Three Plus One Spacetime: The Special Status of Observers and Hyperbolicity (A 1997 GR–QC Note)

On the dimensionality of spacetime

Some superstring theories have more than one effective low-energy limit, corresponding to classical spacetimes with different dimensionalities. We argue that all but the 3+1-dimensional one might correspond to ``dead worlds, devoid of observers, in which case all such ensemble theories would actually predict that we should find ourselves inhabiting a 3+1-dimensional spacetime. With more or less than one time-dimension, the partial differential equations of nature would lack the hyperbolicity property that enables observers to make predictions. In a space with more than three dimensions, there can be no traditional atoms and perhaps no stable structures. A space with less than three dimensions allows no gravitational force and may be too simple and barren to contain observers.