Tuesday, March 03, 2020

Could string theorists be finally approaching the discovery of number theoretical physics?

I have been shaking my head from despair caused by the incredible slowness - or rather inability - of superstring people to realize the importance of number theory for physics. The popular article String Theory and Number Theory Have More in Common Than You Think, Maaaaaan however
gives hopes that superstring people are finally beginning to approach the discovery of adelic physics in which both real and p-adic numbers fields whose extensions are labelled by the hierarchy of extensions of rationals is central, and discretization of space-time surfaces defined by them defines measurement resolution. They do not of course mention TGD as the source of inspiration, why should they?

For adelic physics the article "Philophy of adelic physics" or the article published in a book by Springer which has reached considerable attentions from mathematicians .

The invariance of the scattering of scattering amplitudes associated with the discretization of space-time under Galois group associated with the extension of rationals would be in TGD very important discrete number-theoretical symmetry besides other symmetries of TGD: the latter mean huge extension of conformal symmetries of superstring models.

The basic notion is cognitive representation providing discretization of space-time surfaces consisting of points of 8-D imbedding space with coordinates in the extension of rationals. The number of these points is in the generic case finite so that the construction of scattering amplitudes in finite measurement resolution becomes rather simple. Number theoretical functions like L functions invariant or transforming like irreducble representations under Galois group are expected to be important in the construction. This number theoretical discretization is completely unique unlike typical discretizations.

Number theory would have most important applications to TGD based quantum biology and dark matter could be understood as phases of ordinary matter with effective Planck constant heff=n×h0 with n the dimension of extension of rationals. Galois groups could also provide a number theoretical representation for discrete subgroups of ordinary symmetries

The latest application of Galois symmetry is to TGD based quantum biology. One ends up to the analog of color confinement for Galois group and to the observation that self as sequence of "small" state function reductions (SSFRs) correspond to a a sequence of decompositions of the integer defined by the order n of Galois group (dimension for the extension of rationals) to its prime factors so that Universe would be doing number theory at the basic level!: see this.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

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