caused by a rotating gravitating mass (frame dragging), or bear on the measurements of light deflection and gravitational time delay made by non-local observers. Active, passive, and inertial masses By definition of active and passive gravitational mass, the force on due to the gravitational field of is: Likewise the force on a second object of arbitrary mass2 due to the gravitational field of mass0 is: By definition of inertial mass: If and are the same distance from then, by the weak equivalence principle, they fall at the same rate (i.e. their accelerations are the same) Hence: Therefore: In other words, passive gravitational mass must be proportional to inertial mass for all objects. Furthermore, by Newton's third law of motion: must be equal and opposite to It follows that: In other words, passive gravitational mass must be proportional to active gravitational mass for all objects. The dimensionless Eötvös-parameter is the difference of the ratios of gravitational and inertial masses divided by their average for the two sets of test masses "A" and "B". Tests of the weak equivalence principle Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. An obvious test is dropping different objects, ideally in a vacuum environment, e.g., inside the Fallturm Bremen drop tower. See: Experiments are still being performed at the University of Washington which have placed limits on the differential acceleration of objects towards the Earth, the Sun and towards dark matter in the Galactic Center. Future satellite experiments – STEP (Satellite Test of the Equivalence Principle), and Galileo Galilei – will test the weak equivalence principle in space, to much higher accuracy. With the first successful production of antimatter, in particular anti-hydrogen, a new approach to test the weak equivalence principle has been proposed. Experiments to compare the gravitational behavior of matter and antimatter are currently being developed. Proposals that may lead to a quantum theory of gravity such as string theory and loop quantum gravity predict violations of the weak equivalence principle because they contain many light scalar fields with long Compton wavelengths, which should generate fifth forces and variation of the fundamental constants. Heuristic arguments suggest that the magnitude of these equivalence principle violations could be in the 10−13 to 10−18 range. Currently envisioned tests of the weak equivalence principle are approaching a degree of sensitivity such that non-discovery of a violation would be