Zero - Charles Seife [65]
This argument holds everywhere in the universe—in the center of the earth and in the deepest vacuum of space. This means that in a sufficiently small volume, even in a vacuum, we have some uncertainty about the amount of energy inside. But uncertainty about the energy in a vacuum sounds ridiculous. The vacuum, by definition, has nothing in it—no particles, no light, nothing. Thus, the vacuum should have no energy at all. Yet according to Heisenberg’s principle, we cannot know how much energy there is in a volume of the vacuum at any given time. The energy in a tiny volume of vacuum must be fluctuating constantly.
How could the vacuum, which has nothing in it, have any energy at all? The answer comes from another equation: Einstein’s famous E = mc2. This simple formula relates mass and energy: the mass of an object is equivalent to a certain amount of energy. (In fact, particle physicists don’t measure the mass of the electron, say, in kilograms or pounds or any of the usual units of mass or weight. They say that the electron’s rest mass is 0.511 MeV [million electron volts]—a lump of energy.) The fluctuation in the energy in the vacuum is the same thing as a fluctuation in the amount of mass. Particles are constantly winking in and out of existence, like tiny Cheshire cats. The vacuum is never truly empty. Instead, it is seething with these virtual particles; at every point in space, an infinite number are happily popping up and disappearing. This is the zero-point energy, an infinity in the formulas of quantum theory. Interpreted strictly, the zero-point energy is limitless. According to the equations of quantum mechanics, more power than is stored in all the coal mines, oil fields, and nuclear weapons in the world is sitting in the space inside your toaster.
When an equation has an infinity in it, physicists usually assume that there is something wrong; the infinity has no physical meaning. The zero-point energy is no different; most scientists ignore it completely. They simply pretend that the zero-point energy is zero, even though they know it is infinite. It’s a convenient fiction, and it usually doesn’t matter. However, sometimes it does. In 1948 two Dutch physicists, Hendrick B. G. Casimir and Dik Polder, first realized that the zero-point energy can’t always be ignored. The two scientists were studying the forces between atoms when they realized that their measurements didn’t match the forces that had been predicted. In a search for an explanation, Casimir realized that he had felt the force of nothing.
The secret to the Casimir force lies with the nature of waves. In ancient Greece, Pythagoras saw the peculiar behavior of waves that traveled up and down a plucked string—how certain notes were allowed and others were forbidden. When Pythagoras strummed a string, the string sounded a clear note, the tone known as the fundamental. When he gently placed his finger in the middle of the string and plucked again, he got another nice, clear note, this time one octave above the fundamental. One-third of the way down yielded another nice tone. But Pythagoras realized that not all notes are allowed. When he placed his finger randomly on the string, he seldom got a clear note. Only certain notes can be played on the