• Trick or Truth Essay Contest (2015)

  • The Unreasonable Effectiveness of Mathematics in Physics: the Sixth Hilbert Problem, and the Ultimate Galilean Revolution. For a mathematization of Physics by Giacomo Mauro D\'Ariano

Dear Giacomo,

Your ideas are wonderful and I'm sorry I only got to your essay now. You are making a compelling argument for returning to the old and profound purposes that have now been forgotten. Hilbert Sixth problem is equivalent to searching for a Holy Grail of physics, in that it is a quest for finding coherence and meaning. I think such a theory would have an unseen rigorousness and you are doing a very good presentation of the motives. I think your speech about geometrization is raising the important point that geometry helps in finding intuitively a physical interpretation of mathematics because it shows the relational structure. I will end with the beginning and I will say that I was greatly amused by how you (truthfully) characterized Wigner's statement as romantic. Excellent work! Wish you good luck in your work and in the contest!

Warm regards,

Alma

    Giacomo,

    Your essay was interesting and well argued, and I found myself in agreement with much of it, importantly in strong agreement with the need for proper physical theories to found the mathematical descriptions. (John Hodge directed me to it as agreeing with my own methodology and I'm glad I managed to read it)

    I see you teach QM, so I hope you may read my essay if only to consider and comment on the physical 'quasi classical' mechanism I identify allowing a mechanical derivation of the results we assign as 'quantum non-locality'.

    You may also be able to understand the highly compressed (experimental) video of a physical dynamic model based on the same foundations, i.e. using your approach to put your theory into practice. To answer the chicken and egg question; here is a viable chicken. It also has an egg inside, which has a viable chicken embryo inside, which has a group of spin states configured to give the ability to produce eggs, etc. The particles clearly came first.

    Possible physical mechanism and implications video

    A comprehensive analysis paper on Bell's 'theorem' etc. and the limits of the D'espagnolet Wigner ineqaulity identified in my essay is available which I hope you may look at after the contest.

    Well done and best of luck in the final dash. But do please comment even after scoring.

    Peter

      Excellent point! Nevertheless, I ask myself if the business of physics is only interpretation of mathematics provided that in quantum mechanics we can analogically extend our labs operations to the external world (assuming that spontaneous physical processes determine outcomes in ways that cannot be totally dissimilar to those controlled by us) and nevertheless we cannot extend our interpretation too far precisely because the latter processes are uncontrolled. In a way it seems to me that you say the same when you speak of physics as "connecting experimental observations", while the "portraying phenomena" can be still true but with a narrower scope.

      Best,

      Gennaro Auletta

        Dear Ian

        thank you for your compliments and your interesting comments. You reminded to me to buy the Eddington book on Amazon about the physical law, which can be a great source of inspiration for me. I know from our last discussion (in Boston, am I correct)? that you are not a structuralist. I didn't know that Steven French was your external advisor. How can it be that then you don't completely agree with me?

        Let me answer to your two pints, very briefly.

        The power of mathematics in physics is mostly resides in the mathematical induction (not in the physical one, which is logically fallacious, as Hume first noticed). With the mathematical induction, with a couple of modus ponens you prove an infinite large set of true assertions. But as you know, you do not prove the assertion for n=infty! Working with infinity is for mathematical convenience only, for describing analytically asymptotics. If you avoid the "actual infinity" but you work only with the "potential infinity" how can you get an unprovable assertion from 1+1=2, 1+2=3, 1+3=4, ...? Moreover, a theory should be required to be computable, namely allowing a finite-state machine one must be able to describe a finite portion of reality. Clearly you can incur into incompleteness if you want describe the whole universe. But not for a finite portion of reality, as long as you keep it discrete! Again, continuum is a limiting case of discrete ...

        Second point: About causality, you forget that in my work with Chiribella and Perinotti on the axiomatic derivation of quantum theory we have a precise mathematical definition of causality, which has exactly the physical interpretation that a physicist would agree with.

        Finally: there are bias that are universally shared. For example: we believe in logic, we believe in the universal validity of a law (or we treated it as such), we believe in isotropy of the low, we believe in locality of interaction. If you don't share one of this biases (which are examples of the principles from which we derive also free QFT), then I would be very interested in knowing which one you don't share. Don't tell me that the law is not universal, as Lee Smolin says, otherwise you are required to provide a higher level law accounting for the variation of the low-level law--otherwise you are giving up the theory. For how long would be a law required to be valid in order to be a law? A century? a second?

        And, finally: I don't care about objective reality. What I care is that the theory is describing objective experimental data. My daughter still believes that Santa Claus is an objective reality, but the only objective facts are the presents that she gets.

        Thank you again very much for your compliments and stimulating comments.

        I will look forward to meeting you soon again. I'll be in Chicago the full August. If you'll pass by, please let me know.

        My very best regards

        Mauro

        Dear Michel

        thank you for your really nice compliments: you read my essay several times, really? I have been in China with a bad internet, and just back in Italy I find visitors. I will read you essay tonight.

        There is maybe a misunderstanding about my essay, anyway. A crucial point in my essay is the physical interpretation of the theory, starting from axioms up to all of their consequences. Mathematicians cannot do this work. You need to know physics! Physics is not only of theory (I take the word "theory" very seriously here). Physics is made of laws of limited validity, heuristics, models, etc. or of theories that are not completely mathematical. When I interpret the results or the axioms of a Theory (with capital T) I can either refer to observations, or to heuristics, models or theories (with lowercase t) which just synthesize a huge set of observations, but they don't have the logical coherence of a Theory, whence, are not strictly logically falsifiable (according to Popper, they are a little magical).

        You know that I am a theoretical physics, but you don't probably know that I started my research work as an experimentalist in my early post graduate years! There I learn one thing from my mentor (prof. Attilio Rigamonti): you want to really understand what's going on, then you must solve the problem at hand with whatever means are needed. If you need to know new mathematics, then learn it! The goal is a logical proof of your thesis, not an exhibition of technical knowledge. But later in my experience I discovered that most theoreticians learn some mathematics and then they seek the problem that may be addressed with the math that they know. I'm not this kind of scientist. And I'm definitely not a mathematician: I don't have the training. I just want to understand. One of the main lessons from Einstein is that if you really pursue the logic of what follows from your principles, you may discover new mathematics previously unknown to physicists. And I find this is marvelous!

        Thank you again for your feedback and for your nice compliments.

        My best regards

        Mauro

        Dear Alma,

        I'm delighted that you really share exactly all points I raised! And, let me say that I really love your assertion saying "Hilbert Sixth problem is equivalent to searching for a Holy Grail of physics, in that it is a quest for finding coherence and meaning." Yes! You are right. This is the Holy Grail of physics! And, it maybe the Holy Grail of Popper (Popper said that when you find a theory is like when you find the Holy Grail: you may never know if it is the true one, up to when you falsify the theory, and then you know it wasn't).

        As I told to Michel, I'm just back from China with an horrible internet. I can now enjoy reading your own essay, of which I'm now very curious.

        Thank you again for your wonderful and unique comment!

        My best wishes to you.

        Mauro

        Peter

        thank you for your post, and nice compliments, and a pleasure to meet you again in this competition. As I wrote in the last entries of this blog, I'm just back from China with an horrible internet. It is 1 AM here, and I am coming back from a dinner with a visitor. But I have still some hours to read your essay in time for voting it, looking at your video, and writing something on your blog.

        Thank you again

        My best regards

        mauro

        Dear Gennaro

        thank you for your compliments and your point raised! The essay would indeed need a little expansion to be complete. In short, the role of physics is not just the interpretation, but to build also the whole pragmatic knowledge to build up the interpretation, namely as I wrote in my answer to Michel Planat:

        Physics is not only made of theory (I take the word "theory" very seriously here). Physics is made of laws of limited validity, heuristics, models, etc. or of theories that are not completely mathematical. When I interpret the results or the axioms of a Theory (with capital T) I can either refer to observations, or to heuristics, models or theories (with lowercase t) which just synthesize a huge set of observations, but they don't have the logical coherence of a Theory, whence, are not strictly logically falsifiable (according to Popper, they are a little magical).

        I hope this answers your legitimately raised point.

        See you in july!

        My very best

        Mauro

        Dear Giacomo,

        It is perfectly true that I red your essay several times from the beginning. I did the same for some essays that I did not comment and did not rate. It is interesting that our scientific evolution can be compared. I started as an engineer and did my "state thesis" in applied physics (nonlinear wave propagation), I did a lot of experiments at that time and also later. I arrived at quantum physics only twelve years ago and one training was to organize the ICSSUR'05 conference that you know about because you were in the scientific committee. As you I was not trained as a mathematician but always was fascinated by the tricks it provides. I knew about dessins d'enfants but it took 20 years before I found the opportunity to use them in quantum contexts. The Grail for me would be to use them in large scale physics or in biology.

        Thanks for your comment on my page.

        My best regards,

        Michel

        Dear Mauro,

        I am very glad I summarized all your points properly, for it means I understood them well. It was my pleasure doing so!

        I hope your trip to China was as fruitful as you planned it to be. Welcome back!

        Warmest regards,

        Alma

        Mauro

        Thanks for your kind comments on my blog. I responded there, reproduced below; (though I'm a little confused which is your christian name!)

        Giacomo,

        Interesting response. I see that view as rather 'dumbing down' the problem to that of the chicken and egg, suggesting the two views of 'which came first' are irreconcilable. In my first lines I accept your case, then reconcile it coherently with reality.

        I've derived the chicken/egg solution elsewhere nearby; to simplify, It's a chicken, which contains an egg, which contains a chicken embryo, which contains the physical constituents required to form an egg, with a chicken inside, etc etc, chicken soup all the way down!

        So at the bottom, when our microscopes get enough resolution do you think we'll find a mathematical formula written out? Will it be in Arabic numerals, perhaps Roman? Babylonian? or even Mayan? Or do you not agree that it's more likely to be some fundamental relative motion, spin or OAM state of motion DESCRIBABLE or representable by a simple equation (in Arabic or whatever system the observer wishes)?

        In the same way SR and QM are probably only irreconcilable due to inadequate understanding I feel our approaches are Ying and Yang, both essential and more "inseperable" than irreconcilable, except perhaps in blinkered or 'tunnel' vision.

        Do you really not agree? If so what would you expect to 'observe' as 'information' being processed at the smallest (sub-planck?) scale? A micro computer?

        I'm not convinced we generally think things through thoroughly enough before pinning our colours to them them. Can you convince me?

        Best wishes

        Peter

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