A geometrical origin for the covariant entropy bound

Causal diamond-shaped subsets of spacetime are naturally associated with operator algebras in quantum field theory, and they are also related to the Bousso covariant entropy bound. In this work we argue that the net of these causal sets to which are assigned the local operator algebras of quantum theories should be taken to be non-orthomodular if there is some lowest scale for the description of spacetime as a manifold. This geometry can be related to a reduction in the degrees of freedom of the holographic type under certain natural conditions for the local algebras. A non-orthomodular net of causal sets that implements the cutoff in a covariant manner is constructed. It gives an explanation, in a simple example, of the non-positive expansion condition for lightsheet selection in the covariant entropy bound. It also suggests a different covariant formulation of the entropy bound