Einstein's Equivalence of Energy and Mass

If a body is in motion with a very high velocity, v, (comparable to the speed of light c), it has a relativistic mass, m(v), that is different from the mass when it is at rest, m0. The relationship between the “rest mass” and the “relativistic mass” is shown in the equation below.

If v/c is « 1, the square root in the denominator can be expanded in a series and truncated after the second term. This results in the following equation:

The factor m0v2/2 corresponds to the kinetic energy ΔE obtained as a result of the high velocity. The addition to the rest mass, Δm, is therefore ΔE/c2. These considerations led Albert Einstein (pictured above) to a postulate that formed a cornerstone of his special theory of relativity:

Thus, already in 1905 the basic formula for the peaceful use of nuclear energy had been found, although it was not put into practice until almost 50 years later.