To Explain the World: The Discovery of Modern Science

by Steven Weinberg

Science is not now what it was at its start. Its results are impersonal. Inspiration and aesthetic judgment are important in the development of scientific theories, but the verification of these theories relies finally on impartial experimental tests of their predictions.

Aristotle called the earlier Greek philosophers physiologi, and this is sometimes translated as “physicists,”14 but that is misleading. The word physiologi simply means students of nature (physis), and the early Greeks had very little in common with today’s physicists. Their theories had no bite. Empedocles could speculate about the elements, and Democritus about atoms, but their speculations led to no new information about nature—and certainly to nothing that would allow their theories to be tested.

There is a narrow sense of poetry, as language that uses verbal devices like meter, rhyme, or alliteration. Even in this narrow sense, Xenophanes, Parmenides, and Empedocles all wrote in poetry. After the Dorian invasions and the breakup of the Bronze Age Mycenaean civilization in the twelfth century BC, the Greeks had become largely illiterate. Without writing, poetry is almost the only way that people can communicate to later generations, because poetry can be remembered in a way that prose cannot. Literacy revived among the Greeks sometime around 700 BC, but the new alphabet borrowed from the Phoenicians was first used by Homer and Hesiod to write poetry, some of it the long-remembered poetry of the Greek dark ages. Prose came later.

There remains a poetic element in modern physics. We do not write in poetry; much of the writing of physicists barely reaches the level of prose. But we seek beauty in our theories, and use aesthetic judgments as a guide in our research. Some of us think that this works because we have been trained by centuries of success and failure in physics research to anticipate certain aspects of the laws of nature, and through this experience we have come to feel that these features of nature’s laws are beautiful.17 But we do not take the beauty of a theory as convincing evidence of its truth.

For example, string theory, which describes the different species of elementary particles as various modes of vibration of tiny strings, is very beautiful. It appears to be just barely consistent mathematically, so that its structure is not arbitrary, but largely fixed by the requirement of mathematical consistency. Thus it has the beauty of a rigid art form—a sonnet or a sonata. Unfortunately, string theory has not yet led to any predictions that can be tested experimentally, and as a result theorists (at least most of us) are keeping an open mind as to whether the theory actually applies to the real world. It is this insistence on verification that we most miss in all the poetic students of nature, from Thales to Plato.

After Philip’s death in 336 BC Aristotle returned to Athens, where he founded his own school, the Lyceum. This was one of the four great schools of Athens, the others being Plato’s Academy, the Garden of Epicurus, and the Colonnade (or Stoa) of the Stoics. The Lyceum continued for centuries, probably until it was closed in the sack of Athens by Roman soldiers under Sulla in 86 BC. It was outlasted, though, by Plato’s Academy, which continued in one form or another until AD 529, enduring longer than any European university has lasted so far.

One of Aristotle’s classifications was pervasive in his work, and became an obstacle for the future of science. He insisted on the distinction between the natural and the artificial. He begins Book II of Physics4 with “Of things that exist, some exist by nature, some from other causes.” It was only the natural that was worthy of his attention. Perhaps it was this distinction between the natural and the artificial that kept Aristotle and his followers from being interested in experimentation. What is the good of creating an artificial situation when what are really interesting are natural phenomena?

(Aristotle distinguished four kinds of cause: material, formal, efficient, and final, of which the final cause is teleological—it is the purpose of the change.)

No one in the history of philosophy has been as influential as Aristotle. As we will see in Chapter 9, he was greatly admired by some Arab philosophers, even slavishly so by Averroes. Chapter 10 tells how Aristotle became influential in Christian Europe in the 1200s, when his thought was reconciled with Christianity by Thomas Aquinas. In the high Middle Ages Aristotle was known simply as “The Philosopher,” and Averroes as “The Commentator.” After Aquinas the study of Aristotle became the center of university education.

The progress of science has been largely a matter of discovering what questions should be asked.

I agree with Lindberg that it would be unfair to conclude that Aristotle was stupid. My purpose here in judging the past by the standards of the present is to come to an understanding of how difficult it was for even very intelligent persons like Aristotle to learn how to learn about nature. Nothing about the practice of modern science is obvious to someone who has never seen it done.

The intellectual relations between Egypt and the Greek homeland in Hellenistic times were something like the connections between America and Europe in the twentieth century.

The sailing time between Athens and Alexandria during the Hellenistic and Roman periods was similar to the time it took for a steamship to go between Liverpool and New York in the twentieth century, and there was a great deal of coming and going between Egypt and Greece. For instance, Strato did not stay in Egypt; he returned to Athens to become the third director of the Lyceum.

But there were great differences in the intellectual climates of Alexandria and Athens. For one thing, the scholars of the Museum generally did not pursue the kind of all-embracing theories that had preoccupied the Greeks from Thales to Aristotle. As Floris Cohen has remarked,4 “Athenian thought was comprehensive, Alexandrian piecemeal.” The Alexandrians concentrated on understanding specific phenomena, where real progress could be made. These topics included optics and hydrostatics, and above all astronomy, the subject of Part II.

Again and again, it has been an essential feature of scientific progress to understand which problems are ripe for study and which are not. For instance, leading physicists at the turn of the twentieth century, including Hendrik Lorentz and Max Abraham, devoted themselves to understanding the structure of the recently discovered electron. It was hopeless; no one could have made progress in understanding the nature of the electron before the advent of quantum mechanics some two decades later.

As a physicist whose research is on subjects like elementary particles and cosmology that have no immediate practical application, I am certainly not going to say anything against knowledge for its own sake, but doing scientific research to fill human needs has a wonderful way of forcing the scientist to stop versifying and to confront reality.5

Formulas like E = mc2 and F = ma are at the heart of modern physics. (Formulas were used in purely mathematical work by Diophantus, who flourished in Alexandria around AD 250, but the symbols in his equations were restricted to standing for whole or rational numbers, quite unlike the symbols in the formulas of physics.)

It was essential for the discovery of science that religious ideas be divorced from the study of nature. This divorce took many centuries, not being largely complete in physical science until the eighteenth century, nor in biology even then.

As we will see, the Moon and planets also travel through the zodiac, though not on precisely the same paths. The particular path through these constellations followed by the Sun is known as the “ecliptic.” Once the zodiac was understood, it was easy to locate the Sun in the background of stars. Just notice what constellation of the zodiac is highest in the sky at midnight; the Sun is in the constellation of the zodiac that is directly opposite. Thales is supposed to have given 365 days as the time it takes for the Sun to make one complete circuit of the zodiac.

One of the most remarkable achievements of Greek astronomy was the measurement of the sizes of the Earth, Sun, and Moon, and the distances of the Sun and Moon from the Earth. It is not that the results obtained were numerically accurate. The observations on which these calculations were based were too crude to yield accurate sizes and distances. But for the first time mathematics was being correctly used to draw quantitative conclusions about the nature of the world.

It is easy to see why the idea of the Earth’s motion did not take hold in the ancient world. We do not feel this motion, and no one before the fourteenth century understood that there is no reason why we should feel it.

Much of the story of the emergence of modern science deals with the effort, extending over two millennia, to explain the peculiar motions of the planets.

The complications of epicycles, equants, and eccentrics have given Ptolemaic astronomy a bad name. But it should not be thought that Ptolemy was stubbornly introducing these complications in order to make up for the mistake of taking the Earth as the unmoving center of the solar system. The complications, beyond just a single epicycle for each planet (and none for the Sun), had nothing to do with whether the Earth goes around the Sun or the Sun around the Earth. They were made necessary by the fact, not understood until Kepler’s time, that the orbits are not circles, the Sun is not at the center of the orbits, and the velocities are not constant.

For fifteen hundred years the debate continued between the defenders of Aristotle, often called physicists or philosophers, and the supporters of Ptolemy, generally referred to as astronomers or mathematicians. The Aristotelians often acknowledged that the model of Ptolemy fitted the data better, but they regarded this as just the sort of thing that might interest mathematicians, not relevant for understanding reality.

Al-Mamun sent a mission to Constantinople that brought back manuscripts in Greek. The delegation probably included the physician Hunayn ibn Ishaq, the greatest of the ninth-century translators, who founded a dynasty of translators, training his son and nephew to carry on the work. Hunayn translated works of Plato and Aristotle, as well as medical texts of Dioscorides, Galen, and Hippocrates. Mathematical works of Euclid, Ptolemy, and others were also translated into Arabic at Baghdad, some through Syriac intermediaries. The historian Philip Hitti has nicely contrasted the state of learning at this time at Baghdad with the illiteracy of Europe in the early Middle Ages: “For while in the East al-Rashid and al-Mamun were delving into Greek and Persian philosophy, their contemporaries in the West, Charlemagne and his lords, were dabbling in the art of writing their names.”

the Roman Empire decayed in the West, Europe outside the realm of Byzantium became poor, rural, and largely illiterate. Where some literacy did survive, it was concentrated in the church, and there only in Latin. In Western Europe in the early Middle Ages virtually no one could read Greek.

Ptolemy in the Almagest had argued that if the Earth rotated, then clouds and thrown objects would be left behind; and as we have seen, Buridan had argued against the Earth’s rotation by reasoning that if the Earth rotated from west to east, then an arrow shot straight upward would be left behind by the Earth’s rotation, contrary to the observation that the arrow seems to fall straight down to the same spot on the Earth’s surface from which it was shot vertically upward. Oresme replied that the Earth’s rotation carries the arrow with it, along with the archer and the air and everything else on the Earth’s surface, thus applying Buridan’s theory of impetus in a way that its author had not understood.

Grosseteste had a great influence on Roger Bacon, who in his intellectual energy and scientific innocence was a true representative of the spirit of his times. After studying at Oxford, Bacon lectured on Aristotle in Paris in the 1240s, went back and forth between Paris and Oxford, and became a Franciscan friar around 1257. Like Plato, he was enthusiastic about mathematics but made little use of it. He wrote extensively on optics and geography, but added nothing important to the earlier work of Greeks and Arabs. To an extent that was remarkable for the time, Bacon was also an optimist about technology: Also cars can be made so that without animals they will move with unbelievable rapidity. . . . Also flying machines can be constructed so that a man sits in the midst of the machine revolving some engine by which artificial wings are made to beat the air like a flying bird.14 Appropriately, Bacon became known as “Doctor Mirabilis.”

This work of Copernicus illustrates another recurrent theme in the history of physical science: a simple and beautiful theory that agrees pretty well with observation is often closer to the truth than a complicated ugly theory that agrees better with observation.

Never entirely emancipated from Platonism, Kepler tried to make sense of the sizes of the orbits, resurrecting his earlier use of regular polyhedrons in Mysterium Cosmographicum. He also played with the Pythagorean idea that the different planetary periods form a sort of musical scale. Like other scientists of the time, Kepler belonged only in part to the new world of science that was just coming into being, and in part also to an older philosophical and poetic tradition.

The work of Copernicus and Kepler made a case for a heliocentric solar system based on mathematical simplicity and coherence, not on its better agreement with observation. As we have seen, the simplest versions of the Copernican and Ptolemaic theories make the same predictions for the apparent motions of the Sun and planets, in pretty good agreement with observation, while the improvements in the Copernican theory introduced by Kepler were the sort that could have been matched by Ptolemy if he had used an equant and eccentric for the Sun as well as for the planets, and if he had added a few more epicycles. The first observational evidence that decisively favored heliocentrism over the old Ptolemaic system was provided by Galileo Galilei.

By November Galileo had improved the magnification of his spyglass to 20 times, and he began to use it for astronomy. With his spyglass, later known as a telescope, Galileo made six astronomical discoveries of historic importance.

Not even Galileo’s experiments with inclined planes illustrate so well the new aggressive style of experimental physics as these experiments on air pressure. No longer were natural philosophers relying on nature to reveal its principles to casual observers. Instead Mother Nature was being treated as a devious adversary, whose secrets had to be wrested from her by the ingenious construction of artificial circumstances.

Descartes and Bacon are only two of the philosophers who over the centuries have tried to prescribe rules for scientific research. It never works. We learn how to do science, not by making rules about how to do science, but from the experience of doing science, driven by desire for the pleasure we get when our methods succeed in explaining something.

Writers about Newton sometimes stress that he was not a modern scientist. The best-known statement along these lines is that of John Maynard Keynes (who had bought some of the Newton papers in the 1936 auction at Sotheby’s): “Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago.”* But Newton was not a talented holdover from a magical past. Neither a magician nor an entirely modern scientist, he crossed the frontier between the natural philosophy of the past and what became modern science. Newton’s achievements, if not his outlook or personal behavior, provided the paradigm that all subsequent science has followed, as it became modern.

Newton carried out two decisive experiments. First, after using a prism to create separate rays of blue and red light, he directed these rays separately into other prisms, and found no further dispersion into different colors. Next, with a clever arrangement of prisms, he managed to recombine all the different colors produced by refraction of white light, and found that when these colors are combined they produce white light.

The dependence of the angle of refraction on color has the unfortunate consequence that the glass lenses in telescopes like those of Galileo, Kepler, and Huygens focus the different colors in white light differently, blurring the images of distant objects. To avoid this chromatic aberration Newton in 1669 invented a telescope in which light is initially focused by a curved mirror rather than by a glass lens. (The light rays are then deflected by a plane mirror out of the telescope to a glass eyepiece, so not all chromatic aberration was eliminated.) With a reflecting telescope only six inches long, he was able to achieve a magnification by 40 times. All major astronomical light-gathering telescopes are now reflecting telescopes, descendants of Newton’s invention.

In his 1678 Treatise on Light, Huygens described light as a wave of disturbance in a medium, the ether, which consists of a vast number of tiny material particles in close proximity. Just as in an ocean wave in deep water it is not the water that moves along the surface of the ocean but the disturbance of the water, so likewise in Huygens’ theory it is the wave of disturbance in the particles of the ether that moves in a ray of light, not the particles themselves. Each disturbed particle acts as a new source of disturbance, which contributes to the total amplitude of the wave. Of course, since the work of James Clerk Maxwell in the nineteenth century we have known that (even apart from quantum effects) Huygens was only half right—light is a wave, but a wave of disturbances in electric and magnetic fields, not a wave of disturbance of material particles. Using this wave theory of light, Huygens was able to derive the result that light in a homogeneous medium (or empty space) behaves as if it travels in straight lines, as it is only along these lines that the waves produced by all the disturbed particles add up constructively. He gave a new derivation of the equal-angles rule for reflection, and of Snell’s law for refraction, without Fermat’s a priori assumption that light rays take the path of least time.

Copernicus had placed the Earth among the planets, Tycho had shown that there is change in the heavens, and Galileo had seen that the Moon’s surface is rough, like the Earth’s, but none of this related the motion of planets to forces that could be observed on Earth. Descartes had tried to understand the motions of the solar system as the result of vortices in the ether, not unlike vortices in a pool of water on Earth, but his theory had no success. Now Newton had shown that the force that keeps the Moon in its orbit around the Earth and the planets in their orbits around the Sun is the same as the force of gravity that causes an apple to fall to the ground in Lincolnshire, all governed by the same quantitative laws. After this the distinction between the celestial and terrestrial, which had constrained physical speculation from Aristotle on, had to be forever abandoned. But this was still far short of a principle of universal gravitation, which would assert that every body in the universe, not just the Earth and Sun, attracts every other body with a force that decreases as the inverse square of the distance between them.

There is a remarkable scholium at the end of Section I of Book I, in which Newton remarks that he is no longer relying on the notion of infinitesimals. He explains that “fluxions” such as velocities are not the ratios of infinitesimals, as he had earlier described them; instead, “Those ultimate ratios with which quantities vanish are not actually ratios of ultimate quantities, but limits which the ratios of quantities decreasing without limit are continually approaching, and which they can approach so closely that their difference is less than any given quantity.” This is essentially the modern idea of a limit, on which calculus is now based. What is not modern about the Principia is Newton’s idea that limits have to be studied using the methods of geometry.

In Proposition 19 Newton notes that the planets must all be oblate, because their rotation produces centrifugal forces that are largest at the equator and vanish at the poles. For instance, the Earth’s rotation produces a centripetal acceleration at its equator equal to 0.11 feet/second per second, as compared with the acceleration 32 feet/second per second of falling bodies, so the centrifugal force produced by the Earth’s rotation is much less than its gravitational attraction, but not entirely negligible, and the Earth is therefore nearly spherical, but slightly oblate. Observations in the 1740s finally showed that the same pendulum will swing more slowly near the equator than at higher latitudes, just as would be expected if at the equator the pendulum is farther from the center of the Earth, because the Earth is oblate.

Though unfair to Newton, Hutchinson and Berkeley were not entirely wrong about Newtonianism. Following the example of Newton’s work, if not of his personal opinions, by the late eighteenth century physical science had become thoroughly divorced from religion.

Another obstacle to the acceptance of Newton’s work was the old false opposition between mathematics and physics that we have seen in a comment of Geminus of Rhodes quoted in Chapter 8. Newton did not speak the Aristotelian language of substances and qualities, and he did not try to explain the cause of gravitation. The priest Nicolas de Malebranche (1638–1715) in reviewing the Principia said that it was the work of a geometer, not of a physicist. Malebranche clearly was thinking of physics in the mode of Aristotle. What he did not realize is that Newton’s example had revised the definition of physics.

Starting already in Newton’s lifetime, his theory of gravitation was opposed in France and Germany by followers of Descartes and by Newton’s old adversary Leibniz. They argued that an attraction operating over millions of miles of empty space would be an occult element in natural philosophy, and they further insisted that the action of gravity should be given a rational explanation, not merely assumed. In this, natural philosophers on the Continent were hanging on to an old ideal for science, going back to the Hellenic age, that scientific theories should ultimately be founded solely on reason. We have learned to give this up. Even though our very successful theory of electrons and light can be deduced from the modern standard model of elementary particles, which may (we hope) in turn eventually be deduced from a deeper theory, however far we go we will never come to a foundation based on pure reason. Like me, most physicists today are resigned to the fact that we will always have to wonder why our deepest theories are not something different.

The methods for applying Newton’s theory to problems involving more than two bodies were developed by many authors in the late eighteenth and early nineteenth centuries. There was one innovation of great future importance that was explored especially by Pierre-Simon Laplace in the early nineteenth century. Instead of adding up the gravitational forces exerted by all the bodies in an ensemble like the solar system, one calculates a “field,” a condition of space that at every point gives the magnitude and direction of the acceleration produced by all the masses in the ensemble. To calculate the field, one solves certain differential equations that it obeys. (These equations set conditions on the way that the field varies when the point at which it is measured is moved in any of three perpendicular directions.) This approach makes it nearly trivial to prove Newton’s theorem that the gravitational forces exerted outside a spherical mass go as the inverse square of the distance from the sphere’s center. More important, as we will see in Chapter 15, the field concept was to play a crucial role in the understanding of electricity, magnetism, and light.

When Einstein’s theory was confirmed in 1919 by the observation of a predicted bending of rays of light by the gravitational field of the Sun, the Times of London declared that Newton had been shown to be wrong. This was a mistake. Newton’s theory can be regarded as an approximation to Einstein’s, one that becomes increasingly valid for objects moving at velocities much less than that of light. Not only does Einstein’s theory not disprove Newton’s; relativity explains why Newton’s theory works, when it does work. General relativity itself is doubtless an approximation to a more satisfactory theory.

In general relativity a gravitational field can be fully described by specifying at every point in space and time the inertial frames in which the effects of gravitation are absent. This is mathematically similar to the fact that we can make a map of a small region about any point on a curved surface in which the surface appears flat, like the map of a city on the surface of the Earth; the curvature of the whole surface can be described by compiling an atlas of overlapping local maps. Indeed, this mathematical similarity allows us to describe any gravitational field as a curvature of space and time.

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.* 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 ...

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.

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.