Test of the Equivalence Principle Using a Rotating Torsion Balance

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 $\Delta a_{\mathrm{N},\mathrm{Be}\mathrm{\text{−}}\mathrm{Ti}}=(0.6\pm 3.1)\times {10}^{-15}\mathrm{m}/{\mathrm{s}}^2$ improves limits on equivalence-principle violations with ranges from 1 m to $\infty$ by an order of magnitude. The Eötvös parameter is ${\eta }_{\mathrm{Earth},\mathrm{Be}\mathrm{\text{−}}\mathrm{Ti}}=(0.3\pm 1.8)\times {10}^{-13}$. 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 ${\eta }_{\mathrm{DM},\mathrm{Be}\mathrm{\text{−}}\mathrm{Ti}}=(-4\pm 7)\times {10}^{-5}$. Space-fixed differential accelerations in any direction are limited to less than $8.8\times {10}^{-15}\mathrm{m}/{\mathrm{s}}^2$ with 95% confidence.

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Figure 1

Cross section of the apparatus (upper part). The entire torsion balance is suspended below a continuously rotating turntable. Gravity gradient compensator masses were placed around the pendulum to reduce coupling to ambient gravitational gradients. The pendulum (lower part) carries four Ti and four Be masses in a composition dipole.

Figure 2

Shown are measured differential accelerations towards north (top) and west. After the first four data runs, the Be and Ti test bodies were interchanged on the pendulum frame. A violation of the equivalence principle would appear as a difference in the means (lines) of the two data sets. The offset acceleration is due to systematic effects that follow the pendulum frame but not the composition dipole. The data have been corrected for tilt and gravity gradients, but only the statistical uncertainties are shown.

Figure 3

New upper limits on Yukawa interactions coupled to baryon number with 95% confidence. The uncertainties in the source integration is not included in this plot. The numbers indicate references. The shaded region is experimentally excluded. Preliminary models for $10\mathrm{km}<\lambda <1000\mathrm{km}$ indicate that the limit on $\alpha$ is smaller than the dashed line.

Figure 4

The averaged differential acceleration of Be and Ti towards north and west as a function of sidereal time. The dashed line represents a hypothetical signal of $20\times {10}^{-15}\mathrm{m}/{\mathrm{s}}^2$. The solid line is the best fit toward the galactic center [$\Delta a=(-2.1\pm 3.1)\times {10}^{-15}\mathrm{m}/{\mathrm{s}}^2$].