Physics: E = mc2 Explained


Most people have heard of Einstein’s famous equation: E = mc2.  But how many of us really understand on even a basic level what it means?

PBS’ NOVA explains “energy = mass times the speed of light squared” in “relatively” layman’s terms: “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 X-rays or whatever—and electromagnetic radiation travels at a constant speed of roughly 670,000,000 miles per hour.

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 captured within a walnut or any other chunk of matter. And because the speed of light squared is a huge number—448,900,000,000,000,000 in units of mph—the amount of energy bound up into even the smallest mass is truly mind-boggling.”

Einstein’s equation has helped us to understand the most basic processes in nature and in the development of many of today’s technologies including: PET scans, radiocarbon dating, space technologies, and nuclear energy.

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