New tests of the universality of free fall

Abstract

We use a continuously rotating torsion balance to make new tests of the universality of free fall (UFF). We study differential accelerations of Be-Cu and Be-Al test-body pairs in the fields of Earth, the Sun, our Galaxy, and in the direction of the cosmic microwave dipole. We also compare the acceleration towards the Sun and our galactic center of Cu and single-crystal Si in an Al shell (this pair of bodies approximates the elemental compositions of Earth's core and the Moon or Earth's crust, respectively). In terms of the classic UFF parameter \ensuremath{\eta}, our Earth-source results are \ensuremath{\eta}(Be,Cu)=(-1.9\ifmmode\pm\else\textpm\fi{}2.5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ and \ensuremath{\eta}(Be,Al)=(-0.2\ifmmode\pm\else\textpm\fi{}2.8)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ where all errors are 1\ensuremath{\sigma}. Thus our limit on UFF violation for Be and a composite Al/Cu body is \ensuremath{\eta}=(-1.1\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$. Our solar-source results are \ensuremath{\Delta}a(Be,Cu) =(-3.0\ifmmode\pm\else\textpm\fi{}3.6)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ cm/${\mathrm{s}}^{2}$, \ensuremath{\Delta}a(Be,Al)=(+2.4\ifmmode\pm\else\textpm\fi{}5.8)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ cm/${\mathrm{s}}^{2}$, and \ensuremath{\Delta}a(Si/Al,Cu)=(+3.0 \ifmmode\pm\else\textpm\fi{}4.0)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ cm/${\mathrm{s}}^{2}$. This latter result, when added to the lunar laser-ranging result that senses both composition-dependent forces and gravitational binding-energy anomalies, yields a nearly model-independent test of the UFF for gravitational binding energy at the 1% level.A fivefold tighter limit follows if composition-dependent interactions are restricted to vector forces. Our galactic-source results test the UFF for ordinary matter attracted toward dark matter, yielding ${\mathrm{\ensuremath{\eta}}}^{\mathrm{DM}}$(Be,Cu)=(-1.3\ifmmode\pm\else\textpm\fi{}0.9)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$, ${\mathrm{\ensuremath{\eta}}}^{\mathrm{DM}}$(Be,Al)=(+1.8\ifmmode\pm\else\textpm\fi{}1.4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$, and ${\mathrm{\ensuremath{\eta}}}^{\mathrm{DM}}$(Si/Al,Cu)=(+0.7 \ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$. This provides laboratory confirmation of the usual assumption that gravity is the dominant long-range interaction between dark and luminous matter. We also test Weber's claim that solar neutrinos scatter coherently from single crystals with cross sections \ensuremath{\sim}${10}^{23}$ times larger than the generally accepted value and rule out the existence of such cross sections.