Tuesday, December 27, 2011
Adele Quantum Mechanics and Riemann Dynamics
Adele Quantum Mechanics and Riemann Dynamics L. Edgar Otto 27 December 2011
Inspired by reading Prime Obsession this general subject HERE a recent paper involving those mentioned in Derbyshire's book.
This is a book that will survive as a great and informative read whatever idea we have of the proof of the Riemann Hypothesis. In it I find the beginning of a serious and formal mathematical and physical (interestingly the author says to Gauss and Riemann these were not yet thought of as separate divisions) as well as a work of foundational philosophy. It shows the how of a generalization of the idea of p-adic numbers.
Two related concepts in my estimation- that by Russel we could not find an adequate definition of a number (not even its class concept) and If Godel uses primes in his proof in light of at least the approach of Adele then clearly there is more to the problem than still meets our eye when we try to understand a deeper meaning of what primes are. As the author says some believe and some do not that this approach holds water as respected mathematicians so even p-adic theory as a position is already a matter of controversy as to the acceptance by the math and physics community.
I might add that in the bounds of horizontal flat lines and the Big O problem that if we also include Weiestrass for the ideas of the Plane then we could imagine a sort of mirror 1/Big O perhaps but as usual the notation is lacking. We also can imagine a mirror of the quasic plane in terms of complex numbers in bounds that resemble parabolas, and this perhaps involving the mirror hidden quasic diagonal that would balance the idea of a quantum dynamics as a unification of the Riemannian variety (again with this issues asking if a system is complete (even when consistent). There is very much more to be explored and even now what I have posted is most likely very much behind papers. I would not at this point assume that the hypothesis is either true or false, or is either but intermittently- for it is such concepts at issue here as a matter of intuitions without the mathematics or training that seem to make parallels in my isolated understanding (indeed, the hypothesis is intimate to these ideas but I doubt just in the description of how it related to particle shells as classical entities only for matters of probability- especially the idea that primes are maximally random in all conceptual universes.
I wonder, considering the efforts put into this problem if we might consider the hypothesis the very heart of unification's to come as so many go different ways in the pursuit of systems of physics- again something perhaps a little beyond its truth or falsehood as a reachable and practical proof. Certainly it involves any idea of condensates and more advanced thermodynamics.
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