Test of the Equivalence Principle Using a Rotating Torsion Balance

Abstract

We used a continuously rotating torsion balance instrument to measure the acceleration difference of beryllium and titanium test bodies towards sources at a variety of distances. Our result $\ensuremath{\Delta}{a}_{\mathrm{N},\mathrm{Be}\mathrm{\text{\ensuremath{-}}}\mathrm{Ti}}=(0.6\ifmmode\pm\else\textpm\fi{}3.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{m}/{\mathrm{s}}^{2}$ improves limits on equivalence-principle violations with ranges from 1 m to $\ensuremath{\infty}$ by an order of magnitude. The E\"otv\"os parameter is ${\ensuremath{\eta}}_{\mathrm{Earth},\mathrm{Be}\mathrm{\text{\ensuremath{-}}}\mathrm{Ti}}=(0.3\ifmmode\pm\else\textpm\fi{}1.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$. By analyzing our data for accelerations towards the center of the Milky Way we find equal attractions of Be and Ti towards galactic dark matter, yielding ${\ensuremath{\eta}}_{\mathrm{DM},\mathrm{Be}\mathrm{\text{\ensuremath{-}}}\mathrm{Ti}}=(\ensuremath{-}4\ifmmode\pm\else\textpm\fi{}7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. Space-fixed differential accelerations in any direction are limited to less than $8.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{m}/{\mathrm{s}}^{2}$ with 95% confidence.