Essay Abstract

Unity of mathematical and physical structures has been particularly impressive within the framework of quantum field theory. The confluence of abstract models in QFT with the natural world suggests a fusion of math and physics where the distinction between map and territory disappears at the deepest level. As a thesis that illuminates the miraculous powers of mathematical physics, the possibility of an actual merger between the description and the described is explored. While map and territory remain separate in many scientific disciplines, this clear distinction will prove untenable in fundamental physics. This central thesis will be laid out in both an entertaining and educating fashion within the setting of a fictitious opera. The stage will serve as a metaphor for the world and the intention is to tell an amusing, but still well-structured and instructive story for a general audience in this non-technical essay.

Author Bio

The author is a graduate student in Mathematics and Physics at the University of Technology in Munich (TUM) with a long-standing interest in the deep connection between the two fields - and a love to travel the world.

Essay removed at author's request.

Hi Martin,

I don't intend disturbing your wonderful opera. Let me merely tell you that your merger between the description and the described goes back to ancient time.

Enchanted,

Ben Akiba

    Dear Eckard,

    thanks for attending the opera! Glad you were in the audience and liked the performance. Of course the main thesis is not an entirely new (radical) idea, but I tried to present it in a creative way via an approach that might get a general audience interested and entertained at the same time. Hopefully others will visit the opera and enjoy the presentation as well!

    Tickets are still available and everybody is invited :)

    "Geography = Earth" would maybe be a better analogy in your picture, as both geography and geology are descriptions/maps and earth the territory under study. I argue that in fundamental physics this distinction might not survive.

    Martin -

    Thank you, a marvelous if somewhat mind-numbing opera! I'd love to get the CD when it comes out...

    If the implication is that, fundamentally, math and physics merge, then what do we do with the messy parts of mathematics: Those nasty infinities, for example, or the Godellian gaps?

    Regards - George Gantz

      Dear Martin Seltmann,

      Interesting essay and a great read. I especially liked the detail you presented on Dirac's work. I dont know if you have seen it, but there is a great video of Dirac himself here (very poor audio, headphones are required) where he gives a very nice historical summary of his work as well as comments on Pauli, Heisenburg and others.

      In my essay here I try to produce particles that match the properties of the S(3), SO(3) groups and match the symmetries SU(2) (electrons) and SU(3) (quarks and hadrons) of the particles of the standard model.

      I would especially be interested in your thoughts on my representation of the "Dirac electron".

      Regards and best of luck on your essay, you deserve a good rating.

      Ed Unverricht

        For some reason the Dirac video link did not post properly. Youtube address to copy and paste: https://www.youtube.com/watch?v=vwYs8tTLZ24&list=PLjNexov924eRr3L8aCirRyVCRN5rGi29W

        5 days later

        Dear Martin

        Thanks to George Gantz who mentioned on my page that our ideas for a unified physics-math at the smallest scale were similar, and that our essays are contiguous on the fqxi page! Having said that my simple reference of how the positron emerged from Dirac's equations should be contrasted with your highly professional treatment, clothed with a dense mathematical fabric that I can only dream of understanding fully.

        Your ballet (not so much opera?) was highly enjoyable for me because in many cases I could see how the dancers (to whom spin comes naturally!) could be the spinning nodes I envisioned in my Beautiful Universe Theory (BU) . I once made a model of Dirac's string idea in an effort to see how that might emerge from (BU). Reading in your essay how puzzling it is that the electron should know its orientation I could confidently say that the node lattice serves as a natural 'background' to itself showing each part of the universe large or small how it is connected to another via the dielectric tensegrity of the magnetic +- attraction and ++ or -- repulsion of adjacent local nodes. In (BU) the map=territory where orientations and directions, chirality and symmetry are real.

        My fqxi essay treats the fascinating business of the mathematical abilities of the slime mold, as far from your elegant ballet dancers as can be imagined, but all in the service of the basic idea we share.

        With best wishes for your success

        Vladimir

          Dear George,

          due to the length limitations of this essay contest, I chose QFT as the focus of my opera. Of course there is much more to physics and many other areas have to be investigated. Presumably physics will involve all of mathematics - including the work of Goedel, as recent findings already foreshadow: http://fqxi.org/community/articles/display/198

          I wish you great success in the contest!

          Best wishes,

          Martin

          Dear Ed Unverricht,

          thank you very much for your comments and link! I will read your essay this weekend.

          Best wishes and good luck,

          Martin

          Dear Vladimir,

          I would like to thank you for your kind words. Good to hear that you liked my treatment of orientation entanglement - this topic still always puzzles and fascinates me.

          Yes, it is really a funny coincidence that our essays share some ideas and are next to each other in the queue. And now they are even right next to each other in the community ranking, with your essay ahead of mine :)

          Wish you all the best and good luck!

          Martin

          Dear Mr. Seltmann,

          I thought that your essay was exceptionally well written and I wish I could write in my native language as flawlessly as you did. I certainly hope that your essay fares well in the competition.

          Warm regards,

          Joe Fisher

            6 days later

            Dear Mr. Fisher,

            thank you so much for your kind words. I am not a native speaker of English, but I tried my best to tell an entertaining and informative story at the same time. The essay had quite a good rating in the beginning, but was later seriously downvoted by a few "1 point" ratings. It took quite some time and serious effort to write the opera, but it seems that the attention to detail and good writing style is not necessarily valued. As there is now feedback given after the low extremely ratings, I have no way to know what could be improved.

            Best wishes and good luck to you!

            Martin

            9 days later

            Dear Martin,

            Very interesting and important essay metaphor "Map = Territory" and in-depth analysis of the fundamental connection of Mathematics and Physics. Very good figurative metaphors, the method of presentation, deep figurative representation of problems in physics and your ideas. I fully agree with the conclusion: "To really bridge the gap between math and physics, one has to build on all pillars in a more general approach until map and territory truly become one."

            Today in fundamental science there is a deep crisis of understanding, crisis of representation and interpretation. This profound existential crisis of basic science - universal human problems. Mathematics and Physics require a deep ontological justification (basification). In fundamental Physics is necessary to introduce an ontological standard justification along with the empirical standard.

            Ontological revolution Planck-Einstein must be completed. John Wheeler left physicists good covenant: "Philosophy is too important to be left to the philosophers". This problem is well formulated Edmund Husserl in "Origin of Geometry»: "Only to the extent, to which in case of idealization, the general content of spatio-temporal sphere is apodictically taken into account, which is invariant in all imaginable variations, ideal formation may arise, that will be clear in any future for all generations and in such form will be transferable by the tradition and reproducible in identical intersubjective sense ."

            Your essay clearly shows that it is necessary the ontological extension of space. My high appreciation.

            I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory and information - polyvalent phenomenon of the ontological (structural) memory of Universum as a whole. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld", as a picture of the world poets and philosophers.

            Kind regards,

            Vladimir

            Dear Martin,

            I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

            All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

            Joe Fisher

            6 days later

            Martin,

            "A model can only represent certain limited aspects of the described physical system, so one must not equate the mathematical theories (map) to the real world (territory)"

            A simplified picture is a good description of modeling weather, considering failures to accurately predict due to many variables not modeled and modeling only parts of weather patterns, used to dispute Wigner's unreasonable effectiveness of math but misses the point of incomplete inputs.

            Your opera is quite clever and reminds me of supernova sonification: http://www.astronomy.com/magazine/2014/09/web-extra-listen-to-two-supernova-songs, though its speaks of perceptions representing the classical world.

            You cover this relationship with your zooming in and out -- that's clever.

            A very good way of representing and of simplifying an esoteric topic.

            My essay looks at studies and results in quantum biology, DNA mapping, and BB simulation to prove math's efficacy: http://fqxi.org/community/forum/topic/2345.

            I would like your view of it.

            ]

            Jim

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