A dialog on quantum gravity

The debate between loop quantum gravity and string theory is sometimes lively, and it is hard to present an impartial view on the issue. Leaving any attempt to impartiality aside, I report here, instead, a conversation on this issue, overheard in the cafeteria of a Major American University.Comment: 20 page

Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity

Connes' formula defines a distance in loop quantum gravity, via the spinfoam Dirac operator. A simple notion of spectral distance on a graph can be extended do the discrete Lorentzian context, providing a physically natural example of Lorentzian spectral geometry, with a neat space of Dirac operators. The Hilbert structure of the fermion space is Lorentz covariant rather than invariant.Comment: 4 page

Is Time's Arrow Perspectival?

We observe entropy decrease towards the past. Does this imply that in the past the world was in a non-generic microstate? I point out an alternative. The subsystem to which we belong interacts with the universe via a relatively small number of quantities, which define a coarse graining. Entropy happens to depends on coarse-graining. Therefore the entropy we ascribe to the universe depends on the peculiar coupling between us and the rest of the universe. Low past entropy may be due to the fact that this coupling (rather than microstate of the universe) is non-generic. I argue that for any generic microstate of a sufficiently rich system there are always special subsystems defining a coarse graining for which the entropy of the rest is low in one time direction (the "past"). These are the subsystems allowing creatures that "live in time" ---such as those in the biosphere--- to exist. I reply to some objections raised to an earlier presentation of this idea, in particular by Bob Wald, David Albert and Jim Hartle.Comment: 6 pages, 4 pretty figures. substantial text overlap with arXiv:1407.3384. in revision references adde

A note on the foundation of relativistic mechanics. I: Relativistic observables and relativistic states

Is there a version of the notions of "state" and "observable" wide enough to apply naturally and in a covariant manner to relativistic systems? I discuss here a tentative answer.Comment: 7 pages, no figures. Completely revised versio

A note on the foundation of relativistic mechanics. II: Covariant hamiltonian general relativity

I illustrate a simple hamiltonian formulation of general relativity, derived from the work of Esposito, Gionti and Stornaiolo, which is manifestly 4d generally covariant and is defined over a finite dimensional space. The spacetime coordinates drop out of the formalism, reflecting the fact that they are not related to observability. The formulation can be interpreted in terms of Toller's reference system transformations, and provides a physical interpretation for the spinnetwork to spinnetwork transition amplitudes computable in principle in loop quantum gravity and in the spin foam models.Comment: 7 pages, no figures, 2nd part of gr-qc/011103