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As the speed of one inertial frame of reference relative to another is increased, its rods appear increasingly foreshortened and its clocks more and more slowed down. As this relative speed approaches c, both of these effects increase indefinitely. The relative speed of the two frames cannot exceed c if light and other electromagnetic phenomena are to travel at the speed c in all directions when viewed from either frame of reference. Hence the special theory of relativity forecloses relative speeds of frames of reference greater than c. As an inertial frame of reference can be associated with any material object in uniform non rotational motion, it follows that no material object can travel at a rate of speed exceeding c.
This conclusion is self-consistent only because under the Lorentz transformations the velocity of a body with respect to one inertial frame of reference is related to its velocity with respect to another frame not by the Newtonian rule that the difference in velocities equals the relative velocity between the two frames but by a more involved formula, which takes into account the changes in scale length, in clock time, and in simultaneity (see figure).
The mass of a material body is a measure of its resistance to a change in its state of motion caused by a given force. The larger the mass the smaller the acceleration. If a material body is already moving at a speed approaching the speed of light, it must offer increasing resistance to any further acceleration so as not to cross the threshold of c. Hence the special theory of relativity leads to the conclusion that the mass of a moving body m is related to the mass that it would have if at rest, m0.
In the Special Theory of Relativity energy E and momentum p are given from the these formulas. Classic Physics accepts that all bodies have an amount of mass, but relativistic Physics accepts more. In the above formulas we could assume tham if m=0, a body would still carry energy and it would have a momentum. The energy of the body would be
Ε = p c
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