Once Before Time - Martin Bojowald [22]
In addition, one has to fight with the peculiarities of quantum theory: for instance, the abrupt change of the state of a system even as it is being measured, and the impossibility of complete knowledge as a result of fundamental uncertainty. The wave function, describing all the information contained in a quantum system, must brutally collapse during a measurement, condemned by the uncertainty principle to an incomplete confession. But it is worthwhile to accept this challenge, for quantum theory does have welcome consequences, too—in particular, concerning singularities.
ATOMIC STABILITY:
THE PRICE OF LIVING LONG
Conceptually, if not historically, the beginning of quantum theory is marked by a stability problem not unlike that of gravitational situations. A hydrogen atom consists of a positively charged proton as the nucleus and a negatively charged electron in orbit. An electron’s mass is only about half a thousandth as much as the proton, suggesting the classical picture of a light electron orbiting around a heavy proton. By electric attraction, the electron is forced to move in a circular manner, just as gravity compels the moon to circle the earth. The radius of the electron’s orbit may be seen as the radius of a hydrogen atom, and has a size of about 50-billionth of a millimeter.
This picture has a serious problem. According to Maxwell’s theory of electromagnetism, an electric charge moving along a trajectory that is not a straight line must radiate waves. As a general phenomenon, this is similar to the emission of gravitational waves in a double pulsar, whose radius shrinks in time as a result of the energy loss; as described in the preceding chapter, measuring consequences of the energy loss has allowed impressive tests of general relativity. In the case of electromagnetic radiation by moving charges such as the electron, the analogous phenomenon is much more common; it is often exploited, for instance when generating X-rays or cell phone signals.
The emission of waves also means that the electron loses energy through its motion, can no longer resist the electric attraction, and thus approaches the proton. Energy lost is sent out by the atom as visible light or in the form of invisible electromagnetic waves. Maxwell’s equations can be used to compute the amount of energy loss, showing that the emission must proceed much faster than that of gravitational waves by a double pulsar: A bound electron would lose all its energy after just a fraction of a second and then collide with the proton. In contrast to the slow shrinking of a double pulsar, this behavior is in disastrous conflict with the observation that hydrogen atoms exist stably for extremely long times. The classical picture fails miserably—not only for hydrogen but for all atoms. Matter, if it obeyed classical laws, could not be stable, because its constituent atoms could not exist even for a second. This problem may not be as damning as that of singularities in general relativity, where even space and time would reach their limits and literally nothing could survive. On the other hand, the problem of atomic stability is more concrete; we would, after all, be affected by instabilities of matter in a very personal way.
Quantum theory resolves the stability problem of atoms in an elegant, but unfortunately quite counterintuitive, manner. To see how this can happen, we first have to shed some light on the general principles of quantum theory.
THE WAVE FUNCTION: FLUCTUATIONS, SUPERPOSITIONS, LIMITATIONS
Now that Yossarian looked back, it seemed that Nurse Cramer, rather than the talkative Texan, had murdered the soldier in white; if she had not read the thermometer and reported what she had found, the soldier in white might still be lying there alive exactly as he had been lying there all along, encased from head to toe in plaster and gauze.…
—JOSEPH HELLER, Catch-22
Quantum theory implies that protons,