That Famous Equation and You

By BRIAN GREENE
The New York Times
September 30, 2005

During the summer of 1905, while fulfilling his duties in the patent office in Bern, Switzerland, Albert Einstein was fiddling with a tantalizing outcome of the special theory of relativity he'd published in June. His new insight, at once simple and startling, led him to wonder whether "the Lord might be laughing ... and leading me around by the nose."

In the century since, E = mc² has become the most recognized icon of the modern scientific era. Yet for all its symbolic worth, the equation's intimate presence in everyday life goes largely unnoticed. There is nothing you can do, not a move you can make, not a thought you can have, that doesn't tap directly into E = mc². Einstein's equation is constantly at work, providing an unseen hand that shapes the world into its familiar form. It's an equation that tells of matter, energy and a remarkable bridge between them.

Before E = mc², scientists described matter using two distinct attributes: how much the matter weighed (its mass) and how much change the matter could exert on its environment (its energy). A 19th century physicist would say that a baseball resting on the ground has the same mass as a baseball speeding along at 100 miles per hour. The key difference between the two balls, the physicist would emphasize, is that the fast-moving baseball has more energy: if sent ricocheting through a china shop, for example, it would surely break more dishes than the ball at rest. And once the moving ball has done its damage and stopped, the 19th-century physicist would say that it has exhausted its capacity for exerting change and hence contains no energy.

Before 1905, the common view of energy and matter thus resembled a man carrying around his money in a box of solid gold. After the man spends his last dollar, he thinks he's broke. But then someone alerts him to his miscalculation; a substantial part of his wealth is not what's in the box, but the box itself. Similarly, until Einstein's insight, everyone was aware that matter, by virtue of its motion or position, could possess energy. What everyone missed is the enormous energetic wealth contained in mass itself.

As you read this text, E = mc² is at work. The processes in the eye and brain, underlying perception and thought, rely on chemical reactions that interchange mass and energy, once again in accord with Einstein's formula.

Brian Greene, a professor of physics and mathematics at Columbia, is the author of "The Elegant Universe" and "The Fabric of the Cosmos."