Secret Link Between Pure Math & Physics Uncovered

Abstract

Number theorist Minhyong Kim  has speculated about very interesting general connection between number theory and physics. The reading of a popular article about Kim's work  revealed that number theoretic vision about physics provided by  TGD has led to a very similar ideas and suggests a concrete realization of  Kim's ideas.  In the following I briefly summarize what I call  identification problem. The identification of points of algebraic surface with coordinates, which are rational or in extension of rationals, is in question.  In TGD framework the imbedding space coordinates for points of space-time surface   belonging to the extension of rationals defining the adelic physics in question are common to reals and all extensions of p-adics induced by the extension. These points define what I call cognitive representation, whose construction means solving of  the  identification problem. Cognitive representation defines  discretized coordinates for a point of "world of classical worlds" (WCW)  taking the role of the space of spaces in Kim's approach. The symmetries of this space are proposed by Kim to help to solve the identification problem. The maximal isometries of WCW  necessary for the existence of its Kahler geometry provide  symmetries identifiable as symplectic symmetries.  The discrete subgroup respecting extension of rationals acts as symmetries  of cognitive representations of space-time surfaces in WCW, and one can identify symplectic invariants characterizing the space-time surfaces at the orbits of the symplectic group.