So Much Energy in the Air

It does not happen often that you get such an epiphany from an op-ed article. Sept. 27 was “E=mc² day” — the 100th anniversary of the publication of the most famous equation in history. On Sept. 30, the New York Times ran an article by Brian Greene describing the meaning of Einstein’s equation in everyday life. The string theorist and NOVA showman, author of the Elegant Universe book and documentary, was able to say something truly surprising — at least to me.

Sure, most of us have heard — and some of us have studied in physics classes — what the equation says: that energy can be converted into matter and matter into energy, as in the atomic bomb, and all that. And some of us have also learned more about Einstein’s 1905 theory of special relativity — namely, that an object’s mass is relative: stuff that travels past you appears more massive than when it is at rest. These counterintuitive effects of speed on mass are negligible for, say, rain drops falling on your head, but they become very substantial as an object’s speed approaches the speed of light. That much is known and seen every day, with astonishing precision, by physicists, for example using atom smashers (see my brief article in Symmetry magazine).

But, Greene claimed, there’s more to E=mc2 than that. “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,” he wrote.

Whatever you do, from driving your car to listening to your MP3 player, you are converting mass into energy according to E=mc². This was already starting to sound dubious to me. But then, Greene went on to something even weirder: “Experiments have shown that the subatomic particles making up matter have almost no mass of their own. But because of their motions and interactions inside of atoms, these particles contain substantial energy — and it’s this energy that gives matter its heft. Take away Einstein’s equation, and matter loses its mass.”

“What?,” I thought to myself somewhat presumptuously. Greene must be losing it.

The op-ed sparked lively lunchtime discussions among my colleagues and me at AIP and APS. Some of the most profound consequences of special relativity It turned out, of course, that I was wrong and Greene was right, and I learned that there was a lot more to special relativity that I thought.

It turns out that any form of energy stored in a system, whether it’s the chemical energy in gasoline or the electric energy in batteries, counts as mass, according to E=mc². And the quarks and electrons that form the atoms in your body really are very light. Most of the mass of atoms comes from the energy stored in them in the form of bonds between the particles in the nucleus and (to a lesser extent) the electrical bond between the nucleus and the electrons.

Steve Blau of Physics Today finally clarified this to me over lunch with an enlightening example. Think of two weights connected by a spring. Then compress the spring until the two weights are next to each other, and connect them with a string to keep the spring compressed. By doing so, you have added energy to the system, energy which is stored in the spring. Now cut the string and watch the two weights fly off in opposite directions. If you measure each of the weights’ masses now, you will find them slightly heavier than before, due to the speed they gained. Yet the total mass of the system hasn’t changed. The additional mass came from the compressed spring, which was a little heavier when it stored energy. Note that there was no matter converted into energy in the sense of what happens when matter and antimatter annihilate.

The same thought experiment can be done with two weights put next to each other with some dynamite in between. Setting off the explosive will make the weights heavier by giving them speed, and that additional mass must have come from somewhere — in this case, from the chemical energy stored in the dynamite.

Every single atom in our bodies contains the equivalent of several loaded springs. Fortunately, the strings that keep them tight are stronger, preventing each one of us from turning into a supernova.

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THE EINSTEIN YEAR

So Much Energy in the Air

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