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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.
In classical mechanics, there being no upper limit to velocity it is possible that as a particle is given more and more acceleration, its speed may go on increasing progressively and may well become greater than , –in fact, it may have any velocity whatever.
This is firmly denied by the theory of relativity. It may legitimately be asked, therefore, as to what will happen if the particle is continually accelerated. Certainly, its velocity v goes on increasing and hence also its mass in accordance with the mass-velocity relation . But as approaches , and therefore and hence the mass of the particle , as shown graphically, from which it is clear that for velocities right up to 50% of , the increase in mass from the value of the rest mass or inertial mass is quite inappreciable. (more…)