A sensitive, systematic search for feeble, macroscopic forces arising from the exchange of hypothetical ultra-low-mass bosons was made by observing the differential acceleration of two different test body pairs toward two different sources. Our differential accelerometer—a highly symmetric, continuously rotating torsion balance—incorporated several innovations that effectively suppressed systematic errors. All known sources of systematic error were demonstrated to be negligible in comparison to our fluctuating errors which are roughly 7 times larger than the fundamental limit set by the fact that we observe an oscillator at room temperature with a given damping time. Our $1\sigma$ limits on the horizontal differential acceleration of Be/Al or Be/Cu test body pairs in the field of the Earth, $\Delta a_{\perp }=(2.1\mathrm{}\pm 2.1)\times {10}^{-11\mathrm{}}$ cm ${\mathrm{s}}^{-2\mathrm{}}$ and $\Delta a_{\perp }=(0.8\mathrm{}\pm 1.7)\times {10}^{-11\mathrm{}}$ cm ${\mathrm{s}}^{-2\mathrm{}}$, respectively, set improved bounds on Yukawa interactions mediated by bosons with masses ranging between $m_b{c}^2\approx 3\times {10}^{-18\mathrm{}}$ and $m_b{c}^2\approx 1\times {10}^{-6\mathrm{}}$ eV. For example, our constraints on infinite-range vector interactions with charges of $B$ and of $B-L$ are roughly 10 and 2 times more sensitive than those obtained by Roll, Krotkov and Dicke using the field of the Sun. Furthermore we set stringent constraints down to $\lambda =1\mathrm{}$ m, while those of solar experiments are weak for $\lambda <1\mathrm{}$ AU. In terms of the weak equivalence principle in the field of the Earth, our $1\sigma$ result corresponds to $\frac{m_i}{m_g\left(\mathrm{Cu}\right)}-\frac{m_i}{m_g\left(\mathrm{Be}\right)}=(0.2\mathrm{}\pm 1.0)\times {10}^{-11\mathrm{}}$. Our results also yield stringent constraints on the nonsymmetric gravitation theory of Moffat and on the anomalous acceleration of antimatter in proposed "quantum gravity" models, and have implications for lunar-ranging tests of the strong equivalence principle. Our $1\sigma$ limit on the differential acceleration of Be/Al test body pairs toward a 1.5 Mg Pb laboratory source, $\Delta a=(-0.15\mathrm{}\pm 1.31)\times {10}^{-10\mathrm{}}$ cm ${\mathrm{s}}^{-2\mathrm{}}$, provides constraints on Yukawa interactions with ranges down to 10 cm, and on interactions whose charge is $B-2L$.

• Received 16 May 1990

DOI:https://doi.org/10.1103/PhysRevD.42.3267