Topological Geometrodynamics (TGD)
Topological Geometrodynamics (thesis in 1983) and topics related to it have been my main research interest for 30 years now. TGD is an attempt to unify fundamental interactions by assuming that physical space-times can be regarded as sub-manifolds of certain 8-dimensional space, which is product of Minkowski space and 4-dimensional complex projective space CP2. One could end up with TGD as a generalization of string model obtained by replacing 1-dimensional strings with 3-dimensional light-like surfaces, or as an attempt to construct Poincare invariant theory of gravitation (Poincare group acts in imbedding space rather than on space-time surface). One outcome is the notion of many-sheeted space-time involving notions like topological field quantization and field body. The huge conformal symmetries of the theory are essentially due to the light-likeness of 3-surfaces. The empirically motivated generalization of quantum theory by introducing hierarchy of Planck constants forces a generalization of imbedding space to a book like structure and different pages of the book corresponds to mcroscopic quantum phases which behave relative to each other like dark matter.
Quantum TGD can be deduced from several principles: physics as geometry of the "world of classical worlds"; physics as a generalized number theory and associativity as fundamental dynamical principle; quantum TGD as almost topological quantum field theory; finite measurement resolution as basic principle of physics; zero energy ontology,... Zero energy ontology combined with the notion of finite resolution to an almost unique generalization of S-matrix (M-matrix) defined as Connes tensor product identified as time-like entanglement coefficients between positive and negative energy parts of zero energy states. A unification of thermodynamics and quantum theory is obtained. One prediction is the assignment of new macroscopic time scale to elementary particles: in case of electron this corresponds to 10 Hz fundamental biorhytm.
The recent formulation of quantum TGD proper relies heavily on the basic principles of TGD inspired theory of consciousness. The notion of self replaces the notion of observer in this theory: an infinite self hierarchy having interpretation in terms of collective levels of consciousness is predicted. Also models for qualia, sensory representations, intentional action, etc. emerge. The new view about relationship between experienced and physical time allows to resolve the basic paradox of quantum measurement theory. The generalization of quantum hologram principle is equally crucial common concept.
p-Adic numbers have turned out to be much more fundamental than I believed first. With the realization that TGD reduces to a generalized number theory, it became clear that space-time decomposes into real and p-adic regions. The only possible interpretation for p-adic regions is as correlates for intentional action and cognition and thus the mind stuff of Descartes. The fusion of real and p-adic physics to single coherent whole forces a generalization of number concept obtained by gluing real and p-adics along rationals and common algebraics. p-Adicity leads to precise predictions for elementary particle masses and it is possible to understand the origin of the elementary particle mass scales number theoretically. p-Adic length scale hypothesis which is cornerstone of TGD and is now deducible from basic quantum TGD.
TGD implies a radical generalization of the concept of space-time. This has consequences in all branches of physics, in particular in biology. TGD predicts a lot of New Physics, and the most interesting new physics is related to how bio-systems manage to be macroscopic quantum systems. The new notion of space-time provides a rather concrete view about bio-control and coordination and explains several strange findings of cellular biology and neurophysiology.
For a somewhat long summary of TGD see the article Brief summary of TGD.
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