# Question 78528

Jan 30, 2017

Einstein's famous equation tells us that energy and mass are interchangeable.

#### Explanation:

As part of his work on Special Relativity, Einstein applied his transformation equations to time, displacement, velocity, momentum and finally to kinetic energy.

The full derivation is complicated, but it showed that when an object gained kinetic energy (gained speed) its mass also increased, and approached infinity as the speed approached the speed of light, $c$.

When this last derivation was through, he had come up with a new, previously unknown term that came to be known as the rest energy of an object. This is energy the object contained even when it was not moving (remember, he was a relativistic version of kinetic energy at the time).

Einstein quickly realized that this term was pointing to a sort of equivalence between mass and energy, an equivalence that was dramatically demonstrated with the detonation of the first atomic bomb. Here, a small portion of the mass of the fission material was converted to pure energy. Since $c$ is a large number (3xx10^8m/s)#, ${c}^{2}$, the proportionality constant that determined how much energy could be obtained from the loss of a given amount of mass, is an enormous number. Enormous amounts of energy could be released this way.

Since that time, it has also been demonstrated that energy can "congeal" into mass - particles of matter and antimatter are produced in just this way.

An amazing result from this simple-looking equation.