Zero - Charles Seife [62]
The so-called Rayleigh-Jeans law, named after the physicists Lord Rayleigh and Sir James Jeans, worked fairly well. It did a good job of predicting the amount of large-wavelength, low-energy light that comes off a hot object. At high energies, though, the equation faltered. The Rayleigh-Jeans law predicted that an object gives off more and more light at smaller and smaller wavelengths (and thus higher and higher energies). Consequently at realms close to zero wavelength, the object gives off an infinite amount of high-energy light. According to the Rayleigh-Jeans equation, every object is constantly radiating an infinite amount of energy, no matter what its temperature is; even an ice cube would be radiating enough ultraviolet rays, x rays, and gamma rays to vaporize everything around. This was the “ultraviolet catastrophe.” Zero wavelength equals infinite energy; zero and infinity conspired to break a nice, neat system of laws. Solving this paradox quickly became the leading puzzle in physics.
Rayleigh and Jeans had done nothing wrong. They used equations that physicists thought were valid, manipulated them in an accepted way, and came out with an answer that didn’t reflect the way the world works. Ice cubes don’t wipe out civilizations with bursts of gamma rays, though following the then-accepted rules of physics led inexorably to that conclusion. One of the laws of physics had to be wrong. But which one?
The Quantum Zero: Infinite Energy
To physicists, vacuum has all particles and forces latent in it. It’s a far richer substance than the philosopher’s nothing.
—SIR MARTIN REES
The ultraviolet catastrophe led to the quantum revolution. Quantum mechanics got rid of the zero in the classical theory of light—removing the infinite energy that supposedly came from every bit of matter in the universe. However, this was not much of a victory. A zero in quantum mechanics means that the entire universe—including the vacuum—is filled with an infinite amount of energy: the zero-point energy. This, in turn, leads to the most bizarre zero in the universe: the phantom force of nothing.
In 1900, German experimenters tried to shed some light on the ultraviolet catastrophe. By making careful measurements of how much radiation came off objects at various temperatures, they showed that the Rayleigh-Jeans formula was, indeed, failing to predict the true amount of light that comes from objects. A young physicist named Max Planck looked at the new data and within hours came up with a new equation that replaced the Rayleigh-Jeans formula. Not only did Planck’s formula explain the new measurements, it solved the ultraviolet catastrophe. The Planck formula did not zoom off to infinity as the wavelength decreased; instead of having the energy get bigger and bigger as the wavelength goes down, it got smaller and smaller again (Figure 47). Unfortunately, though Planck’s formula was correct, its repercussions were more troubling than the ultraviolet catastrophe it solved.
Figure 47: Rayleigh-Jeans goes off to infinity, but Planck stays finite.
The problem arose because the ordinary assumptions of statistical mechanics—the laws of physics—did not lead Planck to his formula. The laws of physics had to change to accommodate the Planck formula. Planck later described what he did as an “act of desperation”; nothing less than desperation would compel a physicist to make such a seemingly nonsensical change in the laws of physics: According to Planck, molecules are forbidden to move in most ways. They vibrate only with certain acceptable energies, called quanta. It is impossible for molecules