Author Commentary Below: A few notations from this notebook to indicate topics covered. Author’s page numbering is ignored, any page numbers referenced below are from the scanned PDF documents
Mainly Gauge Gravity ideas, Using Chapter 6 of the Chinese book as Launching Point
(p. 16) Today we return to the issue of energy and more generally of conserved quantities that follow from the starting point of variational principles. In fact, it is important to recall That Santilli’s work in theoretical mechanics considers variation principles as fundamental. In his Vol. II we simply see the search for the most general analytic, algebraic, symplectic laws that can follow from variational principles. This is a key moment in my project …
(p. 25-27) The fact that the energy density at a point P is an unobservable quantity is due to the fact that the point P is unobservable, not because the energy is not present, in some global sense … It appears to me that this issue of what exactly is the energy density of the gravitational field is actually central to quantum gravity. Indeed, is there any example of a quantum system with no Hamiltonian that has been successfully quantized, and the result successfully compared with experiment. Here we also must finally fully come to terms with the notion of observer in the quantum theory. According to the standard interpretation of quantum theory an observer is a (large) system (classical) that registers and stores the results of quantum measurements. In GR it is a coordinate system…So what is it?
(p. 37) What do we mean when we say an action has a Lie algebroid symmetry?
(p. 97) Now we have a simple derivation of the gravitational Wong equations.
(p. 110) The teleparallel version of the general theory of relativity is a wonderful reformulation of that theory. It involves an incredible shift in philosophical outlook and most significantly, it revives Poicare’s idea of geometric conventionalism. Geometric conventionalism is the doctrine that the choice of geometric properties in space is a matter of convention. Physical theory is divided into 2 parts: i) The geometry ii) The theory of physical objects. A gauge theory determining which physical events are real.
(p. 112) Develop the idea that a lack of definition for energy is the reason why quantization of gravity has not worked yet. This touches on the meaning of supersymmetry.
Additional notes dated: June 2011 https://gaugegravity.com/notebook-6-2011/
(p. 3) More on non commutativity and gauge gravity. How does noncommutativity enter gauge gravity?