Warped Passages - Lisa Randall [59]
The Beginning of Quantum Mechanics
Quantum physics developed in stages. It began as a series of random assumptions that matched observations, although no one understood why they matched. These inspired guesses, which had no underlying physical justification but did have the virtue of giving the right answers, were embodied in what is now known as the old quantum theory. This theory was defined by the assumption that quantities such as energy and momentum couldn’t have just any arbitrary values. Instead, the possibilities were confined to a discrete, quantized set of numbers.
Quantum mechanics, which developed from the humble antecedent of the old quantum theory, justifies the mysterious quantization assumptions that we’ll shortly encounter. Furthermore, quantum mechanics provides a definite procedure for predicting how quantum mechanical systems evolve with time, greatly increasing the theory’s power. But at the outset quantum mechanics developed only in fits and starts, since no one at the time really understood what was going on. At first, the quantization assumptions were all there were.
The old quantum theory began in 1900, when the German physicist Max Planck suggested that light could be delivered only in quantized units, just as bricks can only be sold in discrete chunks. According to Planck’s hypothesis, the amount of energy contained in light of any specific frequency could only be a multiple of the fundamental energy unit for that particular frequency. That fundamental unit is equal to a quantity, now known as Planck’s constant, h, multiplied by the frequency, f. The energy of light with a definite frequency f could be hf, 2 hf, 3 hf, and so on, but according to Planck’s assumption you could never find anything in between. Unlike bricks, whose quantization is arbitrary and nonfundamental—bricks can be split apart—there is a minimum energy unit of light of a given frequency which is indivisible. Intermediate values of energy could never occur.
This remarkably prescient suggestion was made to address a theoretical puzzle known as the blackbody ultraviolet* catastrophe. A blackbody is an object, such as a piece of coal, that absorbs all incoming radiation and then radiates it back.† The amount of light and other energy it emits depends on its temperature; temperature completely characterizes a blackbody’s physical properties.
However, the classical predictions for the light radiated from a blackbody were problematic: classical calculations predicted that far greater energy would be emitted in high-frequency radiation than physicists had seen and recorded. Measurements showed that different frequencies do not contribute democratically to blackbody radiation; the very high frequencies contribute less than the lower ones. Only the lower frequencies emit significant energy. This is why radiating objects are “red-hot” and not “blue-hot.” But classical physics predicted a large amount of high-frequency radiation. In fact, the total emitted energy predicted by classical reasoning was infinite. Classical physics faced an ultraviolet catastrophe.
An ad hoc way out of this dilemma would have been to assume that only frequencies below some specific upper limit could contribute to radiation from a blackbody. Planck disregarded this possibility in favor of another, apparently equally arbitrary, assumption: that light is quantized.
Planck reasoned that if radiation at each frequency consisted of whole-unit multiples of a fundamental quantum of radiation, then no high-frequency radiation could be emitted because the fundamental unit of energy would be too large. Because the energy contained in a quantum unit of light was proportional to frequency, even a single unit of high-frequency radiation would contain a large amount of energy. When the frequency was high enough, the minimum energy a quantum would contain would be too large for it to be radiated. The blackbody could radiate only the lower-frequency quanta. Planck’s hypothesis