What Can We Do on Gravity with Antihydrogens? *

We discuss the implications of the proposed gravitational redshift experiment on antihydrogens. We show that the result should be the same as on hydrogens in spite of different free-fall accelerations (WEP violation) which may occur if there is a vector fifth-force field. We emphasize the experiment is unique in the sense that it tests the Equivalence Principle expressed in its ultimate form, proposed to be called UEP, directly without being disturbed by the effect of possible presence of a scalar fifth-force field. Trying to see how antiparticles respond to gravity has a long history, but the efforts have been hampered mainly by the presence of the electrostatic force which overwhelms the gravitational force. In this respect antihydrogens, if sufficient number of them are available [1], should have an obvious advantage. If gravity is precisely what Einstein envisioned, antiparticles should fall with the same acceleration as particles, a manifestation of the Equivalence Principle (EP). Expecting violation of this sacred ingredient in General Relativity (GR) is, however, not entirely a trivial idea because almost any of the modern versions of unification program suggest possible occurrence of hitherto unknown fields which might mimic the ordinary gravitational field. In fact there are some fields that couple to the “ordinary” matter fields, like quarks, leptons and gauge fields in the standard model, basically as weakly as the gravitational coupling. But they have nothing to do with the spacetime geometry at least in 4 dimensions. For this reason they might be called “non-geometric gravitational fields” (NGGFs). They are simply part of “matter fields,” which were sharply distinguished by Einstein from the metric field. Some of them might be as heavy as the Planck mass hence remaining permanently unobservable, but some others can be extremely light or nearly massless, thus manifesting themselves as “fifth forces” [2]. It should be pointed out that fields of this kind fail generically to observe compositionindependence in their matter coupling, hence violating universal free-fall (UFF). This UFF is one of the aspects of EP. To emphasize a special position of UFF in the more general concept of EP, people give this a special name; Weak Equivalence Principle (WEP). Put in the other way around, WEP is a privilege enjoyed only by a force endowed with spacetime geometry. No other forces, including those due to NGGFs, share this luxury. For this reason, testing WEP is a way to probe a fifth force. Even combined with another way of probing departure from a purely inverse-square law, no solid evidence for the fifth force has been reported. This does not imply, however, that its Delivered at The International Workshop on JHF Science (JHF98), KEK, Tsukuba, Japan, March 4-7, 1998. E-mail address: [email protected]