String Theory and the Space-Time Uncertainty Principle

TL;DR

This paper clarifies and develops the space-time uncertainty principle in string theory, showing its consistency with high-energy string scattering, M-theory length scales, and dualities, while connecting it to noncommutative geometry and D-branes.

Contribution

It provides a detailed analysis of the space-time uncertainty principle, its implications for string theory and M-theory, and introduces a noncommutative geometric interpretation of string dynamics.

Findings

High-energy string scattering aligns with the space-time uncertainty principle.

String theories in 10 dimensions exhibit a characteristic length scale related to M-theory.

Noncommutative geometry offers a new perspective on string coordinates and the uncertainty principle.

Abstract

The notion of a space-time uncertainty principle in string theory is clarified and further developed. The motivation and the derivation of the principle are first reviewed in a reasonably self-contained way. It is then shown that the nonperturbative (Borel summed) high-energy and high-momentum transfer behavior of string scattering is consistent with the space-time uncertainty principle. It is also shown that, in consequence of the principle, string theories in 10 dimensions generically exhibit a characteristic length scale which is equal to the well-known 11 dimensional Planck length $g_s^{1/3}\ell_s$ of M-theory as the scale at which stringy effects take over the effects of classical supergravity, even without involving D-branes directly. The meanings of the space-time uncertainty relation in connection with D-branes and black holes are discussed and reinterpreted. Finally, we present a novel interpretation of the Schild-gauge action for strings from a viewpoint of noncommutative geometry, which conforms to the space-time uncertainty relation by manifestly exhibiting a noncommutativity of quantized string coordinates dominantly between space and time. We also discuss the consistency of the space-time uncertainty relation with S and T dualities.