A brief summary of various competing visions about the basic principles of quantum Topological Geometrodynamics (TGD) and about tensions between them is given with emphasis on the recent developments.
- Physics as the classical spinor field geometry of the world of classical worlds is the oldest and best developed approach to TGD and means generalization of Einstein's program of geometrizing classical physics so that it applies to entire quantum physics.
- Parton level formulation of quantum TGD as an almost topological quantum field theory using light-like 3-surfaces as fundamental objects allows a detailed understanding of super-conformal symmetries generalizing those of super string models. A category theoretical interpretation of M-matrix as a functor is possible. This picture has tight connections to the physics as configuration space geometry approach and implies it.
- Physics as generalized number theory represents third vision about TGD. Number theoretic universality meaning a fusion of real and p-adic physics to single coherent whole forces a formulation in terms of so called number theoretic braids. The symmetries of classical number fields strongly suggest the interpretation in terms of standard model symmetries and a number theoretic interpretation of the imbedding space M4× CP2. Associativity condition would define laws of classical and quantum TGD. The notion of infinite prime defines a third thread in the braid of number theoretical ideas and it is now possible to give a surprisingly realization for the number theoretic Brahman=Atman identity (algebraic holography) based on the generalization of the number concept by allowing infinite number of real units representable as ratios of infinite integers having interpretation as representations for physical states of super-symmetric arithmetic QFT. The infinitely rich number theoretic anatomy for the points of number theoretic braids allows to represent the information about quantum state of the Universe which remains below measurement resolution.
- The idea about hierarchy of Planck constants was inspired by certain empirical facts. The hierarchy leads to a generalization of the notion of imbedding space emerges naturally from the requirement that the choice of quantization axes has a geometric correlate also at the level of imbedding space. The physical implication is the identification of dark matter in terms of a hierarchy of macroscopically quantum coherent phases with quantized values of Planck constant having arbitrarily large values and playing a key role, not only in biology but also in astrophysics and cosmology of TGD Universe. The hierarchy of Planck constants can be seen as necessary for the realization of quantum criticality. The generalization of imbedding space is also essential for the construction of the Kähler function of configuration space.
- The fifth vision about quantum TGD is that the mere finiteness of measurement resolution fixes the scattering matrix of quantum TGD. In zero energy ontology S-matrix must be generalized to M-matrix identified as time-like entanglement coefficients between positive and negative energy parts of zero energy states. M-matrix can be regarded as a "complex square root" of density matrix expressible as product of a real square root of density matrix and unitary S-matrix: thermodynamics becomes part of quantum theory. Hyper-finite factors of type II1 (HFFs) emerge naturally through Clifford algebra of the "world of classical worlds" and allow a formulation of quantum measurement theory with a finite measurement resolution. The notion of finite measurement resolution expressed in terms of inclusion of HFFs with included algebra defining the measurement resolution leads to an identification of M-matrix in terms of Connes tensor product and a simple argument shows that M-matrix is unique apart from the presence of the square root of density matrix needed by thermodynamics. Coupling constant evolution corresponds to a hierarchy of measurement resolutions and p-adic coupling constant hypothesis follows as a consequence with an additional prediction assigning to particles an additional time scale characterizing temporal distance between positive and negative energy parts of corresponding zero energy state: for electron this time scale is .1 second, fundamental biorhythm. Thus zero energy ontology implies a direct connection between elementary particle physics and biology.
- Consciousness theory interpreted as generalization of quantum measurement theory the most plausible vision about quantum TGD and has already shown its power and brought into theory notions which cannot be imagined in the standard conceptual framework of quantum physics.
Thursday, April 24, 2008
Topological Geometrodynamics: an Overall View
The participation in a conference inspired me to write a brief overall view about the recent situation in TGD. This was badly needed since even the last year has brought many important steps of progress. I glue here only the abstract of the article.