2 is for squared
There is only one 'number' represented in Einstein's great equation and it designates that the speed of light, c, must be squared. A number which is squared is simply one that is multiplied by itself. Squaring 4 equals 16, for example.
In E=mc2, the speed of light is multiplied by itself, 670 million (miles an hour) by 670 million, giving the preposterously large number of 448,900,000,000,000,000. But why square the speed of light at all? The answer lies with the discovery made by a brilliant French aristocrat, Emilie du Chatelet.
At the age of 23, du Chatelet discovered a talent for advanced mathematics which she relished. So much so that she began to formulate ideas of her own; ideas that challenged the great physicists, including Sir Isaac Newton.
Newton stated that the energy (or force) of a moving object could simply be expressed as its mass multiplied by its velocity. But while corresponding with a German scientist called Gottfried Leibniz, du Chatelet learned that Leibniz considered the energy of a moving object is better described if its velocity is squared. But how to test this? Du Chatelet tried an experiment that would prove her point – dropping lead balls into clay.
Newton's formula says that doubling the velocity of a ball would double its energy and so one would expect it to travel twice as far into the clay. But if the velocity is squared, as Leibniz and du Chatelet believed, the force should be four times greater, and the ball should travel four times the distance into the clay.
Du Chatelet conducted her lead ball experiment and sure enough, doubling the velocity of the ball (by dropping it from twice the height) resulted in the ball travelling four times further into the clay. This simple but brilliant experiment proved that when calculating the energy of moving objects, the velocity at which they travel must be squared.
The energy of an object is a function of its velocity squared – it is for this reason that the speed of light in Einstein's equation must be squared.
This was a factor that profoundly changed the meaning of Einstein's equation – since c is already a large number, once squared it is vast. Thus, a vast amount of energy (E) can be associated with a very small amount of mass (m) because mass is always multiplied by the speed of light (c) squared – a vast number. Under these laws, even a tiny amount of mass will equate to a huge amount of energy.