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The mass of a body, when subjected to a gravitational attraction but no acceleration (i.e., its gravitational mass) is the same when it is subjected to an acceleration but no gravitational attraction (i.e., its inertial mass).
This gave Einstein the idea that a gravitational field can be imitated by a field of acceleration and this, ultimately, led to the formulation of his general theory of relativity, wherein if showed that a non-accelerating or inertial frame of reference in which there is a gravitational field is physically equivalent to a reference frame accelerating uniformly with reference to the inertial frame but in which there is no gravitational field. This means, in other words, that experiments carried out in the two frames, under the same conditions, will yield identical results. This is called the Principle of Equivalence.