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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
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