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

To the point

Only a 3+1 dimensional universe can support observers, since having more or fewer dimensions would prevent stable atoms and predictive physics, turning other dimensionalities into dead worlds and explaining why ours can support life and measurement.

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arxiv.org

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.