E = mc^{2}. It's the world's most famous equation, but what
does it really mean? "Energy equals mass times the speed of light squared."
On the most basic level, the equation says that energy and mass (matter) are
interchangeable; they are different forms of the same thing. Under the right
conditions, energy can become mass, and vice versa. We humans don't see them
that way—how can a beam of light and a walnut, say, be different forms of
the same thing?—but Nature does.
So why would you have to multiply the mass of that walnut by the speed of
light to determine how much energy is bound up inside it? The reason is
that whenever you convert part of a walnut or any other piece of matter to pure
energy, the resulting energy is by definition moving at the speed of light.
Pure energy is electromagnetic radiation—whether light or Xrays or
whatever—and electromagnetic radiation travels at a constant speed of
300,000 km/sec (186,000 miles/sec).
Why, then, do you have to square the speed of light? It has to do with
the nature of energy. When something is moving four times as fast as something
else, it doesn't have four times the energy but rather 16 times the
energy—in other words, that figure is squared. So the speed of light
squared is the conversion factor that decides just how much energy lies within
a walnut or any other chunk of matter. And because the speed of light squared
is a huge number—90,000,000,000 (km/sec)^{2}—the amount of
energy bound up into even the smallest mass is truly mindboggling.
Here's an example. If you could turn every one of the atoms in a paper
clip into pure energy—leaving no mass whatsoever—the paper clip
would yield 18 kilotons of TNT. That's roughly the size of the bomb that
destroyed Hiroshima in 1945. On Earth, however, there is no practical way to
convert a paper clip or any other object entirely to energy. It would require
temperatures and pressures greater than those at the core of our sun.

Now Check This Out!
E = mc^{2}: A Biography of the World's Most Famous Equation
by David Bodanis. Berkley Books, 2000.
Explore the innovative thinkers behind each piece of the equation, its
synthesis by Einstein, and its impact on society.
Einstein 1905: The Standard of Greatness
by John S. Rigden. Harvard University Press, 2005.
Examine the impact of Einstein's work during 1905—the "miraculous
year" when he published E = mc^{2} and four other universechanging
papers.
NOVA—Einstein's Big Idea
www.pbs.org/nova/einstein
Get to know Einstein and his ideas through a time line of significant events
in his life, interactive simulations of the speed of light and the effect of
motion on time, and essays explaining E = mc^{2} and Einstein's other
contributions. 

