Tour De Force

Warning: make sure you are sitting down before you attempt to look at this 642 page draft of the new book, Noncommutative Geometry, Quantum Fields and Motives, by Matilde Marcolli and Alain Connes.

Not content with introducing QFT, NCG, Connes’ Standard Model, the Riemann hypothesis, motives and the kitchen sink, they finish up (from page 611) with a section entitled The analogy between QG and RH. The preface makes it abundantly clear that the book is primarily about this, as yet mysterious, correspondence. Unfortunately, I suspect I will find most of the book extremely mysterious as long as I live.


2 Responses so far »

  1. 1

    Doug said,

    Hi Kea, anonymous,

    I have only skimmed the material in the paper ‘Quantum signatures … dynamics’.

    These comments are my effort to assist myself in understanding the paper. There are meant to orient to my perspective, not to dispute.

    I tend to be oriented to mathematical game theory as used by engineers and economists.

    J von Neumann is credited with founding this type of mathematics with his “minimax theorem”.

    Many have enhanced his ideas over the years:
    John Nash introduced “equilibrium’ during the discussion of cooperative and noncooperative games.
    Tamer Basar and Geert Jan Olsder in ‘Dynamic Noncooperative Games’, chapter 8 demonstrated the value of pusuit evasion games [with trajectory curves] in their engineering version of Hamiltonion mechanics. This has found extensive use in robotics.
    Leonhard Euler was an expert in the trajectory curves of ballistics.

    1 – Are planetary and satellite orbits a type of equilibium as are electron shells, consistent with a possible outcome of pursuit evasion?
    2 – Electron k-capture appears analogous to comets crashing into planets [Jupiter 1997] and both consistent with successful ballistic targeting?
    3 – Beta radiation [electron escape] appears consistent with escape velocity and target evasion?

  2. 2

    Matti Pitkanen said,

    Dear Kear, anomymous, and Doug,

    Also I skimmed the article of Arkady Khodolenko and wrote comments at my blog.

    Resonance conditions provide alternative manner to end up with the quantization rules implied directly by Bohr orbitology in simple systems like harmonic oscillator and hydrogen atom. Number theoretic arguments also favor rational multiples of the basic units and thus the resonance rules which as such are too general to imply Bohr rules.
    In TGD framework the fact that space-time surface correspond to preferred extremals of Kahler action realizes quantization rules as exact part of quantum theory.

    Comment to Doug: TGD indeed leads to a in interpretation of planetary systems as very much analogous to atoms. Also the interior of Sun is predicted to have onion like structure and the analog of Titius-Bode in terms of p-adic length scales suggests itself strongly.

    An important prediction is that stationary states can comove but do not expand themselves cosmically except via quantum phase transitions increasing gravitational Planck constant. The findings of Masreliez provide empirical support for this prediction. At the level of cosmology this explains the accelerated expansion as associated with quantum critical
    phase transition periods if critical cosmology – highly unique from the imbeddability constraint -serves as space-time correlate for the transition period. “Cosmological constant” characterizes the density of dark matter rather than energy and no genuine cosmological term is needed.

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