In 1865 James Clerk Maxwell had unified electricity and magnetism by developing his equations of electromagnetism. It was soon realized that these equations supported wave-like solutions in a region free of electrical charges or currents, otherwise known as vacuums. Later experiments identified light as having electromagnetic properties and Maxwell’s equations predicted that light waves should propagate at a finite speed *c* (about 300,000 km/s). With his Newtonian ideas of absolute space and time firmly entrenched, most physicists thought that this speed was correct only *in one special frame*, absolute rest, and it was thought that electromagnetic waves were supported by an unseen medium called the *ether*, which is at rest in this frame.

Let an object in a rest frame simultaneously emit two light waves with the same energy *E*/2 in opposite directions (now having equal but opposite momenta), the object remains at rest, but its energy decreases by *E*. By the Doppler effect, in another frame, which is moving at the velocity v in one of those directions, the object will appear to lose energy equal to

The difference in energy loss as viewed from the two frames must therefore appear as a difference in kinetic energy seen by the second observing frame. Hence, if *v*/*c* is very small, in the second frame (the one in motion) the object loses an amount of kinetic energy given by

Since the kinetic energy of an object with mass *M* moving with speed *v* is given by (1/2)*Mv*^{2} (for *v/c*≪1), this means that the object has lost an amount of mass given by *E/c*^{2}. In other words, a loss of energy of *E* is equivalent to the loss in mass of *E/c*^{2}. This implies equivalence between the mass and energy content of any object. It turns out that for a particle of mass *M*, this quantity is equal to *M ^{2}c^{2}*. After implementing the Lorentz invariant (and if the frame in which the particle has zero momentum), then the equation

*E=mc*is recovered.

^{2}Vasant Natarajan and Dipitman Sen, “The Special Theory of Relativity,” *Resonance* (April 2005): 32-33, 41-42.