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 nonrotational 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. If all velocities involved have the same direction, then the velocity in one frame, u, is related to the velocity in the other frame, u', by the expression stating that u' equals the sum of u and v divided by 1 plus the product of u and v divided by the square of c:

As long as neither u nor v exceeds the speed of light, c, u' also will be less than c.

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, by a formula in which m equals m₀ divided by the square root of one minus the fraction v²/c²:

This changing value of the mass of the moving body, m, is called the relativistic mass. As v approaches c, the figure within the parentheses approaches zero and the mass m becomes infinitely large.

The relativistic mass formula may be interpreted as indicating that the relativistic mass of a body exceeds its rest mass m₀ by an amount that equals its kinetic energy E, divided by c²: m - m₀ = E/c². Hence the hypothesis that generally the energy is c² times the mass, or E = mc², and that energy and mass are, in fact, equivalent physical concepts, differing only by the choice of their units. This hypothesis has been verified experimentally, in that all massive particles have been converted into forms of energy (for instance, gamma radiation) and conversely have been created out of pure energy. It was in part the recognition of this relationship that led to research out of which grew the technology of nuclear fission and fusion.