2 research outputs found
Evidence for an entropy bound from fundamentally discrete gravity
The various entropy bounds that exist in the literature suggest that
spacetime is fundamentally discrete, and hint at an underlying relationship
between geometry and "information". The foundation of this relationship is yet
to be uncovered, but should manifest itself in a theory of quantum gravity. We
present a measure for the maximal entropy of spherically symmetric spacelike
regions within the causal set approach to quantum gravity. In terms of the
proposal, a bound for the entropy contained in this region can be derived from
a counting of potential "degrees of freedom" associated to the Cauchy horizon
of its future domain of dependence. For different spherically symmetric
spacelike regions in Minkowski spacetime of arbitrary dimension, we show that
this proposal leads, in the continuum approximation, to Susskind's well-known
spherical entropy bound.Comment: 25 pages, 9 figures. Comment on Bekenstein bound added and smaller
corrections. To be published in Class.Quant.Gra
Spacelike distance from discrete causal order
Any discrete approach to quantum gravity must provide some prescription as to
how to deduce continuum properties from the discrete substructure. In the
causal set approach it is straightforward to deduce timelike distances, but
surprisingly difficult to extract spacelike distances, because of the unique
combination of discreteness with local Lorentz invariance in that approach. We
propose a number of methods to overcome this difficulty, one of which
reproduces the spatial distance between two points in a finite region of
Minkowski space. We provide numerical evidence that this definition can be used
to define a `spatial nearest neighbor' relation on a causal set, and conjecture
that this can be exploited to define the length of `continuous curves' in
causal sets which are approximated by curved spacetime. This provides evidence
in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio