Why Beauty is Truth (45 page)

Mind you, he also said, “I can state flatly that heavier than air flying machines are impossible,” and “Landing on the moon offers so many serious problems for human beings that it may take science another 200 years to lick them.” Kelvin's biographer wrote that he spent the first half of his career being right and the second half being wrong.

But he wasn't totally wrong. In his 1900 lecture “Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light,” he put his finger on two crucial gaps in the period's understanding of the physical universe: “The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds. The first involves the question, How could the Earth move through an elastic solid, such as essentially is the luminiferous ether? The second is the Maxwell–Boltzmann doctrine regarding the partition of energy.” The first cloud led to relativity, the second to quantum theory.

Fortunately, the young recipient of Jolly's advice was not daunted. He had no wish to discover
new
things, he said—all he wanted was to develop a better understanding of the known fundamentals of physics. In the
search for this understanding, he brought about one of the two great revolutions in twentieth-century physics, and dispelled Kelvin's second cloud. His name was Max Planck.

Julius Wilhelm Planck was a professor of law in Kiel and Munich. His father and his mother had both been theology professors, and his brother was a judge. So when his second wife, Emma Patzig, presented Julius with a son—his sixth child—the boy was certain to grow up in an intellectual environment. Max Karl Ernst Ludwig Planck was born on 23 April 1858. Europe was in the usual political turmoil, and the boy's earliest memories included Prussian and Austrian troops marching into Kiel during the Danish–Prussian War of 1864.

By 1867 the Plancks had moved to Munich, and Max was being tutored by the mathematician Hermann Müller at the King Maximilian School. Müller taught the boy astronomy, mechanics, mathematics, and some basic physics, including the law of conservation of energy. Planck was an excellent student, and he graduated unusually early, at the age of sixteen.

He was also a talented musician, but he decided to study physics despite Jolly's well-intentioned advice. Planck carried out some experiments under Jolly's supervision but quickly switched to theoretical physics. He kept company with some of the world's leading physicists and mathematicians, moving to Berlin in 1877 to study under Helmholtz, Gustav Kirchhoff, and Weierstrass. He passed his first examinations in 1878 and obtained a doctorate in 1879 with a thesis on thermodynamics. For a time he taught mathematics and physics at his old school. In 1880, his habilitation thesis, on equilibrium states of bodies at different temperatures, was accepted, and he was qualified for a permanent academic career. He duly secured such a position, but not until 1885, when the University of Kiel made him an associate professor. His research focused on thermodynamics, especially the concept of entropy.

Max met Marie Merck, the sister of a friend, and in 1887 they married and rented an apartment. In all, they had four children: Karl, twins Emma and Grete, and Erwin.

In 1889, the year the twins were born, Max was appointed to Kirchhoff's position in Berlin, becoming a full professor in 1892. The family moved to a villa in the Grunewald region of Berlin, close to a number of other leading academics. One, the theologian Adolf von Harnack, became
a close friend. The Plancks were sociable, and famous intellectuals visited their house regularly. These included Einstein and the physicists Otto Hahn and Lise Meitner, who later made fundamental discoveries about nuclear fission, part of the long development leading to the atomic bomb and nuclear power stations. At these events the Plancks continued a tradition of playing music, started by Helmholtz.

For a time life was rosy, but Marie contracted a lung disease, possibly tuberculosis, and died in 1909. A year and a half later, at 52, Max remarried, this time to Marga von Hoesslin, with whom he had a third son, Hermann.

In 1894, a local electrical company was trying to develop a more efficient light bulb, so Max started some industrial contract research. Theoretically, the analysis of a light bulb was a standard physics problem known as “blackbody radiation”—how light would be emitted by a perfectly nonreflective body. Such a body, when heated, emits light of all frequencies, but the intensity of the light, or equivalently its energy, varies with the frequency. A fundamental question was, how does the frequency affect the intensity? Without such basic data, it would be difficult to invent a better light bulb.

There were good experimental results, and one theoretical law, the Rayleigh–Jeans law, had been derived from basic principles of classical physics. Unfortunately, this law disagreed with experiment at high frequencies. In fact, it predicted something impossible: as the light's frequency increases, its energy should become infinitely large. This impossible result became known as the “ultraviolet catastrophe.” Further experiments led to a new law, which fitted the observations for high-frequency radiation, known as Wien's law after its discoverer, Wilhelm Wien.

However, Wien's law went wrong for
low
-frequency radiation.

Physicists were faced with two laws: one working at low frequencies but not at high ones, the other doing the exact opposite. Planck hit on the idea of interpolating between the two: that is, writing down a mathematical expression that approximated the Rayleigh–Jeans law at low frequencies and Wien's law at high frequencies. The resulting formula is now called the Planck law for blackbody radiation.

This new law was deliberately designed to match experiments beautifully, across the entire spectrum of electromagnetic radiation, but it was purely empirical—derived from experiments, not from any basic physical
principle. Planck, pursuing his avowed intention to understand known physics better, was dissatisfied, and he devoted much effort searching for physical principles that would lead to his formula.

Eventually, in 1900, Planck noticed a curious feature of his formula. He could derive it by much the same calculation that Rayleigh and Jeans had employed, provided he made one tiny change. The classical derivation had assumed that for any given frequency, the energy of electromagnetic radiation could in principle take any value whatsoever. In particular, it could get as close to zero as you wished. Planck realized that this assumption was the cause of the ultraviolet catastrophe, and that if he made a different assumption, that troublesome infinity disappeared from the calculation.

The assumption, though, was radical. The energy of radiation of a given frequency had to come as a whole number of “packets” of fixed size. In fact, the size of each packet had to be proportional to the frequency—that is, equal to the frequency multiplied by some constant, which we now call Planck's constant and write using the symbol
h.

These energy packets were called
quanta
(singular:
quantum
). Planck had quantized light.

All very well, but why had experimentalists never noticed that the energy was always a whole number of quanta? By comparing his calculations with the observed energies, Planck was able to calculate the size of his constant, and it turned out to be very, very small. In fact,
h
is roughly 6 × 10
^–34
joule-seconds. Roughly speaking, to notice the “gaps” in the possible range of energies—the values that classical physics permitted but quantum physics did not—you had to make observations that were accurate to the 34th decimal place. Even today, very few physical quantities can be measured to more than six or seven decimal places, and in those days three was asking a lot. Direct observation of quanta required absurd levels of accuracy.

It may seem strange that a mathematical difference so tiny that it can never be seen could have such a huge effect on the radiation law. But the calculation of the law involves adding up all the contributions to the energy from all possible frequencies. The result is a collective effect of all possible quanta. From the Moon you can't spot an individual grain of sand on Earth. But you can see the Sahara. If sufficiently many very tiny units combine, the result can be huge.

Planck's physics thrived, but his personal life was filled with tragedy. His son Karl was killed in action during the First World War. His daughter Grete died in childbirth in 1917, and Emma suffered the same fate in 1919, having married Grete's widower. Much later, Erwin was executed by the Nazis for taking part in the unsuccessful 1944 attempt to assassinate Adolf Hitler.

By 1905, new evidence had turned up that supported Planck's radical proposal, in the form of Einstein's work on the photoelectric effect. Recall that this is the discovery that light can be converted into electricity. Einstein was aware that electricity comes in discrete packages. Indeed, by then physicists knew that electricity is the motion of tiny particles called electrons. From the photoelectric effect, Einstein deduced that the same must be true of light. This not only verified Planck's ideas about light quanta, it explained what the quanta are: light waves, like electrons, must be particles.

How can a wave be a particle? Yet that was the unequivocal message of the experiments. The discovery of particles of light, or photons, quickly led to the quantum picture of the world in which particles are really waves, behaving sometimes like one, sometimes like the other.

The physics community started to take quanta more seriously. The great Danish physicist Niels Bohr came up with a quantized model of the atom, in which electrons move in circular orbits around a central nucleus, with the size of the circle being limited to discrete quanta. The French physicist Louis de Broglie reasoned that since photons can be both waves and particles, and electrons are emitted by suitable metals when they are impacted by photons, then electrons must
also
be both waves and particles. Indeed, all matter must possess this dual existence—sometimes solid particle, sometimes undulating wave. That's why experiments can indicate either form.

Neither “particle” nor “wave” really describes matter at extremely tiny scales. The ultimate constituents of matter are a bit of both—
wavicles.
De Broglie invented a formula to describe wavicles.

Now came a key step, essential to our story. Erwin Schrödinger took de Broglie's formula and turned it into an equation that describes how wavicles move. Just as Newton's laws of motion were fundamental to
classical mechanics, Schrödinger's equation became fundamental to quantum mechanics.