MOTION OF A GYROSCOPE ACCORDING TO EINSTEIN'S THEORY OF GRAVITATION.

The Experimental Basis of Einstein's Theory.-Einstein's theory of gravitation, the general theory of relativity, has been accepted as the most satisfactory description of gravitational phenomena for more than forty years. It is a theory of great conceptual and structural elegance, and it is designed so that it automatically agrees in the appropriate limits with Galileo's observation of the equality of gravitational and inertial mass, with Newton's mechanics of gravitating bodies, and with Einstein's special theory of relativity. Leaving aside the very important matter of elegance, we wish in this section to examine the experimental basis of the theory. This basis consists of the three points of limiting agreement with earlier results just mentioned, together with certain astronomical evidence. The equality of gravitational and inertial mass was originally formulated in terms of equal accelerations for all freely falling test particles, regardless of mass or chemical composition. In this form, it is a consequence of general relativity theory insofar as test particles move in accordance with the geodesic equations for a Riemannian metric. However, the experimental evidence on freely falling particles is not of very great accuracy. Much more precise experiments were performed about half a century ago by E6tv6s and collaborators,' and are now being repeated with improved technique by Dicke.2 Since they make use of particles that are not in free fall but are subjected to nongravitational constraints, the relation with Einstein's theory is not quite so simple as just indicated. On the other hand, we can regard these experiments as establishing with great confidence the principle of equivalence, which we express in the following way: all observations made locally on a system in a static, uniform gravitational field in the absence of local background matter agree with corresponding observations made on the same system when it is subjected to an equivalent acceleration in the absence of the field. This statement of the equivalence principle goes beyond the direct evidence of the Eotv6s experiments. For -one thing, the E6tv6s experiments do not compare observations made in the presence and absence of a gravitational field, but rather compare observations made with an acceleration in one direction and a gravitational field in another. More important, the observations made are not perfectly general, but consist of mass comparisons. However, there is a great deal of physical content to a precise mass measurement, since many of the phenomena known in physics enter into it with sufficient effect to be noticeable;3-5 this occurs through the Hamiltonian of the system, of which the mass is essentially the ground-state eigenvalue. It would be remarkable if the equivalence principle were to apply to the ground states of the Hamiltonians of physics, and not also to the excited states that determine, for example, the transition frequencies. Thus, while this formulation of the equivalence principle is an extrapolation from the direct evidence of the E6tv6s experiments, it is not so great an extrapolation as might at first be supposed. The other points of contact with Einstein's theory of gravitation are most readily