Gravity Sensors and the Principle of Equivalence

The tensor characteristics of the inertial fields created by acceleration and rotation, and the gravitational fields created by masses are discussed. Although it is sometimes thought that it is impossible to distinguish between gravitational and inertial effects because of Einstein's principle of equivalence, these effects do have different, detectable tensor characteristics. The principle of equivalence is only strictly applicable at a point, while the instruments to measure these tensor fields exist over a finite region. The inertial field created by acceleration is a uniform vector field and has no gradients, while the inertial field created by rotation has a uniform cylindrically symmetric tensor gradient but none of higher order. The gravitational field created by a mass is highly nonuniform with essentially no limit to the number of higher order gradients. These differences make it theoretically possible to independently measure gravitation, rotation, and acceleration effects; to do so, some form of differential force sensor with tensor response characteristics must be used. The standard technique is static, using differential accelerometers to sense the spatial gradient characteristics of the fields. A more promising technique is dynamic; by rotation of the differential sensor, the static spatial variations are transformed into temporal variations with various frequency components. It is then possible to distinguish between the various fields by frequency filtering.