* 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*.**Most helpful if notebook is read with

*in Adobe, under ‘View”.*

**Two Page Scrolling****Notebook September 2010 – February 2011: https://gaugegravity.com/wp-content/uploads/2020/05/Notebook-9-2010-2-2011.pdf**

**Gauge Theory and Paralellism, Kleinert, Wong Equations:** **Work is concurrent with Notebook: Wong Equations for Gravitation**

**(p. 33-34)**Concerning Kleinert’s proposal:- Teleparallel gauge 1 / Einstein-Hilbert gauge 2 ⇨⇨ Unified Theory
- 1. Presumably one can incorporate symmetric teleparallel gravity into the scheme.
- 2. Tanimura deduced the curvature (Einstein-Hilbert) formulation of GR from the modified Feynman argument with
**…**

- Teleparallel gauge 1 / Einstein-Hilbert gauge 2 ⇨⇨ Unified Theory
- We have deduced (almost) the equation of motion for a translation gauge theory by taking I
^{α}= P^{α}in the gauge theory approach of Tanimura. We expect to get teleparallel’s EOM.- Both of these approaches should be related by Kleinert’s gauge symmetry.

- Coming at gravity from the non-abelian gauge theory angle often leads to torsion.

**(p. 42)** Perhaps our gauge-gravity has revealed a way to subsume Riemannian Geometry into the Erlangen Programme once we understand the symmetry meaning, or perhaps the “interpretation” of **… **

**(p. 75)**Poincare’s geometric conventionalism–a revival- Teleparallel / Riemannian / Symmetric teleparallel⇒⇨Continuum of possibilities corresponding to gauge choices that correspond to different geometries and different oberservables. c.f. Kleinert

**(p. 77)** It is a *gauge choice* whether to blame gravitational effects on *local translations* or *local rotations*.

**(p. 79)** The month of November is continued in the notebook: **Wong Equations for Gravitation**.

**(p. 93-94)**Let’s examine the possible equivalence of the 3 different formulations of GR- Einstein
- Teleparallel
- Symmetric Teleparallel

- In the symmetric teleparallel approach we covariantize the coordinates which
help in passing to a non-commutative algebraic approach.*may* - The question of gravitational energy momentum conservation will be solved with the understanding of Noether’s theorem extended to include groupoids.
- We must do a study of the nature of supersymmetry in these alternative geometries
**…**. These may be a*very*interesting relation between*paralelizability*and SUSY. Paralelizability is already very desirable from dynamical (initial value) formulations, and in the construction of canonical frames in the teleparallel theory. *It is necessary to provide a Noether’s theorem for groupoids in order to understand gravity!*

**(p. 100) **It’s possible that the *necessity* of requiring asymptotic isometry group in QFT, which is, by the results of AdS/CFT, what make the string theory/field theory model of gravity background dependent, comes from a long-known property of Quantum Theory: the measuring device must be *classical*. In order for the measuring device to be ‘classical’ it must exist in an isotropic spacetime. Can this be justified? *What is truly required of a classical measuring device? *

**(p. 108) **Tuesday, December 14, 2010 Today we play around with noncommutativity and supersymmetry as a consequence of our gravitational formalism.

**(p. 129) **What happens if we do ordinary Yang-Mills but allow the structure constants to fluctuate ever so slightly?

**(p. 137) ** Next layer of physical detail: ___”Points” should be big enough to allow an internal angular and linear momentum.

**(p. 140)** *The fundamental statement is that the physics of 2 harmonic oscillators, with spin and angular momentum, confined to the x-y plane, with an external B-field in the z direction is a supersymmetric system.*** … **so, we have spinning particles subject to 2 external forces.

**(p. 144) On the Question of Background Independence**- The present formulation of string theory suffers from a defect that may indicate the need for a fundamental rethinking of the program: background dependence.

- By “
*background dependence*‘ we mean that any theory in which space and time play a role along with other physical entities and when the following obtains:- 1. We can cannonically associate a group
**g**to the spacetime*irrespective*of the state of other physical entities - 2. We denote the mathematical structure that is associated with spacetime degrees of freedom:
**M** - Typically, when gravitation itself is considered classically (i.e. we are not doing quantum gravity)
**M**is a manifold.

- 1. We can cannonically associate a group
- We call the pair (
**M, g**) the*background*.

- The question of
*background independence*is related to the long-standing philosophical argument (c.f. Leibing) that the correct theory of physics*must*be background independent because space and time are truly*relations*between the other physical entities appearing in the theory.

**(p. 146-147) **A Critique of Relationalism. **…** Actually, to be more precise, we think of spacetime to be made up of relationships between particles, not fields. Spacetime is all the relations between localizable entities. In a field theory the excitations that constitute particles are not the fundamental entities in the theory **… ** We have, at this point to make a distinction between defining spacetime as the set of relations between all possible configurations of particles versus defining spacetime as only relations between *measured* particles. Do we create spacetime by *measuring* local quantities?