Never-ending updating continues

I am continuing the updating of the chapters of "Classical Physics in Many-Sheeted Space-time" related to the relationship of TGD and GRT. The updatings are due to the zero energy ontology, the hierarchy of dark matter labelled by Planck constants, and due to the progress in the understanding of Equivalence Principle. I just finished the elimination of the worst trash from "The Relationship between TGD and GRT" and attach the abstract below.

In this chapter the recent view about TGD as Poincare invariant theory of gravitation is discussed. Radically new views about ontology were necessary before it was possible to see what had been there all the time. Zero energy ontology states that all physical states have vanishing net quantum numbers. The hierarchy of dark matter identified as macroscopic quantum phases labelled by arbitrarily large values of Planck constant is second aspect of the new ontology.

1. The fate of Equivalence Principle

There seems to be a fundamental obstacles against the existence of a Poincare invariant theory of gravitation related to the notions of inertial and gravitational energy.

1. The conservation laws of inertial energy and momentum assigned to the fundamental action would be exact in this kind of a theory. Gravitational four-momentum can be assigned to the curvature scalar as Noether currents and is thus completely well-defined unlike in GRT. Equivalence Principle requires that inertial and gravitational four-momenta are identical. This is satisfied if curvature scalar defines the fundamental action principle crucial for the definition of quantum TGD. Curvature scalar as a fundamental action is however non-physical and had to be replaced with so called Kähler action.

2. One can question Equivalence Principle because the conservation of gravitational four-momentum seems to fail in cosmological scales.

3. For the extremals of Kähler action the Noether currents associated with curvature scalar are well-defined but non-conserved. Also for vacuum extremals satisfying Einstein's equations gravitational energy momentum is not conserved and non-conservation becomes large for small values of cosmic time. This looks fine but the problem is whether the failure of Equivalence Principle is so serious that it leads to conflict with experimental facts.

It turns out that Equivalence Principle can hold true for elementary particles having so called CP₂ type extremals as space-time correlates and for hadrons having string like objects as space-time correlates. This is more or less enough to have consistency with experimental facts. Equivalence Principle fails for vacuum extremals representing Robertson-Walker cosmologies and for all vacuum extremals representing solutions of Einstein's equations. The failure is very dramatic for string like objects that I have used to call cosmic strings. These failures can be however understood in zero energy ontology.

2. The problem of cosmological constant

A further implication of dark matter hierarchy is that astrophysical systems correspond to stationary states analogous to atoms and do not participate to cosmic expansion in a continuous manner but via discrete quantum phase transitions in which gravitational Planck constant increases. By quantum criticality of these phase transitions critical cosmologies are excellent candidates for the modelling of these transitions. Imbeddable critical cosmologies are unique apart from a parameter determining their duration and represent accelerating cosmic expansion so that there is no need to introduce cosmological constant.

It indeed turns out possible to understand these critical phases in terms of quantum phase transition increasing the size of large modelled in terms of "big" cosmic strings with negative gravitational mass whose repulsive gravitation drives "galactic" cosmic strings with positive gravitational mass to the boundaries of the void. In this framework cosmological constant like parameter does not characterize the density of dark energy but that of dark matter identifiable as quantum phases with large Planck constant.

A further problem is that the naive estimate for the cosmological constant is predicted to be by a factor 10¹²⁰ larger than its value deduced from the accelerated expansion of the Universe. In TGD framework the resolution of the problem comes naturally from the fact that large voids are quantum systems which follow the cosmic expansion only during the quantum critical phases.

p-Adic fractality predicting that cosmological constant is reduced by a power of 2 in phase transitions occurring at times T(k) propto 2^k/2, which correspond to p-adic time scales. These phase transitions would naturally correspond to quantum phase transitions increasing the size of the large voids during which critical cosmology predicting accelerated expansion naturally applies. On the average Λ(k) behaves as 1/a², where a is the light-cone proper time. This predicts correctly the order of magnitude for observed value of Λ.

3. Topics of the chapter

The topics discussed in the chapter are following.

1. The relationship between TGD and GRT is discussed applying recent views about the relationship of inertial and gravitational masses, the zero energy ontology, and dark matter hierarchy. One of the basic outcomes is the TGD based understanding of cosmological constant as characterized of dark matter density.

2. The notion of many-sheeted space time interpreted as a hierarchy of smoothed out space-times produced by Nature itself rather than only renormalization group theorist is discussed. The dynamics of what might be called gravitational charges is discussed the basic idea being that the structure of Einstein's tensor automatically implies that metric carries information about sources of the gravitational field without any assumption about variational principle.

3. The theory is applied to the vacuum extremal embeddings of Reissner-Nordström and Schwartschild metric.

4. A model for the final state of a star, which indicates that Z⁰ force, presumably created by dark matter, might have an important role in the dynamics of the compact objects. During year 2003, more than decade after the formulation of the model, the discovery of the connection between supernovas and gamma ray burstsprovided strong support for the predicted axial magnetic and Z⁰ magnetic flux tube structures predicted by the model for the final state of a rotating star. Two years later the interpretation of the predicted long range weak forces as being caused by dark matter emerged.

   The recent progress in understanding of hadronic mass calculations has led to the identification of so called super-canonical bosons and their super-counterparts as basic building blocks of hadrons. This notion leads also to a microscopic description of neutron stars and black-holes in terms of highly entangled string like objects in Hagedorn temperature and in very precise sense analogous to gigantic hadrons.

5. There is experimental evidence for gravimagnetic fields in rotating superconductors which are by 20 orders of magnitudes stronger than predicted by general relativity. A TGD based explanation of these observations is discussed.

For details see the updated chapter The Relationship Between TGD and GRT of "Classical Physics in Many-Sheeted Space-Time".