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Some comments about classical conservation laws in Zero Energy Ontology

In Zero Energy Ontology (ZEO), the basic geometric structure is causal diamond (CD), which is a subset of M4× CP2 identified as an intersection of future and past directed light cones of M4 with points replaced with CP2. Poincare symmetries are isometries of M4× CP2 but CD itself breaks Poincare symmetry.

Whether Poincare transformations can act as global symmetries in the "world of classical worlds" (WCW), the space of space-time surfaces - preferred extremals - connecting 3-surfaces at opposite boundaries of CD, is not quite clear since CD itself breaks Poincare symmetry. One can even argue that ZEO is not consistent with Poincare invariance. By holography one can either talk about WCW as pairs of 3-surfaces or about space of preferred extremals connecting the members of the pair.

First some background.




Poincare transformations act symmetries of space-time surfaces representing extremals of the classical variational principle involved, and one can hope that …

About gauge bosons and their decay vertices in TGD framework

The attempt to understand how unitarity of scattering amplitudes emerges led as side track to a more detailed view about gauge bosons as flux tubes carrying monopole flux and consisting of two long portions with Minkowskian signature and two short portions represented by wormhole contacts. Also a more detailed view about decay vertices emerged.

There question is how elementary particles and their basic interaction vertices could be realized in this framework.




In TGD framework particle would correspond to pair of wormhole contact associated with closed magnetic flux tube carrying monopole flux. Strongly flattened rectangle with Minkowskian flux tubes as long edges with length given by weak scale and Euclidian wormhole contacts as short edges with CP2 radius as lengths scale is a good visualization. 3-particle vertex corresponding to the replication of this kind of flux tube rectangle to two rectangles would replace 3-vertex of Feynman graph. There is analogy with DNA repl…

More about the construction of scattering amplitudes in TGD framework

During years I have considered several proposals for S-matrix in TGD framework - perhaps the most realistic proposal relies on the generalization of twistor Grassmann approach to TGD context. There are several questions waiting for an answer. How to achieve unitarity? What it is to be a particle in classical sense? Can one identify TGD analogs of quantum fields? Could scattering amplitudes have interpretation as Fourier transforms of n-point functions for the analogs of quantum fields?

Unitarity is certainly the issue number 1 and in the sequel almost trivial solution to the unitarity problem based on the existence of super-symplectic transformations acting as isometries of "world of classical worlds" implying infinite number of conserved Noether charges in turn guaranteeing unitarity. Also quantum classical correspondence and the role of string world sheets for strong form of holography are discussed. What is found that number theoretic view justifies the …

About TGD counterparts of classical field configurations in Maxwell's theory

Classical physics is an exact part of TGD so that the study of extremals of dimensionally reduces 6-D Kähler action can provide a lot of intuition about quantum TGD and see how quantum-classical correspondence is realized.

In the following the goal is to develop further understanding about TGD counterparts of the simplest field configurations in Maxwell's theory.

About differences between Maxwell's ED and TGD

TGD differs from Maxwell's theory in several important aspects.




The TGD counterparts of classical electroweak gauge potentials are induced from component of spinor connection of CP2. Classical color gauge potentials corresponds to the projections of Killing vector fields of color isometries.



Also M4 has Kähler potential, which is induced to space-time surface and gives rise to an additional U(1) force. The couplings of M4 gauge potential to quarks and leptons are of same sign whereas the couplings of CP2 Kähler potential to B and L are of opposite sign so that t…

Generalized conformal symmetry, quantum criticality, catastrophe theory, and coupling constant evolution

The notion of quantum criticality allows two realizations: as stationarity of S2 part of the twistor lift of Kähler action and in terms of zeros of zeta are key elements in the explicit proposal for discrete coupling constant evolution reducing to that for cosmological constant.

Quantum criticality from different perspectives

Quantum criticality is however much more general notion, and one must ask how this view relates to the earlier picture.




At the real number side continuous coupling constant evolution makes sense. What does this mean? Can one say that quantum criticality makes possible only adelic physics together with large heff/h0=n as dimension for extension of rationals. This hierarchy is essential for life and cognition.

Can one conclude that living systems correspond to quantum critical values of S(S2) and therefore αK and in-animate systems correspond to other values of αK? But wouldn't his mean that one gives up the original vision that αK is analogous to critica…

Cosmological Axis of Evil as a memory from primordial cosmology

Axis of evil is very interesting CMB anomaly (thanks for Sky Darmos for mentioning it in FB discussion). It has been even proposed that it forces Earth-centeredness. According to the Wikipedia article :

"The motion of the solar system, and the orientation of the plane of the ecliptic are aligned with features of the microwave sky, which on conventional thinking are caused by structure at the edge of the observable universe. Specifically, with respect to the ecliptic plane the "top half" of the CMB is slightly cooler than the "bottom half"; furthermore, the quadrupole and octupole axes are only a few degrees apart, and these axes are aligned with the top/bottom divide."

This is indeed really strange looking finding. To my view it does not however bring pre-Keplerian world view back but is related to the possibility of quantum coherence even in cosmological scales predicted by TGD. It would also reflect the situation during very early cosmology, whi…

Solution of renormalization group equation for flux tubes having minimum string tension and RG evolution in terms of Riemann zeta

The great surprise of the last year was that twistor induction allows large number of induced twistor structures. SO(3) acts as moduli space for the dimensional reductions of the 6-D Kähler action defining the twistor space of space-time surface as a 6-D surface in 12-D twistor space assignable to M4× CP2. This 6-D surface has space-time surface as base and sphere S2 as fiber. The area of the twistor sphere in induced twistor structure defines running cosmological constant and one can understand the mysterious smallness of cosmological constant.

This in turn led to the understanding of coupling constant evolution in terms of the flow changing the value of

cosmological constant defined by the area of the twistor sphere of space-time surface for induced twistor structure.

dlog(αK)/ds = -[S(S2)/(SK(X4)+S(S2)] dlog(S(S2))/ds .

Renormalization group equation for flux tubes having minimum string tension

It came as a further pleasant surprise that for a very important special cas…