To Explain the World: The Discovery of Modern Science

by Steven Weinberg

  This was not because Newton’s theory satisfied a preexisting metaphysical criterion for a scientific theory. It didn’t. It did not answer the questions about purpose that were central in Aristotle’s physics. But it provided universal principles that allowed the successful calculation of a great deal that had previously seemed mysterious. In this way, it provided an irresistible model for what a physical theory should be, and could be.

  This is an example of a kind of Darwinian selection operating in the history of science. We get intense pleasure when something has been successfully explained, as when Newton explained Kepler’s laws of planetary motion along with much else. The scientific theories and methods that survive are those that provide such pleasure, whether or not they fit any preexisting model of how science ought to be done.

  The rejection of Newton’s theories by the followers of Descartes and Leibniz suggests a moral for the practice of science: it is never safe simply to reject a theory that has as many impressive successes in accounting for observation as Newton’s had. Successful theories may work for reasons not understood by their creators, and they always turn out to be approximations to more successful theories, but they are never simply mistakes.

  This moral was not always heeded in the twentieth century. The 1920s saw the advent of quantum mechanics, a radically new framework for physical theory. Instead of calculating the trajectories of a planet or a particle, one calculates the evolution of waves of probability, whose intensity at any position and time tells us the probability of finding the planet or particle then and there. The abandonment of determinism so appalled some of the founders of quantum mechanics, including Max Planck, Erwin Schrödinger, Louis de Broglie, and Albert Einstein, that they did no further work on quantum mechanical theories, except to point out the unacceptable consequences of these theories. Some of the criticisms of quantum mechanics by Schrödinger and Einstein were troubling, and continue to worry us today, but by the end of the 1920s quantum mechanics had already been so successful in accounting for the properties of atoms, molecules, and photons that it had to be taken seriously. The rejection of quantum mechanical theories by these physicists meant that they were unable to participate in the great progress in the physics of solids, atomic nuclei, and elementary particles of the 1930s and 1940s.

  Like quantum mechanics, Newton’s theory of the solar system had provided what later came to be called a Standard Model. I introduced this term in 197121 to describe the theory of the structure and evolution of the expanding universe as it had developed up to that time, explaining:

  Of course, the standard model may be partly or wholly wrong. However, its importance lies not in its certain truth, but in the common meeting ground that it provides for an enormous variety of cosmological data. By discussing this data in the context of a standard cosmological mode, we can begin to appreciate their cosmological relevance, whatever model ultimately proves correct.

  A little later, I and other physicists started using the term Standard Model also to refer to our emerging theory of elementary particles and their various interactions. Of course, Newton’s successors did not use this term to refer to the Newtonian theory of the solar system, but they well might have. The Newtonian theory certainly provided a common meeting ground for astronomers trying to explain observations that went beyond Kepler’s laws.

  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.

  These mathematical tools were used most dramatically in 1846 to predict the existence and location of the planet Neptune from irregularities in the orbit of the planet Uranus, independently by John Couch Adams and Jean-Joseph Leverrier. Neptune was discovered soon afterward, in the expected place.

  Small discrepancies between theory and observation remained, in the motion of the Moon and of Halley’s and Encke’s comets, and in a precession of the perihelia of the orbit of Mercury that was observed to be 43" (seconds of arc) per century greater than could be accounted for by gravitational forces produced by the other planets. The discrepancies in the motion of the Moon and comets were eventually traced to nongravitational forces, but the excess precession of Mercury was not explained until the advent in 1915 of the general theory of relativity of Albert Einstein.

  In Newton’s theory the gravitational force at a given point and a given time depends on the positions of all masses at the same time, so a sudden change of any of these positions (such as a flare on the surface of the Sun) produces an instantaneous change in gravitational forces everywhere. This was in conflict with the principle of Einstein’s 1905 special theory of relativity, that no influence can travel faster than light. This pointed to a clear need to seek a modified theory of gravitation. In Einstein’s general theory a sudden change in the position of a mass will produce a change in the gravitational field in the immediate neighborhood of the mass, which then propagates at the speed of light to greater distances.

  General relativity rejects Newton’s notion of absolute space and time. Its underlying equations are the same in all reference frames, whatever their acceleration or rotation. Thus far, Leibniz would have been pleased, but in fact general relativity justifies Newtonian mechanics. Its mathematical formulation is based on a property that it shares with Newton’s theory: that all bodies at a given point undergo the same acceleration due to gravity. This means that one can eliminate the effects of gravitation at any point by using a frame of reference, known as an inertial frame, that shares this acceleration. For instance, one does not feel the effects of the Earth’s gravity in a freely falling elevator. It is in these inertial frames of reference that Newton’s laws apply, at least for bodies whose speeds do not approach that of light.

  The success of Newton’s treatment of the motion of planets and comets shows that the inertial frames in the neighborhood of the solar system are those in which the Sun rather than the Earth is at rest (or moving with constant velocity). According to general relativity, this is because that is the frame of reference in which the matter of distant galaxies is not revolving around the solar system. In this sense, Newton’s theory provided a solid basis for preferring the Copernican theory to that of Tycho. But in general relativity we can use any frame of reference we like, not just inertial frames. If we were to adopt a frame of reference like Tycho’s in which the Earth is at rest, then the distant galaxies would seem to be executing circular turns once a year, and in general relativity this enormous motion would create forces akin to gravitation, which would act on the Sun and planets and give them the motions of the Tychonic theory. Newton seems to have had a hint of this. In an unpublished “Proposition 43” that did not make it into the Principia, Newton acknowledged that Tycho’s theory could be true if some other force besides ordinary gravitation acted on the Sun and planets.22

  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 regarde
d 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 conceptual basis of general relativity is thus different from that of Newton. The notion of gravitational force is largely replaced in general relativity with the concept of curved space-time. This was hard for some people to swallow. In 1730 Alexander Pope had written a memorable epitaph for Newton:

  Nature and nature’s laws lay hid in night;

  God said, “Let Newton be!” And all was light.

  In the twentieth century the British satirical poet J. C. Squire23 added two more lines:

  It did not last: the Devil howling “Ho,

  Let Einstein be,” restored the status quo.

  Do not believe it. The general theory of relativity is very much in the style of Newton’s theories of motion and gravitation: it is based on general principles that can be expressed as mathematical equations, from which consequences can be mathematically deduced for a broad range of phenomena, which when compared with observation allow the theory to be verified. The difference between Einstein’s and Newton’s theories is far less than the difference between Newton’s theories and anything that had gone before.

  A question remains: why did the scientific revolution of the sixteenth and seventeenth centuries happen when and where it did? There is no lack of possible explanations. Many changes occurred in fifteenth-century Europe that helped to lay the foundation for the scientific revolution. National governments were consolidated in France under Charles VII and Louis XI and in England under Henry VII. The fall of Constantinople in 1453 sent Greek scholars fleeing westward to Italy and beyond. The Renaissance intensified interest in the natural world and set higher standards for the accuracy of ancient texts and their translation. The invention of printing with movable type made scholarly communication far quicker and cheaper. The discovery and exploration of America reinforced the lesson that there is much that the ancients did not know. In addition, according to the “Merton thesis,” the Protestant Reformation of the early sixteenth century set the stage for the great scientific breakthroughs of seventeenth-century England. The sociologist Robert Merton supposed that Protestantism created social attitudes favorable to science and promoted a combination of rationalism and empiricism and a belief in an understandable order in nature—attitudes and beliefs that he found in the actual behavior of Protestant scientists.24

  It is not easy to judge how important were these various external influences on the scientific revolution. But although I cannot tell why it was Isaac Newton in late-seventeenth-century England who discovered the classical laws of motion and gravitation, I think I know why these laws took the form they did. It is, very simply, because to a very good approximation the world really does obey Newton’s laws.

  Having surveyed the history of physical science from Thales to Newton, I would like now to offer some tentative thoughts on what drove us to the modern conception of science, represented by the achievements of Newton and his successors. Nothing like modern science was conceived as a goal in the ancient world or the medieval world. Indeed, even if our predecessors could have imagined science as it is today, they might not have liked it very much. Modern science is impersonal, without room for supernatural intervention or (outside the behavioral sciences) for human values; it has no sense of purpose; and it offers no hope for certainty. So how did we get here?

  Faced with a puzzling world, people in every culture have sought explanations. Even where they abandoned mythology, most attempts at explanation did not lead to anything satisfying. Thales tried to understand matter by guessing that it is all water, but what could he do with this idea? What new information did it give him? No one at Miletus or anywhere else could build anything on the notion that everything is water.

  But every once in a while someone finds a way of explaining some phenomenon that fits so well and clarifies so much that it gives the finder intense satisfaction, especially when the new understanding is quantitative, and observation bears it out in detail. Imagine how Ptolemy must have felt when he realized that, by adding an equant to the epicycles and eccentrics of Apollonius and Hipparchus, he had found a theory of planetary motions that allowed him to predict with fair accuracy where any planet would be found in the sky at any time. We can get a sense of his joy from the lines of his that I quoted earlier: “When I search out the massed wheeling circles of the stars, my feet no longer touch the Earth, but, side by side with Zeus himself, I take my fill of ambrosia, the food of the gods.”

  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.

  15

  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,1 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.2

  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.3

  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.