To Explain the World: The Discovery of Modern Science (37 page)

The joy was flawed—it always is. You didn’t have to be a follower of Aristotle to be repelled by the peculiar looping motion of planets moving on epicycles in Ptolemy’s theory. There was also the nasty fine-tuning: it had to take precisely one year for the centers of the epicycles of Mercury and Venus to move around the Earth, and for Mars, Jupiter, and Saturn to move around their epicycles. For over a thousand years philosophers argued about the proper role of astronomers like Ptolemy—really to understand the heavens, or merely to fit the data.

What pleasure Copernicus must then have felt when he was able to explain that the fine-tuning and the looping orbits of Ptolemy’s scheme arose simply because we view the solar system from a moving Earth. Still flawed, the Copernican theory did not quite fit the data without ugly complications. How much then the mathematically gifted Kepler must have enjoyed replacing the Copernican mess with motion on ellipses, obeying his three laws.

So the world acts on us like a teaching machine, reinforcing our good ideas with moments of satisfaction. After centuries we learn what kinds of understanding are possible, and how to find them. We learn not to worry about purpose, because such worries never lead to the sort of delight we seek. We learn to abandon the search for certainty, because the explanations that make us happy never are certain. We learn to do experiments, not worrying about the artificiality of our arrangements. We develop an aesthetic sense that gives us clues to what theories will work, and that adds to our pleasure when they do work. Our understandings accumulate. It is all unplanned and unpredictable, but it leads to reliable knowledge, and gives us joy along the way.

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Epilogue: The Grand Reduction

Newton’s great achievement left plenty yet to be explained. The nature of matter, the properties of forces other than gravitation that act on matter, and the remarkable capabilities of life were all still mysterious. Enormous progress was made in the years after Newton,
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far too much to cover in one book, let alone a single chapter. This epilogue aims at making just one point, that as science progressed after Newton a remarkable picture began to take shape: it turned out that the world is governed by natural laws far simpler and more unified than had been imagined in Newton’s time.

Newton himself in Book III of his
Opticks
sketched the outline of a theory of matter that would at least encompass optics and chemistry:

Now the smallest particles of matter may cohere by the strongest attractions, and compose bigger particles of weaker virtue; and many of these may cohere and compose bigger particles whose virtue is still weaker, and so on for diverse successions, until the progression ends in the biggest particles on which the operations in chemistry, and the colors of natural bodies depend, and which by cohering compose bodies of a sensible magnitude.
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He also focused attention on the forces acting on these particles:

For we must learn from the phenomena of nature what bodies attract one another, and what are the laws and properties of the attraction, before we inquire the cause by which the attraction is perform’d. The attractions of gravity, magnetism, and electricity, reach to very sensible distances, and so have been observed by vulgar eyes, and there may be others which reach to so small distances as to escape observation.
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As this shows, Newton was well aware that there are other forces in nature besides gravitation. Static electricity was an old story. Plato had mentioned in the
Timaeus
that when a piece of amber (in Greek,
electron
) is rubbed it can pick up light bits of matter. Magnetism was known from the properties of naturally magnetic lodestones, used by the Chinese for geomancy and studied in detail by Queen Elizabeth’s physician, William Gilbert. Newton here also hints at the existence of forces not yet known because of their short range, a premonition of the weak and strong nuclear forces discovered in the twentieth century.

In the early nineteenth century the invention of the electric battery by Alessandro Volta made it possible to carry out detailed quantitative experiments in electricity and magnetism, and it soon became known that these are not entirely separate phenomena. First, in 1820 Hans Christian Ørsted in Copenhagen found that a magnet and a wire carrying an electric current exert forces on each other. After hearing of this result, André-Marie Ampère in Paris discovered that wires carrying electric currents also exert forces on one another. Ampère conjectured that these various phenomena are all much the same: the forces exerted by and on pieces of magnetized iron are due to electric currents circulating within the iron.

Just as happened with gravitation, the notion of currents and magnets exerting forces on each other was replaced with the idea of a field, in this case a magnetic field. Each magnet and
current-carrying wire contributes to the total magnetic field at any point in its vicinity, and this magnetic field exerts a force on any magnet or electric current at that point. Michael Faraday attributed the magnetic forces produced by an electric current to lines of magnetic field encircling the wire. He also described the electric forces produced by a piece of rubbed amber as due to an electric field, pictured as lines emanating radially from the electric charges on the amber. Most important, Faraday in the 1830s showed a connection between electric and magnetic fields: a changing magnetic field, like that produced by the electric current in a rotating coil of wire, produces an electric field, which can drive electric currents in another wire. It is this phenomenon that is used to generate electricity in modern power plants.

The final unification of electricity and magnetism was achieved a few decades later, by James Clerk Maxwell. Maxwell thought of electric and magnetic fields as tensions in a pervasive medium, the ether, and expressed what was known about electricity and magnetism in equations relating the fields and their rates of change to each other. The new thing added by Maxwell was that, just as a changing magnetic field generates an electric field, so also a changing electric field generates a magnetic field. As often happens in physics, the conceptual basis for Maxwell’s equations in terms of an ether has been abandoned, but the equations survive, even on T-shirts worn by physics students.
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Maxwell’s theory had a spectacular consequence. Since oscillating electric fields produce oscillating magnetic fields, and oscillating magnetic fields produce oscillating electric fields, it is possible to have a self-sustaining oscillation of both electric and magnetic fields in the ether, or as we would say today, in empty space. Maxwell found around 1862 that this electromagnetic oscillation would propagate at a speed that, according to his
equations, had just about the same numerical value as the measured speed of light. It was natural for Maxwell to jump to the conclusion that light is nothing but a mutually self-sustaining oscillation of electric and magnetic fields. Visible light has a frequency far too high for it to be produced by currents in ordinary electric circuits, but in the 1880s Heinrich Hertz was able to generate waves in accordance with Maxwell’s equations: radio waves that differed from visible light only in having much lower frequency. Electricity and magnetism had thus been unified not only with each other, but also with optics.

As with electricity and magnetism, progress in understanding the nature of matter began with quantitative measurement, here measurement of the weights of substances participating in chemical reactions. The key figure in this chemical revolution was a wealthy Frenchman, Antoine Lavoisier. In the late eighteenth century he identified hydrogen and oxygen as elements and showed that water is a compound of hydrogen and oxygen, that air is a mixture of elements, and that fire is due to the combination of other elements with oxygen. Also on the basis of such measurements, it was found a little later by John Dalton that the weights with which elements combine in chemical reactions can be understood on the hypothesis that pure chemical compounds like water or salt consist of large numbers of particles (later called molecules) that themselves consist of definite numbers of atoms of pure elements. The water molecule, for instance, consists of two hydrogen atoms and one oxygen atom. In the following decades chemists identified many elements: some familiar, like carbon, sulfur, and the common metals; and others newly isolated, such as chlorine, calcium, and sodium. Earth, air, fire, and water did not make the list. The correct chemical formulas for molecules like water and salt were worked out, in the first half of the nineteenth century, allowing the calculation of the ratios of the masses of the atoms of the different elements from measurements of the weights of substances participating in chemical reactions.

The atomic theory of matter scored a great success when Maxwell and Ludwig Boltzmann showed how heat could be
understood as energy distributed among vast numbers of atoms or molecules. This step toward unification was resisted by some physicists, including Pierre Duhem, who doubted the existence of atoms and held that the theory of heat, thermodynamics, was at least as fundamental as Newton’s mechanics and Maxwell’s electrodynamics. But soon after the beginning of the twentieth century several new experiments convinced almost everyone that atoms are real. One series of experiments, by J. J. Thomson, Robert Millikan, and others, showed that electric charges are gained and lost only as multiples of a fundamental charge: the charge of the electron, a particle that had been discovered by Thomson in 1897. The random “Brownian” motion of small particles on the surface of liquids was interpreted by Albert Einstein in 1905 as due to collisions of these particles with individual molecules of the liquid, an interpretation confirmed by experiments of Jean Perrin. Responding to the experiments of Thomson and Perrin, the chemist Wilhelm Ostwald, who earlier had been skeptical about atoms, expressed his change of mind in 1908, in a statement that implicitly looked all the way back to Democritus and Leucippus: “I am now convinced that we have recently become possessed of experimental evidence of the discrete or grained nature of matter, which the atomic hypothesis sought in vain for hundreds and thousands of years.”
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But what are atoms? A great step toward the answer was taken in 1911, when experiments in the Manchester laboratory of Ernest Rutherford showed that the mass of gold atoms is concentrated in a small heavy positively charged nucleus, around which revolve lighter negatively charged electrons. The electrons are responsible for the phenomena of ordinary chemistry, while changes in the nucleus release the large energies encountered in radioactivity.

This raised a new question: what keeps the orbiting atomic electrons from losing energy through the emission of radiation, and spiraling down into the nucleus? Not only would this rule out the existence of stable atoms; the frequencies of the radiation
emitted in these little atomic catastrophes would form a continuum, in contradiction with the observation that atoms can emit and absorb radiation only at certain discrete frequencies, seen as bright or dark lines in the spectra of gases. What determines these special frequencies?

The answers were worked out in the first three decades of the twentieth century with the development of quantum mechanics, the most radical innovation in physical theory since the work of Newton. As its name suggests, quantum mechanics requires a quantization (that is, a discreteness) of the energies of various physical systems. Niels Bohr in 1913 proposed that an atom can exist only in states of certain definite energies, and gave rules for calculating these energies in the simplest atoms. Following earlier work of Max Planck, Einstein had already in 1905 suggested that the energy in light comes in quanta, particles later called photons, each photon with an energy proportional to the frequency of the light. As Bohr explained, when an atom loses energy by emitting a single photon, the energy of that photon must equal the difference in the energies of the initial and final atomic states, a requirement that fixes its frequency. There is always an atomic state of lowest energy, which cannot emit radiation and is therefore stable.

These early steps were followed in the 1920s with the development of general rules of quantum mechanics, rules that can be applied to any physical system. This was chiefly the work of Louis de Broglie, Werner Heisenberg, Wolfgang Pauli, Pascual Jordan, Erwin Schrödinger, Paul Dirac, and Max Born. The energies of allowed atomic states are calculated by solving an equation, the Schrödinger equation, of a general mathematical type that was already familiar from the study of sound and light waves. A string on a musical instrument can produce just those tones for which a whole number of half wavelengths fit on the string; analogously, Schrödinger found that the allowed energy levels of an atom are those for which the wave governed by the Schrödinger equation just fits around the atom without discontinuities. But as
first recognized by Born, these waves are not waves of pressure or of electromagnetic fields, but waves of probability—a particle is most likely to be near where the wave function is largest.

Quantum mechanics not only solved the problem of the stability of atoms and the nature of spectral lines; it also brought chemistry into the framework of physics. With the electrical forces among electrons and atomic nuclei already known, the Schrödinger equation could be applied to molecules as well as to atoms, and allowed the calculation of the energies of their various states. In this way it became possible in principle to decide which molecules are stable and which chemical reactions are energetically allowed. In 1929 Dirac announced triumphantly that “the underlying physical laws necessary for the mathematical theory of a larger part of physics and the whole of chemistry are thus completely known.”
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