Mass - Inertial and Gravitational Mass

Inertial and Gravitational Mass

Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them. In classical mechanics, Newton's third law implies that active and passive gravitational mass must always be identical (or at least proportional), but the classical theory offers no compelling reason why the gravitational mass has to equal the inertial mass. That it does is merely an empirical fact.

Albert Einstein developed his general theory of relativity starting from the assumption that this correspondence between inertial and (passive) gravitational mass is not accidental: that no experiment will ever detect a difference between them (the weak version of the equivalence principle). However, in the resulting theory, gravitation is not a force and thus not subject to Newton's third law, so "the equality of inertial and active gravitational mass remains as puzzling as ever".

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Inertial and Gravitational Mass - Equivalence of Inertial and Gravitational Masses
... The equivalence of inertial and gravitational masses is sometimes referred to as the "Galilean equivalence principle" or the "weak equivalence principle" ... Suppose we have an object with inertial and gravitational masses m and M, respectively ... If the only force acting on the object comes from a gravitational field g, combining Newton's second law and the gravitational law yields the acceleration This says that the ratio of ...

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