List of Footnotes

1 The author is grateful to Ghanashyam Date and Golam Hossain for discussions and correspondence on this issue.
2 The main motivation in [27Jump To The Next Citation Point] was the use of geometrical rather than coordinate areas to quantize curvature components of the Ashtekar connection via holonomies around closed loops. The geometrical area, measured through the dynamical densitized triad p, then introduces the scale dependence in holonomies appearing in the Hamiltonian constraint. However, this procedure appears somewhat ad hoc because (i) single curvature components quantized through holonomies by Equation (14View Equation) refer to coordinates and thus the coordinate area is, in fact, more natural than an invariant geometrical area, and (ii) the quantization then requires the use of the area operator in the Hamiltonian constraint, which is not understood in the full theory. Thus, the original motivation of [27Jump To The Next Citation Point] refers to an argument within the model but not mirrored in the full theory, and thus is suspicious. In Section 6.4 we will discuss a more direct argument [66Jump To The Next Citation Point] for a scale-dependent discreteness suggested by typical properties of the full dynamics.
3 In [138Jump To The Next Citation Point] the absolute rather than relative change of quadratic fluctuations before and after the bounce in a semiclassical state was found to be bounded from above by another fluctuation. While this does provide limits to the growth of fluctuations, the form of the inequality shows that strong relative changes even by factors much larger than discussed here are easily allowed by this analysis. Relative changes, which are less sensitive to the precise scale of fluctuations, were, however, not considered in [138].
4 The author thanks Christian Wüthrich for discussions.