the three possible gauge groups and the three fermion generations.

Mass gap. The Clay Institute also explicitly asks about finite mass gaps. (This is in the lines preceding the above statement of the millennium problem.) In fact, the strand tangle model even suggests the lack of a finite mass gap for SU(3). The lack of glueballs is deduced in the preprint on QCD. (Of course, this particular argument for infinite mass gaps could contain an error.)

Mass gap, version 2. Surprise: in 2022, the situation changed; glueballs are predicted by the strand tangle model! Strands thus predict a finite mass gap for SU(3).

Mathematics. Given the lack of other quantum field theories in nature, one can ask whether they "exist" in mathematics. However, there are no good reasons to assume they do. The concepts of point particle and of local operator only make sense if they apply to actual physical systems. And there are no such systems in nature anywhere, not even for SU(3) or SU(2).

The lack of points in space and of point particles is known since a long time. The millennium problem discusses a situation that has no connection with reality.

The existence of a mass gap depends on the details of interactions. As the arguments above show, these details are not defined if point particles are assumed to exist. It is probable that the existence of a finite mass gap, as long as point particles are assumed to exist, is an unsolvable mathematical problem - even in SU(3), because the assumptions are not sufficient to fix the outcome.

It may well be that the mistaken assumption of continuous space-time is the reason that the mathematical aspect of the millennium problem has never been solved. In nature, there is only one SU(3) quantum field theory, with exactly one coupling constant. In mathematics, SU(3) "exists" for any value of coupling constant. Again one sees that whatever the quantum Yang–Mills theories mentioned in the problem may be, they have no relation to nature. The strand tangle model explains that there is only one coupling constant; the explanation is deeply related to the lack of other gauge theories. The explanation is lost if space is assumed to be continuous.

The strand tangle model explains the particle spectrum and explains why particle masses are uniquely defined. Both aspects are deeply related to the lack of other gauge theories. Both explanations are lost if space is assumed to be continuous.

In fact, one can state: The assumption of continuous space implies a vanishing Planck length and thus a vanishing quantum of action or a vanishing gravitational constant, or both. This implies the lack of all physical measurement units, including mass units. In other terms, the assumption of mathematically continuous space or time contradicts quantum field theory or gravity or both. Exact continuity contradicts nature, modern physics and its mathematical description. (Arguments and references are found in C. Schiller, From maximum force to physics in 9 lines and relativistic quantum gravity.   pdf) And without quantum field theory or without mass units the Yang-Mills millennium problem makes no sense.

Summary. The strand paper and its sequels thus confirm the well-known statement by Einstein:

Insofern sich die Sätze der Mathematik auf die Wirklichkeit beziehen, sind sie nicht sicher, und insofern sie sicher sind, beziehen sie sich nicht auf die Wirklichkeit. ("As far as the propositions of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.")

It has to be added that many other researchers, some of which are cited below, tend to different opinions. But so far, all experiments confirm the result that there are only three interactions, each with one coupling constant. No experiment ever confirmed the exact continuity of space; none reached even close to the length limit. All experiments also confirm all the other predictions of the strand tangle model, all listed on the bet page.

-     -

Bibliography. These sequels confirm that no other Yang-Mills theories are possible:
C. Schiller, Testing a conjecture on the origin of the standard model, European Physical Journal Plus 136 (2021) 79,;
C. Schiller, Testing a conjecture on the origin of space, gravity and mass, Indian Journal of Physics 96 (2022) 3047–3064,,;
C. Schiller, Testing a conjecture on quantum electrodynamics, Journal of Geometry and Physics 178 (2022) 104551,

Different opinions and attempts to build further Yang-Mills theories are here:
Alexander Dynin, Mathematical quantum Yang-Mills theory revisited II: Mass without mass,
Marco Frasca (2014). Exact solutions for classical Yang-Mills fields arXiv:1409.2351v1.
Marco Frasca (2009). Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case, Mod. Phys. Lett. A 24, 2425-2432 (2009) arXiv:0903.2357v4.
Simone Farinelli, Four Dimensional Quantum Yang-Mills Theory and Mass Gap I: Quantization of the Solution of the Classical Equation,
Agostino Prastaro, Quantum Extended Crystal Super Pde's,
A. Sevostyanov, Towards non-perturbative quantization and the mass gap problem for the Yang–Mills field,, arXiv:2102.03224.
Many additional attempts are found at



In Veltman's book, Appendix E (p 249-272) contains the complete Lagrangian of the standard model.



The whole website follows the tradition of the enlightenment: sapere aude.


Rotating black holes

Also (extremal) rotating black holes have a (smallest) diameter given by 4GM/c2. (The value is achieved between the inner and the outer horizon.) Thus, also rotating black holes do not allow to exceed maximum force or maximum power.


Einstein (1932)

VII. Mein eigentliches Forschungsziel war stets die Vereinfachung und Vereinheitlichung des physikalischen theoretischen Systems. Dies Ziel erreichte ich befriedigend für die makroskopischen Phänomene, nicht aber für die Phänomene der Quanten und die atomistische Struktur. Ich glaube, dass auch die moderne Quantenlehre von einer befriedigenden Lösung des letzteren Problemkomplexes trotz erheblicher Erfolge noch weit entfernt ist.

Found in the original handwriting in A.P. French (Hrsg.), Albert Einstein - Wirkung und Nachwirkung (Vieweg, 1985) p. 5.


Fun from Mark Twain

There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact. (Life on the Mississippi)



Il est dangereux d’avoir raison dans des choses où des hommes accrédités ont tort.



How to check statements about physics

In physics, there is only one criterion for correctness: statements have to agree with experiments, i.e., statements have to agree with observations. In addition, for statements that are general, every single consequence has to agree with experiments and observations. These checks must be done with care. It is also useful to check with existing theory and equations, as long as they in turn agree with experiments. In addition, every counter-argument needs to be looked at and to be checked.

In physics, a single disagreement with experiment is sufficient to falsify a statement.

On this physics website, I check every statement in detail. (I have a pledge about this.) Every now and then, false statements crept in, by mistake, or by sloppy language. All known ones have been corrected.

On this physics website, certain statements may be new to the reader. Maximum force, maximum speed and smallest action are statements about nature that have been tested in particular detail. All checks have been published. Apparent contradictions have been resolved. Like every scientist should do, I still collect every counter-argument I can get. If you know one, feel free to write.

Like every physics author, I get emails claiming that maximum (energy) speed is not valid, that maximum force is not valid, and that action values can be much smaller than hbar - despite the lack of any experimental evidence, and the vast and unanimous evidence to the contrary.

Some of those who make such statements only make a simple mistake that is easily corrected, others are fooling themselves over a longer period of time. Some fool others, and a few even fool students. But only checks with experiments count - and they will prevail.

A note about maximum force. The statement that a particular physical quantity is not limited in value is wrong. The statement cannot be confirmed by any experiment; in addition, it is refuted by every single experiment. Every physical observable has an upper limit. (And a lower limit, for the same reason.) So the question is: what is the upper limit for force? So far, only three numbers have been proposed in the literature: c4/G, c4/2G, c4/4G. My own papers - which can be wrong, of course - explain that the first two numbers are approximations that discard or forget factors of 2. But, as usual in science, the c4/4G statement can be falsified by finding a system that produces a larger force.

A note about the 9 lines summarizing physics. The 9 lines and their claim of completeness can be checked and falsified in many ways. Generally, one has to try to find an observation that disagrees with any of the 9 lines. Specifically, one can:
(1) Find any property of nature that contradicts or disagrees with the 9 lines.
(2) Find any property of nature that does not follow from the 9 lines.
(3) Find a new fundamental force.
(4) Find a new elementary particle or quantum number.
(5) Find a new fundamental constant.
(6) Find a deviation from special relativity.
(7) Find a deviation from general relativity.
(8) Find a deviation from quantum theory, quantum field theory or the standard model.
(9) Find a deviation from thermodynamics.
(10) Find a deviation from the least action principle.
If you point out any such result to me, I'll invite you to a good dinner.


Physics in nature differs from physics in social media

It happened regularly. When colleagues, friends or I have posted a correct statement about physics in a social medium, including wikipedia, there are people answering, loud, clear and convinced, that the statement is wrong.

For example, there are numerous social media where people claim that maximum speed is wrong, that maximum force is wrong, or that action is not quantized.

In social media, it is not important whether a statement agrees with experiments, with observations, or with known equations summarizing experiments and observations.

In social media, statements have to agree with the group's opinion. When social media users want to check a statement, they ask how it is received by their group. They do not ask whether a statement agrees with experiment. Therefore, social media are, by design, in permanent danger to be anti-science.

In social media, the users, even in science groups, want to feel good about themselves. Facts are often secondary. Own checks are often unimportant. Feelings of others decide. Own thinking is often deemed unnecessary. As a result of this delegation of evaluation, statements on physics in social media often differ from statements valid in nature. (This difference is also found in medicine and, to a lesser extent, in other natural sciences.)

Pay attention to yourself and evaluate what you read. The issue is difficult to navigate. General advice is not possible. In life, others are important - but facts are as well. Both people and physics require a long, warm look at reality.


Fun from Schopenhauer

Überhaupt aber wird zur Entdeckung des wichtigsten Wahrheiten nicht die Beobachtung der seltenen und verborgenen, nur durch Experimente darstellbaren Erscheinungen führen; sondern die der offen daliegenden, Jedem zugänglichen Phänomene. Daher ist die Aufgabe nicht sowohl, zu sehn was noch Keiner gesehn hat, als, bei Dem, was Jeder sieht, zu denken, was noch Keiner gedacht hat. Darum auch gehört so sehr viel mehr dazu, ein Philosoph als ein Physiker zu seyn.

Parerga und Paralipomena - Kleine philosophische Schriften - Zweiter Band, Kapitel VI - Zur Philosophie und Wissenschaft der Natur, §77 (Berlin, 1862).


How would the strand tangle model affect science, technology and everything else?

If and as long as the tangle model is correct, society will be affected in the following ways:

Technology: no new effects, no new equations of motion, no new devices, no patents, and no new weapons (fortunately).

Government: no new taxes.

Business: no important effects.

Physics: a new teaching topic, and the new research field of tangle modelling.

Other natural sciences, including medicine: no changes or effects.

Mathematics: more research on knot and tangle shapes.

Computer science: development of dedicated strand motion algorithms, new visualizations, more on qubits and strands.

Arts: apart from noting that `Dante knew it already', no effects.

Religion: no effect – except on pastafarianism.

Publishing and internet: new books, new videos, new memes.

Fashion: new T-shirt designs might become fashionable for a while.

Philosophy and comics: a new topic for discussions will arise.

In short, the strand conjecture, if correct, will have a limited influence on society. Nevertheless, the strand conjecture is fascinatingly beautiful: it describes all of nature with help of a unique and simple principle.


Is the standard model of particle physics ugly?

Yes, says Kaku in the video He says that the standard model is a mess, held together by scotch tape, and that it is so ugly that only a mother can like it.

No, says the tangle model: particle physics follows directly and completely from the fundamental principle. The fundamental principle implies the force spectrum, the particle spectrum, and the fundamental constants. The apparent "choices" of the standard model are unique. Other options are impossible and are excluded.


Fun about mathematics

People like to say that mathematics is purer than physics.

But ponder this: (1) Nothing is simpler than the integers. (2) Can one count without using time? (3) And the harder one: Can one count without using space?

It seems that counting is impossible without either space or time.

Ergo: space and time - and thus relativity and physics - come before mathematics :-)


Notes on the progress so far - about strands

Strands reproduce general relativity, quantum theory and the standard model. There are many more aspects to explore, in fact many really interesting aspects, but the general lines are given.

It is time to interrupt and ask: what should be done next?

Of the 9 lines that summarize physics, strands reproduce the first 8, plus part of line 9. No other approach in the literature appears to achieve this. Therefore, two tasks are left.

(1) Line 9 - with all the masses, mixing angles and coupling constants - must be reproduced with more precision than done so far.

(2) The other task, to make more physics students enjoy strands, cannot be expanded further by own efforts. The website and ResearchGate are sufficient. Social media are useless.


Measuring progress towards unification

How many of the 9 lines describing physics are explained by present unification attempts?

Grand unification predicts a bit more than 5 lines, but also predicts unobserved effects.

Strings/superstrings/supermembranes explain the first 5 lines. Researchers are working on more, and hope to explain all; they also predict unobserved effects.

Loop quantum gravity explains the first 5 lines, and no unobserved effects.

Causal sets explain the first 5 lines, and no unobserved effects.

Twistor unification explains almost 7 lines.

Non-commutative space explains more than 7 lines.

Octonion unification explains more than 7 lines - but predicts unobserved effects.

Tangled strands explain, as told in the published papers, at least 8.2 lines. They predict no unobserved effect. And they promise to explain all 9 lines.


Evaluating unification approaches using the 9 lines containing physics

gravity & alike
GUT Super-
least act.
Explained Assumed Assumed Assumed Assumed Assumed Assumed Assumed
v ≤ c
sp. rel.
F ≤ c4/4G
gen. rel.
W ≥ ℏ
q. theory
S ≥ k ln2
Unexplained Unexplained
nucl. int.
Higher gauge
group, unobserved
Higher gauge
group, unobserved
Unexplained Unexplained Higher gauge
group, unobserved
Higher gauge
group, unobserved
Higher gauge
group, unobserved
Unexplained Unexplained Unobserved
Not yet all
Unexplained Unexplained Unobserved

A box is green if the approach agrees with the line. A box is red if the approach does not explain the line or if it contradicts experiments. A box is orange if the approach predicts unobserved phenomena. Orange boxes thus can become green or red in the future.


Further notes on the 9 lines summarizing physics

More people than expected are surprised by the 9 lines that summarize textbook physics. The written version is C. Schiller, From maximum force to physics in 9 lines and relativistic quantum gravity. The text gives the detailed reasons why the summary is correct.

The 9 lines summarize textbook physics. They summarize standard, conventional physics. There is no new physics in them, no non-conventional physics and no untested physics. They contain quantum theory, general relativity and thermodynamics.

A fun comparison is this: What is the difference between the 9 lines and the statement: "P" - where P describes all of physics? Clearly, you cannot calculate anything from the latter. "P" is not a Lagrangian. In contrast, the 9 lines do contain the Lagrangians of particle physics and that of general relativity.

What about the bottom section by Feynman on the page ? The 9 lines are not of this form, neither are the standard model or general relativity. Instead, the Lagrangians of general relativity and particle physics are well-defined expressions constructed from the 9 lines that measure the action in all known physical processes.

Are the ideas in the article on the 9 lines new? No, all are decades old. In fact, they defined the structure of the free Motion Mountain textbooks since the year 2000. But most lines are much older; the lines defining the standard model were completed in the 1970s.

What about the people who claim that general relativity and the standard model are not described by the 9 lines? They probably did not read the written article with enough care.

Is the article on the 9 lines reductionist? No, because they are not axioms. Also the last section in the accompanying article makes the point.

The Lagrangian of the standard model popularized by Gutierrez has about half a dozen typographic errors. It also lacks neutrino masses and PMNS mixing. I would be interested in completing it. The complete and corrected Lagrangian (maybe without ghost terms) should be part of the report of the particle data group. I also suggested them to add it.

If somebody believes that the 9 lines miss some textbook physics, he is mistaken.

If somebody believes that the 9 lines are unconventional physics, he is mistaken. The 9 lines are a way to tell in a simple manner about things that everybody knows. They follow the rule to explain things in a way that children and grandmothers can understand them.

The 9 lines are so simple that even several physicists dislike them. This shows how prejudices can hold people captive.


Notes on the 9 lines summarizing physics

The 9 lines consist of 5 general principles and 4 lines of specific choices. The full version is C. Schiller, From maxmimum force to physics in 9 lines and relativistic quantum gravity.

Quantum mechanics and quantum field theory is part of the 9 lines, even if it is hard to see.

Together, the 9 lines imply that there is a shortest time and a smallest length.

Continuous space-time, though often added to the 9 lines, is in contrast with them – but only at smallest, Planck scales. Therefore, in practice, space-time can be used.

In fact, space-time must be used to talk about nature. But this necessity is already implicit in the 9 lines: the constants c, G, h-bar, and k all contain meter and second.

The 9 lines are not axioms. They just describe all observations. An axiomatic description of nature is not possible, because on the one hand, the lines imply a smallest length and a smallest time interval, and on the other hand, lines 1 to 7 require the existence of continuous time and space. This apparent contrast lies at the heart of physics.


Physics takes time - the more the shorter it is

Many results in physics became widespread only 30 years after their discovery. This is also valid for maximum force.

The summary of physics in 9 lines is between 20 and 50 years old, depending on how one counts. It has not been published before, and is not widespread yet.

Im sum, physics took 100 years to discover that Planck units, corrected by using 4G instead of G, are limits for all physical observables.

Many look at the 9 lines in disbelief. They do not like the summary, but they cannot give a counterexample.

On the page with the 9 lines, there is just standard, conventional physics: the standard model, general relativity, and thermodynamics. Nothing in it differs from common textbooks. They are condensed in 9 lines.

It is hard to swallow how simple physics can be made. Enjoy.


First of April fun about strands

Since the date is nearing again here a simple summary of the strand conjecture about the standard model of particle physics and general relativity:

1. Imagine strands as fluctuating, scaled-down, uncuttable, massless, endless, knot-free, cooked spaghetti – with Planck radius.

2. Combine this with maximum force, maximum speed, the quantum of action and Dirac's trick, and you get all of physics.

A simple introduction is found on the street physics page. Research details are found on the strand research page.


More First of April fun about strands

Do not write me if you eat spaghetti with meatballs or using spoons. Doing so prevents understanding the strand conjecture.

Worse, eating spaghetti with meatballs is a symptom of mental trouble. So is eating spaghetti using spoons. Fortunately, effective and cheap therapies are readily available, e.g., in your nearest Italian restaurant. After treatment, you are welcome to write.

It seems that the Church of the Flying Spaghetti Monster requires eating spaghetti with meatballs or using spoons – but this is in contrast to the Roman Catholic Church, where of course everybody eats spaghetti with ragù or some other sauce, and always with forks.

In fact, Dante, who was well versed in catholic theology, explained already 700 years ago that God is a tangle of strands permeating the whole universe (in his Paradiso, in the last canto). And Dante knew already then, like every Italian still knows today, that God does not contain meatballs.


Will a final theory have a lot of math?

Some physics researchers criticize strands because there is little math.

There is a simple reason for the lack of math: all of physics – quantum theory, quantum field theory, the standard model, general relativity – can be condensed in 9 lines, and they have little math.

If you believe that a final theory needs a lot of math, think again. Why should this be so? You will not find a reason. Instead, you will find a lot of reasons against it: fundamental physics must be discrete; fundamental physics must be algebraic; fundamental physics cannot have differential equations; etc.


The internet, wikipedia and physics

The internet, including wikipedia, is full of statements such as this one: "In general relativity, gravitation is not a force. Instead, gravitation is due to space-time curvature."

The ethical code of Motion Mountain, the same as the one of every scientist, requires a correction, because the above statement is wrong. The correct statement is: "In general relativity, gravitation is a force that is due to space-time curvature."

Force is a technical term in physics, defined, since hundreds of years, as `momentum change per time', or, more generally, as `an influence that produces acceleration'. Using either definition, gravity is a force. Whoever states the opposite confuses or misleads others.

P.S. A dedicated page corrects Wikipedia's errors about the quantum of action.


Continuous space despite a smallest length

A smallest quantum of action, a maximum force and a maximum speed, when taken together, imply a smallest time and length.

This does not contradict continuity. There are two reasons. First, even though action is quantized, inverse force and inverse speed are not. As a result, length and time are not quantized: they are not multiples of a smallest value.

Second, there is a difference between length and action. Action is quantized, but the measurement accuracy and precision for action itself can be as high as desired. Action and the quantum of action can be measured extremely precisely. The quantization of action is easy to observe. In contrast, length behaves differently. Together with a smallest length, there is also a limit to length measurement precision; it has the same value as the smallest length itself. Length quantization cannot be observed. The same is valid for time. Length and time are thus effectively continuous, while action is quantized.

In summary, length values are not multiples of a quantum of length.


Ethical code of Motion Mountain – and consequences

On this web site, and in the pdfs that it provides, there is no statement on nature that is knowingly false or knowingly misleading. The contact page lists a number of more detailed codes of conduct. And like any honest scientist, I follow them. In particular, all statements about nature have been tested in detail.

An example: There is a maximum force in nature, with the value c4/4G.

Consequence 1. The maximum force allows to approach general relativity in an intuitive and simple way.

Consequence 2. In the past decades, the statement has been checked and tested in all possible ways. This included collecting arguments as thoroughly as possible, via publications and via direct exchanges. All arguments, and in particular dissenting ones, have been carefully evaluated. The results of this evaluation have been published. See for example C. Schiller, Tests for maximum force and power, Physical Review D 104 (2021) 124079. Similar papers exist from other scholars.

The statement of the existence of a maximum force is clear and easy to challenge. There are essentially two ways to do so. One way is to check whether the given force value is a limit at all. This requires to produce or to imagine a situation that yields a force or power larger than the limit. A few attempts have been published, but none survives close scrutiny. The other way is to show that the force limit has a different value. Past suggestions for different values, such as c4/G or c4/2G, when re-evaluated, all yield the value c4/4G.

Consequence 3. The statement that nature has a maximum force c4/4G can be used without fear of being wrong.

Consequence 4. However, remember the statement by Voltaire: il est dangereux d’avoir raison dans des choses où des hommes accrédités ont tort. Many are not yet convinced about maximum force. They can be aggressive. Be careful.

A fun story: the present author was banned from an internet physics group by a physics professor for stating that force has a maximum value. Ignorance arises even among physicists. But the incident and the people involved are not to be taken too seriously.


On fun

Telling about maximum force is fun. Some people enjoy it. That is nice. Maximum force is useful in research.

Others get upset by it. What a pity.

The pages on maximum force and on the physics cube profited from the fun.


On matter

In nature, matter is made of spin 1/2 particles.

One can call something `matter' only when its spin is known.

This is a hint for cosmologists, who like to speak about `dark matter'. They use the term `matter' for anything whose density changes as 1/R^3. But that is not how physicists use the term.


4G may almost be a "limit" of nature

G, the gravitational constant, has an unexpected meaning.

4G is the smallest density times time squared possible in nature - if properly defined.

4G limits the straightness of motion of bodies. If motion were too straight, the product density times time squared would be smaller than the limit.

4G distinguishes free from bound objects.


The Bronshtein limit cube

Writing the last paper, on the request of an anonymous referee, I added that one can define every physical theory in the Bronshtein cube - except classical mechanics - by a physical limit.

I now added the page "the physics cube", with two figures.

• Special relativity is defined by the upper limit c.

• Quantum theory is defined by the upper limit 1/ℏ.

• Classical gravity is defined by the upper "limit" 1/4G.

• General relativity is defined by the upper limit c4/4G.

• Quantum field theory is defined by the upper limit c/ℏ.

• Non-relativistic quantum gravity is defined by the upper limit 1/4Gℏ.

• Relativistic quantum gravity is defined by the upper limit c^3/4Gℏ.

The respective limits are not unique. One can also use minimum limits to define each theory, and also use other exponents or other combinations of exponents.

All theories, apart from classical physics, confirm that there is no trans-Planckian physics. Nothing is infinite in nature. There is a Planck limit for every quantity. (Some limits are for single particles only - see volume VI for more details.)


No sterile neutrinos

As predicted since several years on the page with predictions and bets, the MicroBoone experiment found that there are no sterile neutrinos.


Vacuum and particles

Particles are rotating vacuum defects.

When particles move, they push the vacuum aside.

Particles and vacuum are made of the same constituents.

Vacuum is not a solid; it is more a fluid.

Constituents are fluctuating lines.


Transplanckian physics

There is nothing beyond the Planck scale. There is no energy speed beyond c. Nor any action smaller than ℏ. Nor any force beyond c4/4G. Thinking the opposite is a mistaken belief – it is a fantasy.

There is nothing beyond the Planck scale. No matter. No radiation. No space. No time. No effects. No observations. No phenomena. Nothing.


Maximum force and errors

Maximum force c4/4G is a limit in nature, similar to c. It is a local limit, valid at each point in space-time.

Some of my own older papers are wrong on the locality issue. This is science: errors are made; then they are corrected.

A simple explanation that makes the point clear is here: C. Schiller, Comment on "Maximum force and cosmic censorship", Physical Review D 104 (2021) 068501 10.1103/PhysRevD.104.068501, free preprint here.


Pomposity and depression

This web presence tells about physics in a way that differs from many others: physics is made simple and fascinating.

Simplicity is an unusual goal. In today's world, in order to feel better, people tend to state that their job is complicated or difficult. This site does the opposite, in particular about physics. Pompous people do not like simplicity. However, physics is not an elite occupation. Simple and clear thinking is possible for everybody.

Fascination is personal. Things that fascinate me – such as spiders that fly attached to a vertically hanging silk strand, the beauty of a sunset, the maximum force in nature, or Dirac's trick – do not fascinate everybody. In fact, most topics that one person likes are disliked by many others. In particular, depressed people do not like passion. However, passion is needed in the world. Passion is the antidote to addiction, to inner emptiness, and to lack of purpose.

These aspects set apart these books from others. Only read them if your way to experience nature is similar.


Recognizing nonsense

How can you distinguish the statements on this site from the nonsense that bloats the internet?

Nonsense is untestable. Any statement without details, any statement without experimental evidence, or any statement without bibliographic references is suspicious. If you cannot test or check a statement, be careful: it could be nonsense.

Nonsense is often wrong. A statement that does not apply to situations you know by experience is wrong. If your own tests or checks disagree, be careful: it could be nonsense.


Why angry liars are understandable, but not acceptable

How can you distinguish the statements on this site from false statements – lies – told on the internet by non-experts and often even by other physicists? Anger is a good way for spotting liars – though not a perfect one. For example, people on the internet regularly get angry when you tell them

– that empty space can move – as it does in gravitational waves, for example;
– that infinite physical quantities cannot exist – despite confirmation by every observation;
– that gravity is a force – because the internet is full of the (mistaken) denial of this observation;
– that force is momentum flow – even though this is the definition of force;
– that light moves – as happened to a good friend who tried to insert this observation into the German wikipedia;
– that motion defines space – even though, for example, motion of light defines the metre;
– that motion defines time – even though, for example, motion of atoms defines the second;
– that time is what is read from a clock – as generally done by everybody;
– that maybe no new law of physics will be discovered – because there are no known observations disagreeing with the known laws;
– that there is a maximum force in nature – even though this statement agrees with all experiments;
– that noise reduces measurement precision – even though this statement agrees with all experiments;
– that there is a quantum of action, i.e., a smallest measurable action – even though this statement agrees with all experiments.

All these statements are correct, but denied by various angry liars. One should not be too harsh with them. They are consistent: they lie to themselves as well. Therefore, many of them have numerous followers. This is understandable. As a result, you find many of these lies in physics discussion groups on the internet and in wikipedia, labeled as official, correct answers. This last aspect is not acceptable, however.


Cosmology and beliefs

NASA is moving from science to religion: on the page they write: "All we can truly conclude is that the universe is much larger than the volume we can directly observe." The strand model describes general relativity and cosmology without such statements that are untestable or even wrong.


Probabilities in quantum theory

Probabilities arise in all measurements that attempt to beat the quantum of action ℏ.

In any measurement where the attempted precision tries to go beyond the quantum of action, probabilities arise. Measurements who don't, such as measurements in everyday life, do not show any probabilities.

I do not recall to have seen this statement in print elsewhere. Its simplicity is charming.


Wheeler's statements

These statements and questions are old:

Behind it all is surely an idea so simple, so beautiful, so compelling that when – in a decade, a century, or a millennium – we grasp it, we will all say to each other, how could it have been otherwise? How could we have been so stupid for so long?

How come the quantum?

They are from the paper by J.A. Wheeler, How Come the Quantum?, Ann. NY Acad. Sc. 480(1), 304–316 (1986).

In his book A Journey Into Gravity And Spacetime, Wheeler wrote on the last page:

Someday, surely, we will see the principle underlying existence itself as so simple, so beautiful, so obvious, that we will all say to each other, "Oh, how could we all have been so blind, so long."

Striking. Especially when thinking about strands.


A short introduction to strands

The path to the strand model can be told in 12 one-minute pieces: they lead from classical physics to the complete description of motion. The pieces cover all of fundamental physics, from quantum theory and elementary particle physics to black holes and general relativity. The advantage: instead of describing all of motion in nine lines, strands need just one.


More tetraquarks - as predicted

CERN regularly discovers more and more pentaquarks and tetraquarks. This summer it is the Tcc+. As usual, these are pretty results. The strand model suggested and predicted them in the two published papers on the strand model. In fact, the strand model fully reproduces the quark model, without any extension. The failure to observe composite particles with quantum numbers that contradict the quark model is one of the reasons suggesting that the strand model is correct. Here are the two papers:

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 it at

C. Schiller, Testing a conjecture on the origin of the standard model, European Physical Journal Plus 136 (2021) 79. Download it at

See the research page to download the corresponding preprints. Since years, the prediction and bet page contains the following point: "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."


About "not believing" a law of physics

The equivalence of the force limit c4/4G with general relativity was published in 2005. It was explored and confirmed by many independent scholars. Above all, the existence of the local force limit, already proposed in the 1990s by several authors, is a simple statement that can be checked by anybody. And it has passed all checks.

Some people dislike maximum force: they refuse to check it and simply believe that it is wrong. This is in contrast with all observations and in contrast with general relativity. Some even fool themselves with false checks. Many others are honestly unsure about the issue. The two can be distinguished by their politeness.

In fact, some people even dislike the smallest action value. Again, they refuse to check the statement, which is from 1900, and prefer to believe that it is wrong. This is in contrast with all observations and in contrast with quantum theory. Some even fool themselves with false checks. Again, many others are honestly unsure about the issue. The two can be distinguished by their politeness.

Some people believe that the moon landing did not take place. Once more, facts and experimental evidence are dismissed. This is in contrast with all observations and in contrast with material science. Some even fool themselves with false checks.

The reader might encounter people who are completely sure that maximum force, minimum action or the moon landing are wrong. Some people get deeply upset simply when something unusual is said, even if it is correct. Sadly, even teachers of physics are found among such people, and they go around telling other people that the statements are wrong. Instead, the ones that are not sure are polite and open to physical arguments.

The angry people miss a pretty result: textbook physics can be summarized in 9 lines.

Any physicist and any author has to check his statements continuously. The 9 lines have been checked by millions of experiments. Every line has been checked with publications and books. As required by good scientific practice, every line has been checked by numerous independent and anonymous reviewers. The 9 lines have even been checked by listening in detail to the arguments of several such angry physics teachers who searched for every misleading expression. (One can learn something even from angry men.) The 9 lines hold water: there is no false statement in them.

In fact, such angry physicists miss even more. The 9 lines of physics also suggest a path to unification that differs from the paths explored in the past. Mistaken beliefs about maximum force, minimum action or the moon landing prevent from taking part in this new adventure. The new adventure is introduced here.


Possibly the last law of physics

If the nine lines of physics are correct, and if strands are the complete description of motion, then the expression F ≤ c4/4G for the maximum local force in nature is the last law of nature that was found. Is that really the case?

The question is not easy to settle, because the simple force limit c4/4G is still unknown to many physicists. The limit can be checked by real experiments and thought experiments, and passes all tests.

The statement "c4/4G is the maximum local force" is very easy to falsify: one just has to produce a larger value. A thought experiment realizing a larger value is sufficient for falsification. So far, nobody succeeded, not even the attempts published in 2021. These publications added forces at different points in space, and thus failed to provide an example of a local force value that exceeds the force limit.

The force limit is tied to horizons. It occurs near horizons. Whenever one attempts to exceed the force limit, the next horizon prevents this from happening.

For example, charged black holes do not allow exceeding the force limit, despite the hope to add gravity and electrostatic effects. Nuclear forces cannot be used either.


Physics in nine lines

All of experimentally verified physics can be summarized on one page. Nine lines are sufficient. This way to formulate textbook physics was the starting point for looking for a shorter summary. This led to the strand conjecture.


Strands on PBS television

The animations by Jason Hise were shown on the PBS TV program at - including a brief mention of strands.


Doing research is like walking on a mountain ridge

Like in every aspect of life, on one side there is the danger of vanity, on the other the danger of foolishness. The middle path is the right one. But then, behind you, there are the people who discourage you to take the path at all. The solution is to follow the right inspiration. The path is broader than expected.


Advice to students in physics and mathematics

You will not find a thesis advisor yet. At present, you can only explore strands as a pastime. A few potential topics: Explore the connection with qubits. Improve the calculations of the fundamental constants. Expand the statements of the papers – on tangle classification, on other space defects – into theorems. Solve one of the other problems given on the prize page.


The tiniest theory of nature (new version)

To describe nature, use the speed limit v≤c, the action limit W≥ and the force limit F≤c⁴/4G: this gives quantum theory and general relativity. Realize the limits with crossing switches of strands with Planck radius, form rational tangles, deform them with Reidemeister moves: this gives the particles, the interactions and the Lagrangian of the standard model. Not more, not less.

The strand conjecture is the tiniest theory of nature.


Disappointed by Susskind

Susskind claims that physicists presently know only a small part of fundamental physics. That is wrong, and he knows it: all open questions in fundamental physics fit on one page, whereas all answered questions fill numerous books.

Note added later: Yes, we can summarize physics in 9 lines. Still, the open questions are even shorter: Are the lines right? Where do they come from? In fact, strands even claim to answer them both.



Strands imply that attempts to go beyond the standard model resemble attempts to move faster than the speed of light.


More comments

Recently, somebody wrote of the strand conjecture: "You tell there is no physics beyond the SM and GR? You speak to god lol."

No. Physicists, including myself, use a more accessible source: the library. The statement about the lack of new physics comes from tens of thousands of researchers who have checked it for over 50 years and published the results in physics journals.

The statement is also a prediction that follows logically from the Dirac trick at the Planck scale.

When experiment and theory agree, there is a non-vanishing possibility of correctness.


What is a fundamental theory?

A physicist wrote: "The strand conjecture is not a theory, as it has no Hamiltonian or Lagrangian. It has no equation of motion."

Some physicists forget that special relativity follows from a maximum energy speed c, quantum theory from a minimum action , and general relativity from a maximum force c4/4G. Thus, modern physics follows from inequalities. Those inequalities determine the Lagrangian, the action, and the Hamiltonian.

Any unified theory must explain these extremal values. And it must describe experiments. Any unified theory is not based on a Lagrangian. Lagrangians come after unification.

A unified theory explains and derives the Lagrangians of general relativity and the standard model. Strands do this. That makes studying them fun.

The limits c, G and already derive the central parts of the respective Lagrangians. On top of this, strands also explain the gauge groups, the particle spectrum, the quantum numbers, the masses, the coupling constants and the mixing angles. Strands derive the principle of least action, derive all Lagrangians and describe all experiments.

Strands provide the simplest unified theory.


More gentle fun about Kaku

Michio Kaku says that a complete theory can answer many questions. However, all the questions he lists are already answered by present physics:

What happened before the Big Bang? Nothing, as there was no time.

Where did the big bang come from? Nowhere, as there was nothing and no place.

What lies on the other side of a black hole? Nothing.

Are there other universes? No.

Are there other dimensions? No.

Is time travel possible? No.

Why are we here? To watch ads.

How to escape the Big Freeze and the death the universe? Nobody will have the problem.

Can time go backwards? No; time does not go at all.

Are wormholes possible? No; as quantum gravity showed.

In a sense, his questions are arguments in favour of the strand conjecture, which predicts that no effects and discoveries are left.


Gentle fun about Kaku

Kaku proposes to check any complete theory in this way:

1. Build new accelerators.

2. Look for deviations from the Standard Model.

3. Looking for decays of new subatomic particles.

4. Determine the nature of dark matter.

5. Detect gravity waves from the Big Bang with space-based gravity wave detectors.

6. Look for deviations in inverse square law.

However, he gives no testable predictions on these points. So a check of his ideas is not possible. In contrast, the strand conjecture makes clear predictions on points 1 to 4: no new effects, and no unknown particles. Predictions about points 5 and 6 are still in work.


Do strands modify universal gravity?

After much deliberating, I decided to write this down. The thought arose during the Covid summer of 2020. All this might be straight for the rubbish-bin.

It might be that the following holds: strands might imply that at huge distances, strands hold two masses together more strongly than by universal 1/r2 gravity.

In spinning or orbiting systems, such as an electron around an atom, fluctuations that perform the belt trick continuously untangle the strands of the two subsystems. This untangling allows the spinning and orbiting to continue endlessly.

But at huge distances, such fluctuations possibly might take too long a time. This might occur at galactic distances. In such cases, tangled strands could lead to an additional attraction that keeps the orbiting system closer together than without tangling.

The idea of a tangling effect in gravitation is far-fetched. It is probably best to look for ways to refute it. Does the tangling effect really exist? (Probably not for non-expanding space.) If the tangling effect exists, does it lead to an attraction? (Do tethers have fixed length? No.) Do tethers really limit motion? Is the tangling effect related to expansion, to the Hubble constant or to the cosmological horizon? Do the additional strands due to expansion delay the untangling? (Maybe.) Do really only the additional strands due to expansion hamper the untangling, and not the usual strands that make up space? (Maybe.) How does the tangling effect scale with distance? (Maybe it increases. Maybe it decreases less rapidly that gravitation.) At which scales is the tangling effect larger than the reduction of gravity due to expansion? (Maybe always.) At which scales is the tangling effect larger than universal gravity? (Maybe at galactic scales - but why?) Can one distinguish the tangling effect from the tendency of the universe to keep everything together anyway? (Maybe yes.) Does the tangling effect lead to the external field effect seen in satellite galaxies? Does the tangling effect work differently if the satellite galaxy orbits in a plane that differs from the rotation plane of the central galaxy? What does tangling mean for the equality of inertial and gravitation mass? (Maybe it remains.)

All of this is most probably utterly wrong. But it was fun to imagine.

There could even be an effect due to strands that are common to several particles. This situation might change gravity at long distances as well. (Continuing to collect crazy ideas.)


On mistakes

When doing theoretical research, mistakes occur. That happens to everybody. Acknowledge the mistakes, correct them, and then go on.

Everybody makes mistakes. But when people cannot admit them, life gets sad. Several researchers that I admire are in this trap. What a pity.


The least of theories

The strand conjecture in one statement: Dirac's trick at the Planck scale describes all nature. So far, this statement agrees with all observations. And it contains all the equations of motion for space and particles. The statement appears to be the tiniest of all theories about nature. The figure provides a slightly longer description.

Fundamental principle of the 
strand conjecture

This figure contains general relativity and the standard model of particle physics, as is shown on the research page. Ways to falsify the strand conjecture are listed on the prediction page.


Living physics

The five points mentioned in the previous blog entry, "Enjoying physics", will be discussed for many years to come.

Some counter-arguments to maximum force were uploaded on arxiv in 2021. But they were based on a mistaken reading of the force limit: c4/4G is a local limit. One cannot add forces at different locations to show that the limit is not valid.

An alleged counter-argument to maximum power c5/4G is also found on arxiv. The manuscript does not provide counter-examples, but derives a higher limit.

I predict that the discussion on maximum force, maximum power and maximum mass flow will be similar to that about maximum speed c that occurred a century ago. It will take a long time until a consensus arises.

Another well-known scientist mailed me counter-arguments to the relation between strands and U(1), SU(2) and SU(3). But then he had to admit that his counter-arguments had no merit.

So far, the counter-arguments were not correct, but they might well find something in the future. Research advances in this way.


Enjoying physics

Explaining the fundamental constants of nature (masses, coupling constants and mixing angles) is a problem. Maybe it even is an important problem – though that is not sure. Above all, these constants are riddles. And solving riddles is fun.

1. It was fun to find out that general relativity follows from the maximum force c4/4G.

2. It was fun to find out that both general relativity and quantum theory follow from fluctuating strands: space, curvature, gravity, wave functions and Dirac's equation follow from strands.

3. It was fun to find out that the gauge interactions follow from strand deformations: U(1), broken SU(2) and SU(3) follow from strands.

4. It was fun to find out that the particle spectrum follows from tangles of strands: quarks, leptons, gauge bosons, Higgs and gravitons follow from classifying tangles.

5. It was fun to find out that also the fundamental constants follow from fluctuating tangles of strands.


Known physics beyond the standard model

Only one group of observations beyond the standard model is known without any doubt:

        The coupling constants, the particle masses, and the mixing angles.

Institutions like CERN, DFG, INFN, FOM, CNRS, the Solvay Institutes, RIKEN, NSF, the various science academies, and even private sponsors should invest in understanding these fundamental constant values. This is by far the most important open problem in particle physics and in basic physics.

This statement does not imply that the fundamental constant problem is important when compared to health or peace; it just implies that the other open problems of particle physics and basic physics – dark matter, new collider searches, other dimensions, microscopic black holes, etc. – are clearly less important. Investigating those problems may lead to physics beyond the standard model, whereas the fundamental constants are physics beyond the standard model.

Also, the fundamental constant values determine the world around us: all materials, all shapes, all sizes and all colours. They determine life and beauty.

In addition, proposed explanations of the constants are straightforward to evaluate: They must yield the standard model and must predict values for the constants that agree with measurements. This double check eliminates all fake science.


In fundamental physics, life is too short for experiments and for vixra

There is much to build and read. But there are also many ruins and failed ideas.

Strand unification only needed one idea and no experiment: the extension of the fundamental components, as proposed by Paul Dirac for quantum theory and by Gregorio Weber for black holes.


Physics from Dirac's trick

The strand conjecture extends Dirac's trick to a fundamental principle, by relating it to the Planck units. This has a simple consequence:

    Every equation in physics appears to follow from the Dirac trick at the Planck scale.

It took some time to find this way to express the result of the strand conjecture. It might be the most intriguing formulation.


The clown of fundamental physics

Michio Kaku, the string theorist turned attention grabber, states that the aim of physics is to find a "God equation". According to his twitter messages, it has the following properties:

(1) It must contain general relativity, (2) it must contain the standard model, (3) it must be finite.

Some remarks are appropriate. First, God has nothing to do with it. Secondly, if "equation" means "evolution equation", the answer is: no such equation exists, because points in space-time do not exist at the fundamental scale; they are emergent. Finally, if "equation" can be "inequality", then one possible answer is the Dirac trick at the Planck scale, i.e., the fundamental principle of the strand conjecture. The fundamental principle and the strand conjecture fulfil the three requirements.

Nature and physics have no God Equation, but, if at all, "God inequalities": special relativity derives from maximum speed v≤c, quantum theory from minimal action W≥ℏ, general relativity from maximum force F≤c⁴/4G or maximum power P≤c⁵/4G. See the paper: C. Schiller, General relativity and cosmology derived from principle of maximum power or force, International Journal of Theoretical Physics 44 (2005) 1629–1647. Download it at Read it online for free at


Why the tangle model is worth thinking about

Mainstream. Confirms quantum field theory, the standard model and general relativity.

Correct. Agrees with all experiments.

Serious. Yields the standard model Lagrangian and the Hilbert Lagrangian.

Fascinating. Derives U(1), SU(2) and SU(3).

Fascinating. Derives the particle spectrum.

Fascinating. Explains the fundamental constants.

Empirical. Makes numerous experimental predictions.

Historical. Combines ideas of Planck and Dirac.

Published. In peer-reviewed journals.

Sober. Predicts a high energy desert.

Daring. Simple to imagine.

No misuse. No harm.

Disappointing. No new effects.

Sensible. Yields no nonsense.

Complete. All equations in physics follow.

Elegant. Based just on Dirac's trick at the Planck scale.


Hawking's humour

Hawking ended his book with his typical kind of humour: “However, if we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason - for then we would know the mind of God.”

The humour is in expressions like "ultimate triumph" and "the mind of God". Most statements Hawking makes about the complete theory are neither correct nor serious. Hundreds of results of mathematics range higher on the achievement scale of human reason. And God has no mind, of course. This is neither hype nor nonsense: it is just humour. If you ever heard Hawking talk, you know that such statements were never meant seriously.

After humour is eliminated, the task is clear. A complete theory has to explain the standard model and general relativity, as well as all the constants, numbers and concepts in them. One candidate has been published in a professional physics journal at It is indeed understandable, in broad principle, by everyone.


From a message to James Gleick

We physicists know that a complete description of nature exists. You also know it yourself: you can talk about everything you observe! A complete description (a "ToE") just means doing this with precision.


Fun about Hegel

Hegel famously wrote, and many others agreed: Wie es keine Bewegung ohne Materie gibt, so auch keine Materie ohne Bewegung.

Experiments (and strands) show that he was wrong. True, all matter shows motion. However, there is motion without matter, such as light, or, even more clearly, gravitational waves.

But we could say: Wie es keine Bewegung ohne Fäden gibt, so auch keine Fäden ohne Bewegung.


Experiments vs strands

The hopes for physics beyond the standard model and beyond general relativity are intense and widespread.

Experiments destroy these hopes with regularity, since decades.

Strands predict this state of affairs, at the same time predicting the full standard model and full general relativity.

A single theory, also a simple theory, against everybody else. There are fascinating times ahead.


Prejudices that prevented progress in fundamental physics

There is - and unification must have - observable physics beyond the standard model. (This statement contradicts experiments; it is a wish.)

There is - and unification must have - observable physics beyond general relativity. (This statement contradicts experiments; it is a wish.)

General relativity and quantum theory are incompatible. (I propagated this prejudice myself; it is widely believed, in the hope to get rid of circular definitions, and in the hope to find new physics. But the statement is not proven by any experiment.)

Unification does not need to care about fundamental constants. (This statement contradicts experiments: the constants are the only experimental data beyond the standard model.)

Unification is based on vibrating superstrings. (Vibrating superstrings do not explain the measured fundamental constants.)

Unification is based on an evolution equation. (This statement contradicts experiments. There are no experiments proving that points of physical space exist in nature. On the contrary, all experiments confirm the indeterminacy relation and suggest the lack of points in physical space.)

Conclusion: unification must explain the fundamental constants - without an evolution equation and without observable physics beyond the standard model.


The effects of names

"Strands" are not the only possible name for the fundamental constituents.

Talking about the "snake model" of space is definitely less appealing.

"Worms" are another option. But somehow, talking about the worm model of space lacks charm. On the other hand, the term "vermicelli" – "little worms" in Italian – is the historic term for the modern "spaghetti". The old term is still in use in Italy, for certain types.

Internationally speaking, "spaghetti" might be a better option. Talking about the "spaghetti model" will make appetite – if properly served.

Between Dante's bliss-inducing knot (see further down) and cooked spaghetti: the strand conjecture remains, to a large extent, Italian.


The origin of the standard model

Strands imply: the origin of the standard model is that at Planck scale, everything is connected.


What is beyond the standard model

Strands state: beyond the standard model there are only the fundamental constants – elementary particle masses, mixing angles and coupling constants – plus the number of generations and of interactions, the dimensions of space, and the gauge groups.

In short, strands state that beyond the standard model there is only the origin of the standard model – nothing else.


Why was the flower not noticed?

First reason. Numerous physicists believe that maximum force and power do not exist. Many physicists believe that minimum action does not exist. Some physicists believe that the Planck scale does not exist. All these beliefs are in contrast with every experiment. Wikipedia and various internet forums give these false beliefs a platform.

Second reason. People dislike strands because they cannot imagine that they are indivisible. In everyday life, all connections can be cut. In fundamental physics, they cannot. Strands imply that everything is connected to everything else. In contrast to everyday life, these connections cannot be cut.


The flower

People looking for the final theory are like people looking for an unknown plant in an unknown landscape. Most people are looking for a huge, impressive plant in an exotic setting. Now, it seems that the final theory is a small, beautiful flower in a green meadow on a gentle hill. Most people searching for the final theory run past the hill and past the small flower. They do not notice it, and they do not care about it.


Neutrino masses

Al least two neutrinos do have mass. This is possible inside the standard model and is no proof of physics beyond the standard model.

Incredibly, some physicists are adamant that the standard model forbids neutrino masses. The anonymous referee for a serious physics journal is an example. It is sad to hear such nonsense.


Tethered rotation

The relation between tethered rotation and the Dirac equation was first described by Battey-Pratt and Racey in 1980. They wrote to Dirac, but he did not answer. Unfortunately, Dirac died shortly afterwards.

When Christoph Schiller rediscovered the relation, he was confused. Tethering is the reason for the complexity of the Pauli and the Dirac equations. Tethering is the reason for the operator algebra in both equations. The explanation with tethers is simple and beautiful, but very few seem to be interested in it.

The lack of knowledge about tethered rotation appears to be the main reason that the strand model generates little interest among researchers.


Theoretical physics research in companies

The hardest way to organize fundamental physics research is inside a company. If nature's idea of unification is not that of your boss, who decides how to proceed? The boss of course. Searching for unification inside a company is like searching for a whirlpool inside a church building: it's unlikely to succeed.


Organizing theoretical physics research

The best theoretical physicists I met were quiet characters. But today's world is full of vociferous theorists. They are of little use. We need quiet researchers in quiet institutes. In short: we need ivory towers.


Why so little progress?

The last years have shown that a majority of theorists across the world who work in fundamental physics use their energy to discourage others: they want others to stop searching for unification. The attitude is extremely pervasive. These theorists do not even consider checking a unified proposal against experiment. They dismiss any such proposal right away. If you are an exception, feel free to write.


What is fundamental theoretical research?

A personal definition: question everything, check everything.

Some consequences: (1) points do not exist; (2) elementary particles are not points; (3) other dimensions do not exist.


Are researchers bosons or fermions?

Alain Connes wrote: « I was asked to write some advice for young mathematicians. The first observation is that each mathematician is a special case, and in general mathematicians tend to behave like “fermions” i.e. avoid working in areas which are too trendy, whereas physicists behave a lot more like “bosons” which coalesce in large packs and are often “overselling” their doings, an attitude which mathematicians despise. »

But the world is not that simple. The CERN paper on FCC Physics Opportunities has 1364 authors. However, after reading it, one must admit that they are not overselling the FCC. The future options of particle physics are not that bright. High energy physics is at a crossroad.


A naming question

When is a theory about fundamental physics "of everything" or "unified"? Of course, any such theory has to agree with all observations, experiments and measurements. Of course, such a theory has to agree with quantum field theory, the standard model, general relativity and cosmology – at least under usual experimental conditions. And of course, such a theory has to make testable predictions. But above all, such a theory must explain what is unexplained so far. This includes explaining the particle spectrum and the four interactions, explaining the mass values and mixing angles of all elementary particles, and explaining the value of the coupling constants of the three gauge interactions, ab initio. If your favourite physics theory does not, it is neither "of everything" nor "unified". The strand conjecture is.


2019 – CERN is careful but confused.

In their 2019 report available at, a group writing for CERN states that three questions in fundamental physics are open: dark energy, dark matter, and the baryon-antibaryon asymmetry.

On the one hand, they are more careful than in the past. On the other hand, they state that "more questions than ever remain open". (Is 'three' really 'more than ever'?)

They then conclude that "there is thus exceedingly convincing evidence that there must be Physics Beyond the Standard Model (BSM Physics)". However, neither the three open questions they mention nor the rest of the report provides such evidence.


2019 – Why is G so hard to measure precisely?

G is hard to measure precisely because it is hard to translate its effects into an electrical measurement. Or into an optical one. Or into a magnetic one.

G is hard to measure because its quantum effects are rare. We know only about one for sure: the particle masses. Possibly the extremely small cosmological constant is a second. This rarity is the reason that G does not appear as constant in the new SI, the new international system of units.

(Enjoy exploring these two theses.) Strands make the same point.


2019 – Dare to be simple and clear

Many researchers have difficulties to accept that a unified theory can consist of a few lines and the three fundamental constants c, and G. They cannot conceive that this might be correct. Such a simple description is so strongly opposed to their personal convictions and their dreams that even the agreement with all experiments does not count any more.

Social experiments on two physics forums in two different continents have shown how angry physicists can get. Many cannot conceive how far one can advance in physics with simple ideas. Many cannot recall from their studies that well-chosen algebraic relations do imply differential equations.

My own story was different. I actively searched for a simple way to derive the gauge interactions of the standard model from c, and G. When I found it, I was quite happy. (And I enjoy passing it on to others.) Even cosmology is simple: nature is a single strand.


2019 – Dante on nature, topology and beauty:

Nel suo profondo vidi che s’interna,
legato con amore in un volume,
ciò che per l’universo si squaderna:

sustanze e accidenti e lor costume
quasi conflati insieme, per tal modo
che ciò ch’i’ dico è un semplice lume.

La forma universal di questo nodo
credo ch’i’ vidi, perché più di largo,
dicendo questo, mi sento ch’i’ godo.

Paradiso 33, 85-93.


The translation by Laurence Binyon (but remember: traduttore, traditore):

I beheld the leaves within the unfathomed blaze
Into one volume bound by love, the same
That the universe holds scattered through its maze.

Substance and accidents, and their modes became
As if together fused, all in such wise
That what I speak of is one single flame.

Verily I think I saw with my own eyes
The form that knits the whole world, since I taste,
In telling of it, more abounding bliss.

The translation by Henry W. Longfellow:

I saw that in its depth far down is lying
Bound up with love together in one volume,
What through the universe in leaves is scattered;

Substance, and accident, and their operations,
All interfused together in such wise
That what I speak of is one simple light.

The universal fashion of this knot
Methinks I saw, since more abundantly
In saying this I feel that I rejoice.

Some physicists claim that the laws of nature are or even have to be beautiful. That is not correct. The truth is another: nature itself is beautiful. Though, often, its beauty is hard to see.

Dante goes even further. He says that every aspect of nature shows the love tying it all together. He distinguishes, like many theologians and like all physicists, two general groups of aspects of nature: 'substance' (the conserved quantities of physical systems, such as electric charge and other quantum numbers) and 'accidents' (the quantities describing the state or the initial conditions of systems, such as position, momentum, etc.). Dante finds that the two groups are fused together in one knot that encompasses the whole of nature. Seeing and contemplating this universal knot fills him with joy. (The legend that Dante was thinking about the strand conjecture is apocryphal.)


2009–2019: Whispering the unthinkable

1. The periodic table gives an overview of all elements. Then quantum theory explained its origin, its scope and its details. Once it was finished, no elements remained to be discovered.

2. The standard model of particle physics gives an overview of all particles, all gauge interactions and all fundamental constants. Then strands explained its origin, its scope and its details. Once it was finished, no particles, no interactions and no constants remained to be discovered.

The second paragraph is "unthinkable". Many physicists get angry when these statements are made. A final and complete description that is that simple cannot exist, they claim. This is the biggest hurdle that strands face. Indeed, for many researchers, the idea "nothing left to discover" is a nightmare. And another nightmare is the idea of a complete model of nature that is simple.

Most people that wake up from a nightmare are upset. (But there is still hope: there should be something beyond element 118, so there might be something beyond the standard model.)


2019 – The contrast between convictions and experiment

Some people ask why the opinions of researchers about the strand conjecture are so negative, despite its complete agreement with experiments, and despite the additional results it provides. In a sense, the answer is the list of reasons to bet against the conjecture. In short, almost every researcher in this and in related research fields has different convictions, different thinking habits, different hopes and different dreams. Just ask the theoretical physicists around you.

Dreams are important, and people do not like to change them. When a change is required, people often get disappointed or angry. Understanding and patience are needed. Even if people are impolite. Understanding and patience are needed until people can translate their dreams into the new way of thinking. Then the motivation and the enthusiasm come back. (But this is dangerous. Understanding is not what angry people want.)


2019 – Whispering about the fundamental principle

Peter Woit wrote:

"Unfortunately, we know of no principle or symmetry that would provide a constraint that picks out the Standard Model."

Yes, we do know one: the fundamental principle of the strand conjecture. Describing elementary particles as rational tangles reproduces the gauge groups and the particle spectrum. The fundamental idea is on arxiv since 2009, with particle tangles that are now known to be wrong. The present proposal, with consistent particle tangles, was published in Physics of Particles and Nuclei in 2019. (Of course, there can still be mistakes. This is unusual research with unusual features: it agrees with experiments and makes falsifiable predictions.)


2019 – The whisper of strands

Strands are simple. And nevertheless, they contain the full standard model and general relativity, with all their details.

Strands do not shout. Strands do not predict spectacular effects. They predict that we already know almost everything. Strands whisper. They just add the origin of the fundamental constants.

Strands were waiting to be discovered for almost 90 years. 90 years ago, Dirac used strands in his lectures to explain spin 1/2 to students. Because strands only whisper, it took a long time to notice that strands explained much more - in fact, every aspect of motion.

(With age, hearing ability decreases. Let's hope that there was no misunderstanding.)


2019 – Dante, La Divina Commedia, Paradiso 33, 115-120

Ne la profonda e chiara sussistenza
de l’alto lume parvermi tre giri
di tre colori e d’una contenenza;

e l’un da l’altro come iri da iri
parea reflesso, e ’l terzo parea foco
che quinci e quindi igualmente si spiri.

Dante explains that seeing into the light he could see God. It is an intense experience, one that words cannot describe. Before, seeing the universal knot was like seeing all of nature, and all of God's love. Now, he sees God himself: he sees three coloured circles.

A few lines later, the Divina Commedia ends. To avoid issues with authorities, Dante allowed the publication of the last part only after his death in 1321. (According to legend, he feared that insisting on the three-dimensionality of space - as in 'tre giri' - would bring him trouble with science authorities, who at the time favoured higher dimensions.)

The Italian text and an English translation can be found here: On the three circles, see and also


2019 – On the fear of failure or ridicule in research

The internet allows to produce websites about almost any topic, including crazy 'research' on physics. Nevertheless, fear still abounds. Here is a simple clue.

A list of over 1000 crazy physics 'theories' is available at It appears that the list contains no research on calculating the fine structure constant. Also a literature search in physics research journals yields practically no papers on the topic.

In 2019, the world's most crazy researchers and the world's most professional researchers seem to agree: calculating the fine structure constant is too crazy. This used to be different in the past, when Pauli, Heisenberg, Dirac and Feynman thought about the topic and encouraged others to do so as well. The internet has videos showing Dirac - interviewed by Friedrich Hund - and showing Feynman - in his famous four lectures at the basis of his book 'QED' - mentioning the challenge. These researchers did not fear failure or ridicule. In a few decades, with the rise of the internet, the climate has changed: the lack of fear gave way to a landscape of fear.

By 2019, the landscape of fear had led to a unfortunate consequence: across the world, nobody seems trying to understand the fundamental constants. Researchers prefer inventing new unified models to understanding, let alone calculating, the fundamental constants. This is a sad state. Understanding the constants is obviously an issue that allows progress. It is also sad for a second reason: strands imply that understanding these constants is the only new result of a unified theory. If this prediction is correct, then determining the fundamental constants is the only progress left over in fundamental research. And if this prediction is correct, avoiding to understand the constants implies blocking the only path towards progress! In short, it seems that the fear of ridicule is now halting the progress in fundamental physics. All of it.

P.S. A few details are wrong in the above paragraphs. ResearchGate does have a few authors who try calculating the fine structure constant. But they use numerology, instead of deducing the value from a unified description; they do not advance understanding. The thesis remains valid: the fear of ridicule is an obstacle to fundamental research. (Some researchers state openly that they prefer searching under a lamp to searching in the dark. It is clear why: the lamp is held by colleagues who light up the region without ridicule.)


2019 – On research blogs

This site used to link to a blog on the internet. But the entries about other researchers in that blog are not friendly enough for my taste. Fundamental research needs to be filled with the delight of trying something new and fascinating. This delight is missing in many people. Research needs an environment without scorn and disdain, but an environment with passion and encouragement. Above all, we need an environment without the fear of errors. (Gentle fun is acceptable; but ideally, the fun is directed against oneself.)


2019 – Betting - and paper titles

The tangle model is more serious than a hypothesis or a conjecture. It is a bet. It is a bet about the correct description of nature.

Such bets are rare. The paper on the strand conjecture is one of less than twenty (!) publications in the whole research literature that have both "standard model" and "general relativity" in their title.


2019 – Naming

The tangle model promises to be a complete description of motion. The expression in italics is preferable to the more sensational terms that are used in other fields. The term 'theory of everything' is reserved for unsuccessful esoteric healing attempts, the term 'final theory' is reserved for titles of bad books and films, and the term 'world formula' is reserved for calculating the optimal way to park a car backwards.


2019 – Gravitation

Strands appear to describe gravity in a simple and intuitive way. This preprint makes the point in detail.


2019 – T-shirts and unification

In 1988, Leon Lederman was interviewed by the Chicago Tribune (see Google). ''My goal is to someday put it all on a T-shirt,'' Lederman said with a smile. ''The formula will be the rules that explain the building blocks of the universe, and the glue and cement that makes the big thing that we can touch, and see and smell. We physicists believe that when we write this T-shirt equation it will have an incredible symmetry. We'll say: 'God, why didn't we see that in the beginning. It's so beautiful, I can't even bear to look at it.' ''

Also in 1988, John Barrow - as he confirmed in an email he sent to me - used the T-shirt image as a wish for physics research in his 1988 Gifford Lectures at Glasgow that were a precursor to his book Theories of Everything: The Quest for Ultimate Explanation 1991.

The strand conjecture appears to realize these wishes.


2019 – The unsung fascination of the coupling constants

Observation: The strong coupling constant is the same for each quark type. The fine structure constant is the same for all quarks and all charged leptons. And a similar statement can be made for the weak coupling constant. Equivalently, all charges are quantized. This quantization is "perfect": no deviations from exact integer multiples are observed.

Why is this the case? There does not seem to be a discussion of this issue in the literature. This is a pity, because the observation is hard to explain. Why should an electron behave electrically exactly like all quarks, apart from an integer multiple? After all, they are rather different: they differ in their masses and in their structure - whatever it may be. Nevertheless, apart from an integer multiple, the couplings are observed to be independent of their structure.

The latest preprint about the strand conjecture discusses this issue - and proposes an explanation. It is unclear whether other unification attempts can explain this property.


Early 2019 – Enjoying the beauty of the standard model of particle physics

If the tangle model is correct, the standard model results from a single fundamental principle.
If the tangle model is correct, the list of known elementary particles is complete.
If the tangle model is correct, the origin of gauge interactions and symmetries is understood.
If the tangle model is correct, the fundamental constants can be calculated.
If the tangle model is correct, also gravitation, cosmology, and empty space result from the fundamental principle.
If the tangle model is correct, the Bronshtein cube is confirmed and unification is possible.

It is fair to say that with these potential results, the tangle model has a certain charm. In addition, the tangle model agrees with observations; this turns its charm into downright seduction.

The fascination for the fundamental constants - elementary particle masses, coupling constants and mixing angles - is not shared by many. The quest to understand their origin is not always seen as a problem of fundamental physics. But if you do so, then you will enjoy the tangle model.


2018 – Steps

Some influential researchers complain that there is no progress in unification, despite a record number of researchers. The number of unification proposals in the literature is indeed low. The preprint with a new proposal is now available. Despite the simplicity of the fundamental principle, the explanation of the full set of Feynman diagrams is striking.


Early 2018 – Polishing

Several particle tangles have been updated: now the tangle model reproduces all known experimental data in a consistent way. I gave a talk on the topic at the DPG meeting. A researcher encouraged a publication.


The limitations of the standard model of particle physics

High-energy physics is split in two camps. On the one side, many experimentalists and theorists find that there are no differences between the standard model and experiments. On the other side, certain physicists state that the standard model has flaws.

Behind this split of opinions is a battle for funds. If a researcher proposes a theory that does not predict any new effect, there are no funds. Theorists and experimentalists only get money for searches for something new. Thus, many researchers, to get money, tend to state that the present theory has flaws, tend to back improbable new theories, and finally find nothing.

The situation arises when people crave money. There sometimes is a gap between those seeking truth and those seeking money. So far, there is no reason and no data for stating that the standard model has flaws. It is incomplete, but it has no flaws. The wish for flaws is leading people astray. (December 2017)


Avoiding unification - and exceptions

Not many candidates for unified models have appeared in the past twenty years. You can follow this lack of ideas on arxiv and on the various physics blogs around the world. Researchers seem to avoid unification. But there are exceptions: Nicolai and his group have published a proposal. It is a very "small" expansion of the standard model; it also assumes that general relativity is valid at (almost) all energies. It is a really good sign that researchers are exploring small extensions of present theories instead of big revolutions. That definitely seems the more promising way to proceed. (October 2017)


On defects in space or space-time

Various quantum gravity and cosmology researchers have explored the effects of space(-time) defects on the propagation of light. For example, they explored whether such defects have effects on the sharpness of stellar images. Most scholars assume that these defects are new, so far undiscovered objects. Few of these researchers seem to have asked whether these defects could somehow be the known elementary particles. The reason for avoiding this topic is not clear. (2016)


On T-shirts

Many T-shirts refer to the act of creation. Also the one on the tangle model does so. The text on it reads: "... and there were motion and colours, black holes and quantum particles, life and us all."

Witnesses have confirmed that the T-shirt is a faithful reproduction of God's favourite T-shirt. God likes it because his whole creation is described on it, including quantum theory, general relativity, cosmology, and the standard model of particle physics, with all its fundamental constants.

The same witnesses also confirmed that humans took a long time to find out how simple the act of creation had actually been.


On unknotted tangles

In 2014 a reader mailed me suggesting to avoid knots. In 2015, an anonymous reader posted a similar comment on a blog:

"Christoph Schiller's strand model is not popular because it is wrong. It is not even self-consistent. Since you bring up knot-theory in your post, let's use that as an example here: many known interactions would violate basic knot theory using Schiller's assignment of "knots" to particles. For a concrete example, take a shoelace with an overhand knot and its mirror image (a W+ and a W- particle in Schiller's terms) on it and try to turn it into an unknot (photons) ... it is not possible, and this has been proven by the mathematics of knot theory. If you don't believe this, then play with the knots on the shoelace until you get an intuitive understanding of why this is impossible."

These readers had a point. In the new assignments, all particles are now rational tangles; these tangles are not knotted any more and avoid the issues introduced by overhand knots and other knotted tangles. (2016)


A story about Niels Bohr

It has been told that Niels Bohr alternated his workdays in the following manner: on one day he would write down the most crazy ideas he could image; on the next day he would check them with reality as strictly as possible. He divided his weekdays in this way, alternating between the two poles.


What researchers can learn from entrepreneurs

Businesses have success only if they value their customers. In other words, business must value reality. Entrepreneurs who follow their beliefs usually lead their companies into bankruptcy. Entrepreneurs who follow reality lead their company to success. Not only teachers, also researchers can learn from business people. If you falsely believe that truth is defined by philosophers, or by ideologies, or by your wishes, take a break and stop. Truth is correspondence with facts. You can learn more about truth from a good entrepreneur than from a bad scientist. Some telling examples follow.


On correcting mistakes

Everybody makes mistakes. The important thing is to correct them. The mistaken strand model prediction on the Higgs is an example. Every mistake has a good side. In the case of the mistaken Higgs prediction, the good side was especially influential.


On microscopic models of gravity

Electromagnetic fields obey indeterminacy relations - they are fuzzy. Fields are fuzzy in the same way that the positions of quantum particles are fuzzy: the obey indeterminacy relations. The fuzziness of electromagnetic fields proves that electromagnetic fields are built of many microscopic degrees of freedom. Quantum theory implies that macroscopic electrostatic fields result from a large number of elementary excitations, which are called photons. Electrostatic fields are due to the exchange of virtual photons. As a result, the electromagnetic field has entropy. Indeed, quantum physicists, in particular experts on quantum optics, know since almost a century that electromagnetic fields have entropy.

Also gravitational fields obey indeterminacy relations - they are fuzzy. These fields are fuzzy in the same way that the positions of quantum particles are fuzzy. The fuzziness of gravitational fields proves that gravitational fields are built from many microscopic degrees of freedom. Quantum theory implies that gravitational fields result from a large number of elementary excitations, called gravitons. Static gravitational fields are due to the exchange of virtual gravitons. In other words, space and gravity are made of virtual gravitons buzzing around. And as such, like any system that is made of many components buzzing around, space and gravity have entropy. If you falsely believe that gravity has no entropy, explore the issue and convince yourself - especially if you give lectures.


On the number of dimensions of space

The dimensionality of space is a measured quantity: it is found to be 3 in all experiments ever performed. What is the dimensionality at very small dimensions? Well, we know that there is a minimal measurable length in nature, the Planck length. At the latest at that scale, there is thus no way to measure dimensionality. In other words, a shortest measurable length implies that dimensionality is not defined at Planck scale. If you falsely believe that space has 4, 9, 10 or even more dimensions at Planck scale, take a break and convince yourself that such a statement contradicts every possible experimental check.


On the limitations of the standard model of particle physics

The standard model does not explain many of its assumptions, including the gauge groups, the couplings and the particle masses. The standard model is incomplete. This point is undisputed and correct. On top of that, one finds hundreds of papers claiming that the standard model is also wrong or self-contradictory. Look at these arguments in detail. Even though these arguments have been repeated for over 30 years by thousands of people, every single one is unconvincing. In fact, every one is wrong. This might be the biggest lie of modern theoretical particle physics. So, if you believe any argument that claims that the standard model is wrong (in contrast to the various correct arguments which claim that it is incomplete) then you are victim of indoctrination and prejudice. And indoctrination prevents from reaching the final theory.


On supersymmetry

A well-known researcher claims that supersymmetry is "predicted by experiment". Another, wiser researcher sighed: "Supersymmetry is the only game in town." One Nobel Prize winner repeats in every interview that supersymmetry will be found soon, probably at the LHC. Another Nobel Prize winner consistently repeats that supersymmetry is a "figment of human imagination." Who is right? Supersymmetry relates different particle statistics: fermions and bosons. At the Planck scale, due to the measurement uncertainties induced by quantum gravity effects, particle statistics is not measurable; in short, fermions and bosons are undefined at the Planck scale. As a consequence, supersymmetry is not valid at the Planck scale. Supersymmetry is a point symmetry. At the Planck scale, due to the measurement uncertainties induced by quantum gravity effects, points do not exist. Again, as a consequence, supersymmetry and fermionic coordinates do not exist at the Planck scale. If you falsely believe that supersymmetry and fermionic coordinates exist, take a break and convince yourself that such a statement contradicts every possible experimental check.


On being daring - II

Almost all researchers are state employees, or in similar contractual situations. As a result, they are discouraged to take risks or to be daring. The same is true for reviewers. How can reviewers that are encouraged to play safe during all their life promote daring research? However, finding the final theory requires to take risks and to be daring. Let us see where this contradiction will lead to.


On being daring

"Deru kui wa utareru" - the stake that sticks out will be hammered - is a Japanese saying about what happens when someone sticks his neck out. Lots of people think that they are entitled to hammer. Such impolite people are driven by a mixture of misguided ideology and attraction to violence. Every entrepreneur knows such stories. Every entrepreneur knows that one condition for innovation is a climate without fear. The discussion of the merits and demerits of string theory has shown that such a climate does not exist in many research institutes. As a result of this situation, searching for the final theory is avoided by many. Don't do the same! Cultivate your curiosity and courage - they make you human.


On the rarity of courage

Bibliographic research, using the "web of science" or "google scholar", shows something astonishing. There are only a handful of papers - besides the superstring conjecture - that claim to propose a "final theory" or a "theory of everything". And this during the last one hundred years! This shows how touchy the issue has become. There is a definite lack of courage in present researchers.


On the lack of courage of committees - II

There is an organization that only supports research towards the final theory. It has funded over hundred research projects. How many of the projects it has funded are proposals for a final theory? You will not believe it: just one. Over 99% of the money is wasted. If you ever want to support the search for a final theory, think about what you are doing.


On the lack of courage and vision of committees

There are many cash prizes offered for the solution of various outstanding famous physics or math problems. Did you know that there is not a single cash prize in the whole world for finding the final theory? Do a Google search to convince yourself of how much committees shy away from this topic.


On saying what nobody says - on the limitation of symmetries and on 137

The search for a final theory of physics is often said to follow from the search for the final symmetry of nature. In fact, past research makes the opposite point. All symmetries known in physics fail to fix the coupling strengths and the particle masses. But explaining the coupling strengths, such as the famous fine structure constant 1/137.036, and explaining the particle masses are the main open point in physics! Knowing that a body has spherical symmetry does not determine its radius or its mass. Therefore, anybody who looks for larger symmetries is blocking himself from understanding the fine structure constant and the other open points in fundamental physics.


On saying what nobody says - on the lack of larger symmetries

The search for a final theory of physics is often said to follow from the search for the final, all-encompassing symmetry of nature. Not only is the connection wrong; worse, there is not the slightest evidence that any unknown symmetry exists in nature. No experiment has ever provided an argument that symmetries larger than the known ones exist. In other words, anybody who looks for larger symmetries is putting aside the connection to experiment.


On thinking what nobody thinks - on the requirements for a final theory

The search for a final theory of physics is almost a hundred years old. Despite the effort, there does not seem to be, anywhere in the research literature, a list of requirements that the final theory has to fulfil. The lack of such a canonical list, and even the lack of proposed lists, is a sign for how much researchers forbid themselves to think clearly. Research articles and even physics textbooks are full of another list: the list of issues that are unexplained by both quantum field theory and general relativity. But a list of requirements for the final theory is found nowhere! This lack is a clear sign that many physics researchers are facing an inner hurdle. (Every researcher can test himself on this point.) The lack of a generally discussed requirement list is a bizarre lacune of modern theoretical physics. The sixth volume of the Motion Mountain text proposes such a requirement list in chapter 7. If you are a researcher in fundamental physics and have never put together a list of requirements that the final theory has to fulfil, your research has most probably been driven by personal preferences or prejudices, and not by the desire to really find out. But if you publish your list, you will get into trouble - even if it is correct.


On thinking what nobody thinks - on the final theory

The first half of the sixth volume deduces the requirements for a final theory. They all appear when quantum physics and general relativity are combined. No requirement follows from one theory alone. In fact, as a result of unification, each requirement for the final theory contradicts both quantum physics and general relativity! In other words, researchers searching for a final theory are in a tough situation. It is hard to break loose, and if they do, they are treated with scorn by their peers. The easy way out is to search for unification by remaining in your own research field (either particle physics or general relativity). This approach ensures that at least half the researchers are not against you. But the easy approach is also the wrong one. The correct approach is not the easy one: the correct approach requires to contradict all researchers. In other words, anybody who searches for unification but at the same time wants to appease some present group of researchers is doomed.


On simple mathematics and the final theory

Since the final theory is not based on points and manifolds, the evolution of observables is not described by differential equations. This implies, among others, that the final theory is not described by complicated mathematics. This conclusion is one of the hardest to swallow for most modern physicists. Physicists are used to think that progress in physics has always been tied to progress in mathematics. This is an old prejudice, but it is wrong. Progress never has been tied to math in this way. In fact, the idea that the final theory is simple, i.e., algebraic, is at least 50 years old. In other words, if you think that the final theory requires the most complex mathematical concepts available, reconsider the reasons for your prejudice.


Theory and experiment

The value of a theory is decided by its correspondence with experiment. So far, no experiment yet found a deviation from the standard model of particle physics. This is precisely what is predicted by the strand model, the approach presented in volume VI of the Motion Mountain Physics Text. All other approaches to the final theory predict deviations; so do many researchers in particle physics. Stay tuned.

*    *    *