Platonic Quantum Set Theory Proposal and Fractal-Cantorian Heterotic Kaluza- Klein Spacetime

Abstract

The four basic building blocks of the cosmos hypothesized by the Athenian philosopher Plato and his corresponding theory are replaced by the backbone golden mean based scaling pertinent to each of the four kinds of blocks. In the course of doing this we stretch and generalize Plato’s philosophical ideas to ultimately find out that it is essentially the deep philosophical origin of the golden mean number system of E-infinity Cantorian spacetime theory of high energy physics and quantum cosmology. Subsequently we use this new platonic form of E-infinity quantum set theory to uncover a remarkably rich Kaluza-Klein fractal version of Gross et al’s ingenious Heterotic superstring theory.

The Quantum Entanglement Roots of Newton’s Gravitational Inverse Square Law Via E-Infinity Platonic Transfinite Set Theory

“…i.e. the empty set by a simple extrapolation of A. Connes' noncommutative geometry to bear on R. Penrose fractal tiling universe [2][3], [13][14]. Thus while m 1 and m 2 planets are characterized exactly via their mass m i , the counterpart of m 1 and m 2 in Penrose universe according to equations (1) and (2) must clearly be and where we have…”

“…The reader familiar with E-infinity theory will recall that a pre-quantum particle is fully determined by the bi-dimension [13][14], [22] (1)…”

“…where is the golden mean, i.e. the zero set while the pre-quantum wave is fixed in an analogous way by [13][14], [22] (2)…”

“…The second correspondence must relate the distance between the planets which is analogous to R [1], [12][13][14], [22]. In a Penrose fractal tiling universe there is a natural distance which is the isomorphic length [10][11], [13][14].…”

“…ewton's famous inverse square law has a long history associated not only with classical mechanics and astronomy [1][2] but also with electricity and magnetism [1][2][3][4][5][6] and more recently in connection with the issue of hidden large extra dimensions and modified gravity [2][3] which we assume the reader is familiar with for the purpose of a smooth reading of the present relatively short note . It is in this larger context of Newton's formula stating that the force of attraction between two planets with m 1 and m 2 masses is proportional to the product (m 1 ) times (m 2 ) divided by the square of the distance between the two planets R 2 [1], [6] that we conduct the present investigation and analysis [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”