Foreword

I have seldom in my life felt so astounded as when I first typed the words Topological Geometrodynamics into Google and followed the path of links deeper and deeper into the stupendous intellectual abyss that this phrase leads to. The only adequate analogue must certainly be Alices venture into the depths of the Rabbit Hole! This particular hole features eighteen on-line books and over ten thousand pages of beautiful and highly original mathematics and theoretical physics.

Matti Pitkanen has during many long years looked deeper into the secrets of the universe than any other person that I have known. His study is systematic and meticulous, yet awe-inspiring by the all-encompassing width of his mathematical and physical treasure chest that features such proverbial beasts as zero energy ontology, infinite primes and p-Adic space-time. Yet Matti Pitkanen himself is the first person to acknowledge that his journey is still incomplete: there is no world equation or other forms of a closed formulation, let alone solutions to such systems of equations. Matti Pitkanen humbly describes himself as the scribe of the universe that faithfully records the beauty of the symmetries that he perceives through his equations and operators with a deep physical meaning. Symmetry is indeed the cornerstone of Topological Geometrodynamics, or TGD. On one hand, TGD is a proper generalization of John Archibald Wheelers eponymous theory. On the other, it is a generalized M-theory where particles are represented by 3-surfaces in an eight-dimensional manifold. In the former case, Matti Pitkanens worldsheet is parameterized by a Cartesian product of the 4-dimensional Minkowski space and a compact two-dimensional complex projective sphere. In the second case, this same manifold is conformally symmetric in the sense that it must possess an infinite-dimensional Kähler geometry. This requirement leads to the necessity of infinite-dimensional groups of isometries to exist.

This extremely simple requirement of symmetry results in a number of astonishing deviations from other M-theories with hadronic strings. For example, world sheet diagrams do not describe particle decays, but instead the propagation of particles by different routes. Particle reactions are described by generalized Feynman diagrams where 3-dimensional light-like surfaces are identified with particles. The ensuing four-dimensional space-time surfaces that now replace the vertices of Feynman diagrams are therefore singular, just like Feynman diagrams are as one-dimensional manifolds. The equivalence between the two interpretations of TGD implies that TGD necessarily unifies quantum mechanics with the General Theory of Relativity by purely geometric means.

If you find visions like this strange and counter-intuitive, you have picked the right book! Matti Pitkanens monograph on TGD leads you gently through the beautiful symmetric geometry that features such unusual structures and connections between them, and lets you yourself be the judge of their merit. Please join me on this journey maybe the most courageous intellectual Odyssey that mankind has ever embarked upon!

Joensuu, October 23, 2014, Finland