M. Requardt et S. Roy, (Quantum) spacetime as a statistical geometry of fuzzy lumps and the connection with random metric spaces, CLASS QUANT, 18(15), 2001, pp. 3039-3057
We develop a kind of pregeometry consisting of a web of overlapping fuzzy l
umps which interact with each other. The individual lumps are understood as
certain closely entangled subgraphs (cliques) in a dynamically evolving ne
twork which, in a certain approximation, can be visualized as a time-depend
ent random graph. This strand of ideas is merged with another one, deriving
from ideas, developed some time ago by Menger et al, that is, the concept
of probabilistic- or random metric spaces, representing a natural extension
of the metrical continuum into a more microscopic regime. It is our genera
l goal to find a better adapted geometric environment for the description o
f microphysics. In this sense one may also view it as a dynamical randomiza
tion of the causal-set framework developed by, for example, Sorkin et al. I
n doing this we incorporate, as a perhaps new aspect, various concepts from
fuzzy set theory.