Possible Connection Between Gravitation and Fundamental Length

Abstract

An analysis of the effect of gravitation on hypothetical experiments indicates that it is impossible to measure the position of a particle with error less than $\ensuremath{\Delta}x\ensuremath{\gtrsim}\ensuremath{\surd}G=1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}33}$ cm, where $G$ is the gravitational constant in natural units. A similar limitation applies to the precise synchronization of clocks. It is possible that this result may aid in the solution of the divergence problems of field theory. An equivalence is established between the postulate of a fundamental length and a postulate about gravitational field fluctuations, and it is suggested that the formulation of a fundamental length theory which does not involve gravitational effects in an important way may be impossible.