Constraints on the gravitational properties of antiprotons and positrons from cyclotron-frequency measurements.

A fundamental question in physics which has yet to be addressed experimentally is whether particles of antimatter, such as the antiproton or positron, obey the weak equivalence principle. ' An experiment that will test this principle directly for antiprotons is under development at present. Meanwhile, high-precision experimental results on the equality of the inertial masses of protons and antiprotons have recently become available from an experiment which compares the cyclotron frequencies of the particles in the same magnetic field. (Similar results for electrons and positrons, although at a lower precision, have been in existence for almost ten years. ) These results are usually regarded as very sensitive tests of CPT symmetry. However, in this Letter we will show that they can instead provide tests of the weak equivalence principle for a gravitational coupling to the energy of positrons and antiprotons, under the assumption of exact CPT symmetry. This possibility arises because the frequencies in question constitute local "clocks" and as such are subject to a gravitational redshift, which may be formulated as a test of weak equivalence for their energy content. To see this, we will consider a modified version of Einstein s gedanken experiment in which the gravitational redshift can be derived from conservation of energy in the gravitational field. We start with some local clock based on the photon frequency in the transition A* A+y between a system 2 and its excited state 2*. In a uniform gravitational field, A (A *) has gravitational acceleration g (g*) and inertial mass m (m*), respectively. The relative rates of two such clocks at diA'erent heights in the gravitational field may be compared by exchanging photons. We start with system 4 located at some height hl and system A* above it at height h2, with h2 —h ~ =l. Next, and 4* are interchanged, with the output of an amount of energy, E,„,=(m*g* —mg)l . System 4*, now located at the lower height hl, is allowed to decay to its ground state A by emission of a photon of frequency co~ with @to|=(m* —m)c, which defines the local clock frequency. This photon is allowed to propagate up to height h2, where its frequency will have suAered a generalized redshift to some value co2, according to the local clock at h2,