Are researchers bosons or fermions?Alain Connes: « 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. »
The CERN paper on FCC Physics Opportunities has 1364 authors. However, after reading it, one must admit that they are not overselling the FCC. High energy physics is at a crossroad.
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 exactly like all the 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, their 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)
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)
Arxiv and research status in 2014In the years up to 2014, professional researchers have published up to 40 papers a day in hep-th and gr-qc, with a total of about 50 000 papers. Those presenting a proposal for a final, unified theory can be counted on the fingers of one hand. Clearly, the subject is delicate. Researchers and entrepreneurs share the same choice: do they work for results or do they put other aims first, such as fame, money or fun? The ancients would say: the choice is between the path of virtue on one hand, and the path of superbia, avaritia or luxuria on the other. Various signs indicate that the search for a final, unified theory is not successful because the path of virtue has been lost. On the other hand, moralizing should never be taken too seriously – but sometimes can be a guide.
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 is 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 of 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.
On being trapped by one's own prejudicesA well-known researcher on the final theory stresses in every talk that the final theory must get rid of the concepts of point and manifold. But his own proposal is based on these two concepts! Update: there at least three internationally known researchers living with this contradiction. If you are working on the theory of everything, be aware of such traps.
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.