Improved bounds on the dimension of space-time.

Abstract

We treat the perihelion shift of the planetary motion and the Lamb shift in hydrogen in an arbitrary number of space dimensions. Comparison with experimental data shows that the deviation from dimensionality four of space-time is less than ${10}^{\ensuremath{-}9}$ and 3.6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$, respectively, on the length scales associated with these phenomena.