Essay Abstract

Predictability or otherwise of an event is a property not so much of the event, as of the theory that is used for prediction. Unpredictable events can be considered to be `predictable unpredictables' if there is a theory that predicts the probabilities of their occurrence. Everything else is an unpredictable unpredictable, and these are the most challenging for physics. Guided by an analogy with undecidability in mathematical theories, I consider what kind of physical theory might be required in order to predict those fundamental parameters that in current theories are unpredictable unpredictables.

Author Bio

Emeritus Professor of Pure Mathematics at Queen Mary University of London, specialising in group theory. Previously at the University of Birmingham, and at the University of Cambridge, where I did my PhD. Since 2010, I have worked on trying to understand and if possible improve the group theory that is used in fundamental physics.

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Robert,

" If something exists in the universe, it is, ipso facto, consistent." Correct, but...

Now, every thing or body (not object) in the universe has size, shape, color, brightness as well as distance and attitude relative to me. I guess you agree that none of these properties can be reduced to any other or an abstract 'third'. Further, all those bodies have mass, el. and therm. conductivity, several moments of inertia, some degree of roughness and kind of morphology, etc. pp. These properties are irreducible too. And yet (or as I think: therefore!) every body in the universe is consistent (discernible). Last, also the human senses are organized in an irreducible way; there is nothing in seeing that is in hearing, smelling or feeling.

That is, the world, as we perceive it, is discernible because it is categorically structured, i.e. is an orthogonal system and consistent (better: non-contradictory) for exactly this reason. So, I wonder what you'd say to my provocative thesis that physics either passes (back) under the yoke of orthogonal human knowledge (anti-reductionism) or is condemmed to remain irrelevant academic amusement foerever.

Heinz

    Heinz,

    Thank you for your comments. I read your essay, which contains much of interest. As a mathematician, however, I find these philosophical questions difficult to think about, and I seek refuge in mathematics. My view is that the problems of (for example) interpretation of quantum mechanics are not really philosophical problems, as they are often presented, but mathematical problems. There are some subtle errors in the mathematics, which I think should be corrected. But because they are subtle, it is hard to convince physicists that they are important. When these mathematical errors lead to palpable nonsense such as many-worlds or multiverses, however, I think the time has come to pay a bit more attention to mathematical rigour. But I do agree with you that reductionism has gone too far, and we need to take more account of the fact that no object of any kind exists in isolation: we live in the universe, not outside it.

    Robert.

    "General relativity has been very well tested on a Solar System scale ..." Have physicists overestimated the accuracy of predictions made by general relativity theory and, also, Newton's law of gravity? According to Newton and Einstein, dark-matter-compensation-constant = 0. However, I have suggested the hypothesis that string theory with the finite nature hypothesis implies dark-matter-compensation-constant = (3.9±.5) * 10^-5. Why have gravitational metrologists been unable to improve the accuracy with which Newtons big G is know?

    "Invited Review Article: Measurements of the Newtonian constant of gravitation, G" by C. Rothleitner & S. Schlamminger, Review of Scientific Instruments, volume 88, issue 11, 2017

      Thank you for your comments. I was careful to say that GR has been tested on a Solar System scale. Although I do not mention this in my essay, I do agree with you that on larger scales GR is not necessarily the only game in town. I find the MOND paradigm very persuasive, and if I were trying to build a quantum theory of gravity, I would not consider the theory to be satisfactory if it did not agree substantially with the empirical laws of MOND. The other important clues I think are provided by the flyby anomaly, which indicates that gravitational forces between extended bodies (as opposed to point masses) depend on rotation, and possibly the Pioneer anomaly, although that may have been explained in other ways. It is certainly possible that these effects combine to create unrecognised systematic errors in experiments that attempt to measure Newton's gravitational constant to greater accuracy. I cannot comment on anything that string theory might or might not say.

      Dear Sir,

      Congratulations for such a brilliant essay, which be more remembered for the food for thought it presents than its actual content. I thoroughly enjoyed it.

      A prediction is a statement about the future based upon past experience and knowledge derived from such experience. Hence something is predictable, if 1) we have similar experience in the past and 2) there are no additional factors that can influence the possible outcome. While 1) is simple, the 2) is not. Uncertainty is inherent in Nature. Our knowledge of the universe is never complete. This makes the field wide open. We may not and cannot know all factors that may affect the outcome of any event. This makes everything unpredictable. You are absolutely right here.

      Having said that, there may be limits on such unpredictability. We cannot pin point the precise position of an electron at any specific moment. Yet, we can predict that it will be found somewhere within a fixed band. Experiment proves us right. Thus, these are predictable unpredictable. We use probability and average to predict the outcome based on past experience based on measurement and knowledge derived from such experience. While the laws of physics are same everywhere, the same law is not applicable everywhere. This leads to model-dependent definition of predictability. You are right again: "Something that is predictable in one model can be unpredictable in another".

      But is it same in mathematics - "what is decidable in one model of mathematics can be undecidable in another"? I beg to differ. Your statement is true for mathematical physics, but not for pure mathematics.

      Language is the unambiguous transposition of one's/a system's thoughts/command on another person's/system's mind/CPU. Mathematics does that with numbers. Hence mathematics is a language of Nature. But it only depicts quantitative aspect of Nature. It does not cover all aspects. Hence what is true for mathematics may not be true for physics or biology. For example, if by paying $3000 we can get a bike, by paying $1000 we can get 1/3 of a bike. This statement is mathematically correct. But physically it does not make any sense. There is no equation for the observer, but it has an important role in physics. Thus, physics beyond mathematics cannot be denied. Extending the limited scope of mathematics (scalar numbers) to (vector) physics or biology, makes us fall in the trap of reductionism.

      In mathematics, we have irrational numbers like square-root of 2 or such numbers likeпЃ°. We cannot use it as a fraction of whole numbers. But in physics, we cannot use inderminables. We must chose a limit up to which we can go to determine the nearest fraction. This is the subject matter of my essay in this forum.

      Your poser: "whether a non-standard model can predict (correctly!) some things that are unpredictable in the standard model" is very interesting. In fact, it has the potential to change the direction of modern research. Let me give one example.

      From the times of Newton, measuring the exact value of G, the gravitational constant, is one of the priority areas, as it is used widely in many equations as a constant and any change to its value will make many theories crumble. Yet there was wide disagreement on the precise value of G. Now it has been noticed that it G exhibit a 5.9-year periodic oscillation value. Interestingly, this closely matches the 5.9-year oscillation in length of day (LOD - defined as a frequency measurement such that a positive increase in LOD values means slower Earth rotation rates and therefore longer days) measurements. The aforementioned period is also about half of a solar activity cycle of about 11 years, but the correlation is far less convincing because of the big difference in values. The 5.9 year periodic signal in LOD has previously been interpreted as due to fluid core motions and inner-core coupling. Again, this is not convincing. The G/LOD correlation, whose statistical significance is 0.99764 assuming no difference in phase, points to a totally new direction.

      It is known that unlike other interactions, gravity is a polygamous force. This is because the other interactions are intra-body and follow a symmetry, whereas gravity is interbody and asymmetrical (that is why planetary orbits wobble). That it is related to mass and distance shows that not only the bodies concerned, but all others that influence the two bodies, play an important role in it. While it may not be evident always, the bodies between the Sun and Earth (like Mercury, Venus) are affected by Earth, but the Earth is not affected by these bodies to that extent - the forces being directed at Sun. But what about Jupiter, which is massive enough and the Earth falls in the path of its interaction with the Sun? There is gravitational interaction between Jupiter and Earth. When these are in a straight line with Sun, Jupiter drags Earth away from Sun, which reduces and reaches a peak when Sun is between Earth and Jupiter. This starts to increase again to reach a peak after 11.86 years - the period of Jupiter. Thus, the change is periodic with a 5.93 year periodic cycle.

      This forces us to look at the theory of gravitation afresh. It is also another example of predictable unpredictable bordering the unpredictable unpredictables.

      Now, I will like to give another thought to your unpredictable unpredictables. Decay and Evolution are established facts of Nature. Decay is related to time evolution. Evolution is limited transformation of something without losing its basic characteristics. Can it lead to the rabbit having horns? No one can tell with certainty. It is unpredictable unpredictables. Yet, when look at it closely, does it fulfil the criteria of prediction? We have seen rabbits. We have seen horns on many animals. We make a statement about the future based upon past experience and knowledge derived from such experience. So based on our past experience of a horn being a natural tool to provide protection from danger, and looking at the increasing threat to the rabbit population, they may evolve to grow horns. What we do here is extend a relation (natural mechanism for protection from danger) to two unrelated fields (rabbit and horn), without properly analyzing and without taking into account all possible aspects. Nature has provided a safety mechanism to the rabbit - its speed to run away from danger. Having a pair of horns will hamper that speed. With its limited physical volume and soft body, it will not be able to defend itself from predators. Nature functions creatively. It will not jeopardize safety to life while providing food for others. Hence, horns of a rabbit will never materialize. This way, we can explain one case of unpredictable unpredictables.

        Many thanks for your very interesting comments. From reading your essay I understand that we differ somewhat in our interpretation of undecidability in mathematics, and perhaps even in our understanding of what is or is not mathematics. But I think we can leave this on one side, and concentrate on what is useful for physics. I was particularly interested in your statement that measurements of G are correlated with the length of the day - do you have a reference for this? I was certainly aware that measurements of G are mutually inconsistent, and that no-one knows why. But I was not aware of such a correlation. It may indeed be possible to derive this correlation as a meta-prediction based on the ideas in my essay, though I have not thought seriously about this yet.

        Dear Robert,

        In order for a formula to be just a coincidence, it is necessary to agree with Codata values in all significant digits. It is not case in all of your formulas. Then the next step is to show the predictive value of the formula, if any. You being a mathematician it is easy to understand mathematical tool of your colleague's (Hugh Matlock) with which he show the predictive value of a formulas. You can check out Hugh Matlock's comments on my FQX-i 2013contest article,

        https://fqxi.org/community/forum/topic/1847 .

        If you like, I can send you a formula that shows the exact relationship between n, p and e. It was obtained by the same approach as the last five formulas at the end of my essay. Since you are a mathematician, I think you shall be better than others to understand the role logorithm and exponent in these formulas.

        Your formula e + μ + τ + 3p = 5n correctly predicts that the relation of three leptons must contain proton too, which is a disadvantage of the well-known Koide formula. You can also see the Improved Koide formula at the end of my essay.

        And my recommendation: Forget the Big Bang, stick with the greats of science, Newton, Bošković, Maxwell, Planck, partly Einstein. Also follow mathematics, especially the part we call "discovered mathematics". Then a consistent consistent theory of everything is hidden in their works.

        Regards Branko

          Dear Branko,

          I thank you for your comments. You refer to the Koide formula, which is extraordinarily accurate, and yet not generally accepted as having relevance to physics. Indeed, it differs from experiment by about .01%. This is an extraordinarily small amount, and yet not quite small enough to convince physicists in general that this formula is meaningful. I have been thinking about this, on and off, for five years, and I do not claim to have solved the problem yet. You can read more about my take on these issues on my blog at robwilson1.wordpress.com if you are interested.

          I agree with you that a prediction must agree with CODATA in (almost) all significant digits. I do not agree with you that the same applies to meta-predictions. Nevertheless, at least seven of my meta-predictions do in fact agree with CODATA in all significant digits.

          And the Big Bang? I can take it or leave it. The way I look at the universe, I find it hard to understand why anyone finds it necessary to assume there was a Big Bang. I don't say it didn't happen, I just say, why does anyone think it did? What does it actually explain that cannot be explained in other ways?

          Robert.

          I liked your essay because i twas easy to read and it through up some challenges.

          Your section on Hidden Relations brought to mind the book Bible Code by Michael Drosnin. This book has been thoroughly debunked by mathematicians.

          I am sure that the relations between fundamental particles can be unlocked by better reductionism than we are currently presented with by the Standard Model.

            Thank you for your comments. I do not consider that there is any similarity between my section on "Hidden relations" and the book "The Bible Code". I am a mathematician and I understand the mathematical arguments that are used to debunk "The Bible Code". I consider that these arguments do not say anything very useful about my equations. Of course, anyone is welcome to apply these arguments themselves, and see what conclusions they come to.

            I disagree with you that "better reductionism" will help us to understand mass. The mass of a proton is something fixed and very precisely known, while the masses of the constituents of a proton are at best very vague, and at worst undefined. More reductionism is precisely the opposite of what is required.

            I didn't reply to your comments about predictive value of formulae. Given that my equations are meta-predictions rather than predictions, I do not claim great predictive power for them. But the equation $e + mu+tau+3p=5n$ does predict two or three more significant figures of the tau mass, and the equation involving the Higgs mass predicts one more significant figure of that. Several other equations have some limited predictive power also.

            Dear Robert,

            Thanks for your reply. This is what I like about Big bang:

            "What does it actually explain that can't be explained in other ways?"

            I answer: Nothing.

            The Koide formula is incorrect and lacks a proton. I suggested the correct one: Improved Koide formula.

            I've been to your blog, I don't know anything about group theory. I read a couple of articles.

            Regards Branko

            Dear Branko,

            My take on the Koide formula is explained in my preprint "A proposed new model for the coupling of matter to spacetime" available from my blog. Essentially, it is a 3-dimensional approximation to a formula that must exist in 6-dimensional space. Indeed, it may even be reasonable to regard this 6-space as a 3-dimensional complex space, in which case we can say the Koide formula is the real part of a 3-dimensional complex formula. I do not know what the correct formula is, but you are surely right that it must involve the proton (and the neutron, I believe).

            Robert.

            Maybe I should add something about where the eight "hidden relations" came from. They are not just random equations, but are justified extensively (if heuristically) in terms of group representation theory, in two preprints that are posted on the website of the Isaac Newton Institute, Cambridge: http://www.newton.ac.uk/files/preprints/ni19011.pdf and http://www.newton.ac.uk/files/preprints/ni19013.pdf

            Notice for example the parallel between the 3 generations of electron in e+mu+tau+3p=5n and the three generations of down quark in d+s+b+3pi=5n, which also throws up a parallel between the proton and the pions. The first equation has 12 fundamental particles on the left, and 15 on the right, so needs three neutrinos to balance the spins. The second equation has only 9 on the left, and needs 3 photons to balance the spins. All the equations taken together suggest that the muon and the tau particle, as well as the three heavy quarks, may be better treated as composite particles rather than fundamental, while on the other hand the proton and the pions might be better treated as fundamental. Just a thought.

            Dear Robert,

            I especially liked these deep ontological conclusions:

            "The values, then, can only be explained by one supreme act of randomness at the origin of the universe in the Big Bang. Is this really an adequate physical explanation, or is it just a fairy story?"

            "Predicting the unpredictable requires thinking the unthinkable. Restricting ourselves to thinkable unthinkables has not worked. To make progress, we may have to think unthinkable unthinkables. This is not a safe option. Thinking unthinkable unthinkables can lead to a complete paradigm shift. If we are not prepared for a paradigm shift, then we should not go down this road. "

            "But if we want to go beyond the standard model, we must be prepared to think unthinkable unthinkables."

            "Einstein's hopes of a rigorous consistent theory of all of physics have not been realised. But G¨odel's theorems do not prove that such a theory is impossible."

            "So maybe, just maybe, if we can upgrade the theory from inconsistent inconsistency to consistent inconsistency, then the universe can do the rest, and give us a consistent consistent theory of everything."

            My highest point and hope that to overcome the crisis of understanding, the crisis of interpretation and representation in the philosophical basis of fundamental science, physicists will call upon the paradigm of the whole to help. And the dialectic of "coincidence of opposites"... "Philosophy is too important to be left to the philosophers" (J. Wheeler)

            With kind regards, Vladimir

            Dear Vladimir,

            I thank you for your positive comments. I appreciate the deep ontological arguments about the foundations of quantum mechanics, and the crises of interpretation that arise from them, but the more I think about them, the more I feel that the problem is not so much philosophical as mathematical. There are problems with the mathematics that are not generally appreciated, and to my mind the philosophical problems arise largely because of errors in the mathematics, that lead to mathematical concepts that are difficult to relate to physical reality, for the simple reason that they are mathematically inconsistent. It is hard to discuss these issues seriously, because most people (including me, no doubt) understand at most one of the three subjects of mathematics, physics and philosophy.

            Robert.

              Dear Robert,

              It was a real pleasure to read your clear contribution.

              I understand that you are mostly mathematician and no philosopher, but really you touched very philosophical issues.

              The whole time I was reading your essay I thought"Robert is looking for the reference of reference" a subject that I also give attention and try to reason in my interpretation.

              As a mathematician, you will have some problems with my essay and I respect that, but if you are interested you can find it HERE , I should be interested to hear the opinion from another side.

              Best regards

              Wilhelmus de Wilde

                Dear Wilhelmus,

                Thank you for your kind remarks. I find that philosophy can often be useful as a way of clarifying issues, although I count myself very much an amateur in philosophy. I read your essay, but as you guessed, I found it hard to understand. You treat the problem of consciousness, which I try to avoid, although it plays a prominent role in certain approaches to the interpretation of quantum mechanics. As I mentioned above, I believe that consciousness enters into this debate through a misunderstanding of the underlying mathematics. On the other hand, my approach says absolutely nothing about the problem of consciousness, which remains completely out of my reach, and remains a central philosophical problem.

                Robert.

                Dear Robert,

                You are absolutely right. The problem of justification of mathematics, which is more than a hundred years old, is problem No. 1 for cognition as a whole, especially physics. Some philosophers consider it to be an "eternal problem". I strongly disagree with this. Clearly represented the situation with the foundations of mathematics and logic M. Kline in "Mathematics: Loss of Certainty" and A. Zenkin in SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS. Some mathematicians claim that "as physics has solved all the theoretical problems of chemistry, thereby" closing "chemistry, so mathematics will create a" unified theory of everything "and" close "physics." (Interview with mathematician L. Faddeev The equation of the evil spirit ). How can mathematics "close physics" if the problem of justification is not solved. For some reason, mathematicians are currently facing the age-old problem of the justification of mathematics, "language of Nature", "swept under the rug." Just look at the "Millennium Problems" of the Clay Mathematics Institute...

                The problem of the mathematics justification (and therefore knowledge in general) is a comprehensive ontological problem. Therefore, I define the problem of the mathematics justification more broadly - the problem of the ontological basification of mathematics. I took the concept of "basification" from geology, where "basification" is understood as a hypothetical process of transformation of the granite layers of the Earth's crust into basalt layers. Metaphor: it is time to start "cracking" instead of "granite" - the "basalt" of Science ... Please look at my approach to the problem of the basification of mathematics and knowledge in general. I will be very happy to hear your questions and criticisms.

                With kind regards, Vladimir