String theory and the space-time uncertainty principle

The notion of a space-time uncertainty principle in string theory is clarif ied and further developed. The motivation and the derivation of the princip le are first reviewed in a reasonably self-contained way. It is then shown that the nonperturbative (Borel summed) high-energy and high-momentum trans fer behavior of string scattering is consistent with the space-time uncerta inty principle. It is also shown that, as a consequence of this principle, string theories in 10 dimensions generically exhibit a characteristic lengt h scale which is equal to the well-known 11 dimensional Planck length g(s)( 1/3)l(s) of M-theory as the scale at which stringy effects take over the ef fects of classical supergravity, even without involving D-branes directly. The implications of the space-time uncertainty relation in connection with D-branes and black holes are discussed and reinterpreted. Finally, we prese nt a novel interpretation of the Schild-gauge action for strings from the v iewpoint of noncommutative geometry. This conforms to the space-time uncert ainty relation by manifestly exhibiting a noncommutativity of quantised str ing coordinates between, dominantly, space and time. We also discuss the co nsistency of the space-time uncertainty relation with S and T dualities.