A short introduction to strandsThe 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 eight lines, strands need just one.
About "not believing" a law of physics
The equivalence of the force limit c4/4G with general relativity was published in 2005. 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.
Various physicists dislike maximum force: they refuse to check it and simply believe that it is wrong. This is unfortunate, because it means that they refuse to check that textbook physics can be summarized in eight lines.
As a consequence, this belief prevents from taking part in the search for unification. Indeed, the 8 lines of physics suggest a path to unification that is very different from all other paths explored in the past. Unification would have come faster if maximum force would have been tested more intensely.
In fact, some physicists top this and even dislike the smallest action value. Again, they refuse to check the statement, which dates from 1900, and prefer to believe that it is wrong. They stay behind even more.
Possibly the last law of physics
If the eight 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 eight linesAll of experimentally verified physics can be summarized on one page. Eight 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 televisionThe animations by Jason Hise were shown on the PBS TV program at https://youtu.be/pWlk1gLkF2Y - including a brief mention of strands.
Doing research is like walking on a mountain ridgeLike 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≥ℏ 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.
To state that the speed limit v≤c, the action limit W≥ℏ and the force limit F≤c⁴/4G yield quantum theory and general relativity is not a private theory. It is public. And correct. Since decades.
To state that strands imply the Lagrangian of the standard model is not a private theory. It is public as well. And correct as well.
Strands imply that attempts to go beyond the standard model resemble attempts to move faster than the speed of light.
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 ℏ, 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 ℏ 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.)
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.
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.
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 doi.org/10.1007/s10773-005-4835-2. Read it online for free at rdcu.be/cdG3C.
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 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 rdcu.be/cdwSI. 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.
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.
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.
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 arxiv.org/abs/1902.00260, 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, ℏ 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, ℏ 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:
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: www.danteonline.it/italiano/opere.asp?idope=1&idlang=OR. On the three circles, see divinacommedia.weebly.com/paradiso-canto-xxxiii.html and also arxiv.org/abs/1501.07214.
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 http://editionsassailly.com/dissidents_english.htm. 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 – PolishingSeveral 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-timeVarious 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)
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 BohrIt 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 entrepreneursBusinesses 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 mistakesEverybody 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 spaceThe 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 physicsThe 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 supersymmetryA 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 - IIAlmost 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 courageBibliographic 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 - IIThere 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 committeesThere 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 137The 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 symmetriesThe 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 theoryThe 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 theoryThe 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 theorySince 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 experimentThe 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.
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