Equivalence Principle and Bound Kinetic Energy

We consider the role of the internal kinetic energy of bound systems of matter in tests of the Einstein equivalence principle. Using the gravitational sector of the standard model extension, we show that stringent limits on equivalence principle violations in antimatter can be indirectly obtained from tests using bound systems of normal matter. We estimate the bound kinetic energy of nucleons in a range of light atomic species using Green’s function Monte Carlo calculations, and for heavier species using a Woods-Saxon model. We survey the sensitivities of existing and planned experimental tests of the equivalence principle, and report new constraints at the level of between a few parts in ${10}^6$ and parts in ${10}^8$ on violations of the equivalence principle for matter and antimatter.

Figure 1

Scatterplot of the contribution of ${\beta }^{e+p\pm n}$ and ${\beta }^{\overline{e}+\overline{p}\pm \overline{n}}$ parameters to observable EEP violation in normal nuclides with lifetimes in excess of 1 Gyr, when compared to ${\mathrm{SiO}}_2$, from Eqs. (7, 8). The anomalous fractional acceleration $\beta =f_{{\beta }^{e+p-n}}{\beta }^{e+p-n}+f_{{\beta }^{e+p+n}}{\beta }^{e+p+n}+f_{{\beta }^{\overline{e}+\overline{p}-\overline{n}}}{\beta }^{\overline{e}+\overline{p}-\overline{n}}+f_{{\beta }^{\overline{e}+\overline{p}+\overline{n}}}{\beta }^{\overline{e}+\overline{p}+\overline{n}}$. Tests that compare two or more widely separated species are more sensitive than tests involving neighboring isotopes. Plot (a) shows each species’ relative sensitivity to matter-sector EEP violation, and (b) depicts their sensitivities to antimatter-sector anomalies. Gray points in (a) indicate the range of sensitivities obtained without accounting for nucleons’ kinetic energies. Sensitivities of ${}^6\mathrm{Li}$, ${}^7\mathrm{Li}$, ${}^9\mathrm{Be}$, ${}^{10}\mathrm{B}$, and ${}^{12}\mathrm{C}$ are taken from GFMC calculations, all others from a Woods-Saxon model (see Supplemental Material [24]).