Chapter 2: The Old World: Newton’s Clockwork Universe
chapter 2: THE OLD WORLD: NEWTON’S CLOCKWORK UNIVERSE
LET’S RETURN TO THAT HEADLINE in the Times of November 1919, announcing the verification of Einstein’s theory of relativity: “Newtonian Ideas Overthrown.” Just what were these ideas, and how were they “overthrown” by Einstein? What difference does this make? And how does their development help us understand how the natural sciences work? Let’s begin by reflecting a little on what science is all about.
Thinking about Science
At one level, the natural sciences are about the patient and scrupulous accumulation of observations —whether we are talking about the movements of planets, the behavior of ants, or the patterns of rainfall in a region of the Andes. Yet science is about more than harvesting countless observations. It is a quest for understanding in which we try to discern the deeper patterns and structures of our universe that cause it to behave in certain ways. Science aims to go behind our observations and figure out what deeper truths underlie what we can see of our world.
It’s an idea explored in the writings of the great Renaissance philosopher and scientist Francis Bacon (1561–1626), who compared “natural philosophers” to bees. (The word scientist did not come into use until the 1830s.) Why bees? Because bees do more than just gather pollen; they “transform and digest” what they collect and convert it into something new —honey. In the same way, the scientist both gathers observations and then transforms these by weaving them together into a theory —a way of understanding our world.
The word theory is widely used in science to refer to ways of understanding our world. It comes from the Greek word theoria, meaning “a way of beholding” or “contemplation.” A theory is like a lens that allows us to see through and beyond the world of appearances to grasp something deeper and more fundamental that lies behind it. Like a set of spectacles, a theory allows us to see things in focus, helping us grasp how seemingly disconnected observations are actually part of something greater. Over time, certain theories gain widespread acceptance, becoming a settled part of the furniture of our minds. We get so used to these ideas that they seem natural and self-evidently true. So what happens if they turn out to be wrong? What if a familiar and trusted way of understanding ourselves and our world proves fallible and unreliable? What if a new theory comes along and is shown to be far superior to what we were used to?
Let’s take an example —the movement of the planets. Even in the ancient world, people noticed that some of the objects in the night sky seemed to move around. Names were given to the five star-like objects that moved against the background of the fixed stars: Mercury, Venus, Mars, Jupiter, and Saturn. So what explained the movement of these “wandering stars”? In the second century, the astronomer and mathematician Ptolemy of Alexandria set out a way of understanding the heavenly bodies that would be accepted by most people for more than a thousand years. For Ptolemy, the sun, moon, and planets all revolved in circular orbits at different distances around the Earth.[21] It was a neat model, and it worked reasonably well, partly because, before the invention of the telescope in the sixteenth century, observations of planetary movements weren’t very accurate.
But in the sixteenth century, awkward questions arose as increasingly accurate measurements of the movements of the planets became possible. The Polish astronomer Nicolaus Copernicus published a book arguing that the sun —not the Earth —stood at the center of the known universe. The Earth now had to be seen as simply one among many other planets. Copernicus’s theory was wrong in several respects —for example, he believed that the planets revolved in circular orbits around the sun at uniform speeds. It needed correction before it could provide more reliable predictions of the movement of the planets against the fixed stars of the night sky.
Johannes Kepler corrected those errors through his close study of the movement of the planet Mars in the early seventeenth century. He pointed out that the Earth and other planets actually revolved in elliptical orbits around the sun at variable speeds. Yet Kepler couldn’t explain why this was the case. In many ways, Kepler’s achievement was simply to set out the rules that seemed to govern planetary motion. It remained a mystery why they should behave in this way in the first place. Kepler was unable to offer a theory that accounted for the existence and form of these rules. A bigger picture of the solar system was required to explain this.
As if on cue, the English mathematician and natural philosopher Isaac Newton (1643–1727) stepped up to the plate and ushered in a new and deeper way of understanding our universe.
Isaac Newton and the Laws of Nature
Newton set out his proposals for classical mechanics and gravitational theory in his Philosophiae Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), now usually referred to simply as Newton’s Principia, in 1687. His massive intellectual achievement was summed up by one of the leading poets of his age, Alexander Pope:
Nature and nature’s laws lay hid in night;
GOD said, Let Newton be! and all was light.
So who was Newton? And what was his achievement? Newton developed most of his important work while he was professor of mathematics at Cambridge University. By careful observation, Newton set out a series of principles that governed the behavior of objects on Earth and then argued that these same principles applied to the motion of the moon around the Earth and the planets around the sun. This is the point made in the famous story of Newton and the apple.
This well-known story exists in several forms. The version of the story I was told back in the late 1950s was that Newton was sitting in his garden when an apple fell on his head —happily inflicting no permanent damage! Then, in a moment of devastating intellectual illumination, Newton invented his theory of gravity. It’s a wonderful story. And like so many of these stories, there is an element of truth. Yet there’s also a lot of exaggeration.
One account of this incident was written down by John Conduitt, who became Newton’s assistant at the Royal Mint, which Newton directed in his later years:
In the year 1666 [Newton] retired again from Cambridge to his mother in Lincolnshire. Whilst he was pensively meandering in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from Earth, but that this power must extend much further than was usually thought. Why not as high as the Moon said he to himself & if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition.[22]
This account was written down sixty years after the event. Scholars can hardly be blamed for wondering if Newton might have creatively embellished the story through retelling it over time, perhaps to conceal the fact that another British scientist —Robert Hooke —had developed a similar idea in the 1670s.[23]
The story of Newton’s apple was given a surprising religious twist by the French antireligious philosopher Voltaire, who saw the apple as a symbol of science displacing religion as the cornerstone of human wisdom. Drawing on the tradition that the “forbidden fruit” in the Garden of Eden was an apple, Voltaire suggested that Newton’s scientific discovery ushered in a new era in human history and self-understanding.[24]
Newton, of course, did not see his achievement in these terms. He rather saw himself as clarifying the deeper logic of the universe, discerning certain “laws of nature” that he considered to reflect the wisdom of God as creator. Newton argued that the mysterious and undetectable force he named gravity was the explanation for both an apple falling to the Earth and the moon orbiting around the Earth. Newton had no idea what caused gravity in the first place and refused to speculate about its origins. “It is enough that gravity does really exist, and . . . abundantly serves to account for all the motions of the celestial bodies.”[25]
Initially, Newton’s demonstration of the regularity of these laws of nature was seen as confirming the Christian belief in a God who had created an ordered universe and endowed humanity with the power of reason to discover those laws. Yet some were not so sure. Newton might well have shown that the universe was like a well-designed machine —cold, impersonal, and mechanical. But where was there any sense of beauty or joy? Furthermore, God now seemed to be pointless. Having constructed the universe and set it going, God is left without any significant role. God might retire or even die, but the universe would continue to function according to the laws by which God had caused it to function. Newton, perhaps unwittingly, had laid the groundwork for a self-sustaining and self-regulating universe, with no place for God.[26]
Newton on Space
Newton had demonstrated that the planets moved around the sun and the moon around the Earth according to certain “laws of nature” that could be expressed mathematically. But what did they move through? Newton introduced the idea of space —a vast, empty container that enclosed the sun, planets, and stars. This naturally raised some important questions, most obviously the question of what this “space” was made of. As with gravity, Newton refused to speculate on this question. Space was like an enormous box through which all objects moved in straight lines until some force caused their trajectory to curve. Like gravity, space could not itself be observed. Yet, again like gravity, it made sense of everything else that we observe. For Newton, both gravity and space were legitimate scientific inferences from an observable phenomenon to the unobservable entity that best explains it.[27]
Newton recognized that space and time were not things we observe directly but were rather inferences from those observations. However, many of his interpreters began to think of these as self-evident truths, things so obviously correct that they did not require justification or defense. Einstein would later express his concern about the ease with which such provisional concepts came to be seen as necessarily true and praised the German physicist Ernst Mach for insisting that scientific concepts arise out of experience:
Concepts, which have proved useful in the ordering of things, easily acquire such a degree of authority over us that we forget their earthly origin. We take them as unchangeable givens. They come to bear the stamp of necessities of thought, of a priori givens. The path of scientific advance is often made impassable for a long time through such mistakes.[28]
So what was the significance of Newton’s theories? Basically, Newton was able to demonstrate that a vast range of observational data could be explained on the basis of a simple set of universal principles, such as his laws of motion and the force of gravity. Newton’s theories worked well within the comfort zone of our intuitions about the classical world. Yet when we move away from this narrow world, we encounter the strange world of the very small and very fast —the world which Einstein later made his own.
Newton on Light
As we shall see, one of Einstein’s most significant contributions to modern science concerned the nature of light. So what did Newton have to say on this question? In his Opticks (1704), Newton took the view that a beam of light consisted of a series of rapidly moving small particles or “corpuscles” (from the Latin term corpuscula, “small bodies”). Rays of light were actually beams of tiny particles. Not everyone agreed with Newton here. The great Dutch physicist Christiaan Huygens argued that light was made up of waves and that some aspects of its behavior could be explained using this model. Newton, however, argued that the reflection of light by a mirror was just like throwing a ball at a wall and watching it bounce back.
Light Acting as Both Wave and Particle
Newton’s particle theory of light came to dominate physics during the eighteenth century. It led to some fascinating predictions, two of which are especially important for our purposes. First, if light consisted of a beam of particles, no matter how small, Newton’s theories predicted that these particles would be influenced by gravity. They would travel in a straight line unless they were deflected by gravity. In 1804, the German mathematician Johann Georg von Soldner published a paper calculating the degree to which a beam of light would be deflected by the gravitational field of a star such as the sun.[29] Von Soldner noted that the predicted effect was far too small to be observed by the instruments of his time, so nobody followed through on this.
The second prediction was made by the English natural scientist John Michell in a paper presented to the Royal Society in 1783. Since light consisted of a beam of particles that would be attracted by the gravitational pull of a star, Michell argued that some stars might be so massive that their gravitational forces would prevent beams of light from ever leaving their surfaces. Like Newton’s famous apple, these particles of light would simply fall to the ground. Michell thus proposed that “dark stars” existed, which could not be seen because light was unable to break free from the force of their gravity. Michell’s calculations suggested that this would happen if the star was five hundred times the mass of our sun. Today, we know that Michell was right. We now call these dark stars “black holes.”[30]
Yet during the nineteenth century, a growing body of experimental evidence suggested that light was better understood as a wave. In 1801, the English physicist Thomas Young devised a “double slit” experiment that suggested that light behaves like ripples or waves on a pond of water. By the 1870s, Newton’s view that light consisted of particles had been abandoned in favor of a wave theory of light. It seemed to many that the issue had been resolved. But had it?
The Completeness of Nineteenth-Century Physics?
Many late nineteenth-century scientists believed that physics had finally sorted out all the great questions of the day and all that remained was to achieve greater precision in some measurements of natural properties. Writing in 1871, the great British physicist James Clerk Maxwell warned against any such complacency:
This characteristic of modern experiments —that they consist principally of measurements —is so prominent, that the opinion seems to have got abroad, that in a few years all the great physical constants will have been approximately estimated, and that the only occupation which will then be left to men of science will be to carry on these measurements to another place of decimals.[31]
Maxwell had his doubts about this view. But there was no shortage of those who shared it. In 1894, the leading American physicist Albert A. Michelson gave an address marking the opening of a new physics laboratory at the University of Chicago. Michelson declared that the “future truths of Physical Science are to be looked for in the sixth place of decimals” —in other words, through more accurate measurements of what was already known.[32]
In 1888, the astronomer Simon Newcomb suggested that astronomy was now not so much about “the discovery of new things” as about “the elaboration of those already known.” While a few new discoveries might be expected —such as observing hitherto unknown comets —Newcomb declared that we are “fast approaching the limits of our knowledge.”[33] Robert Millikan, who went on to win the Nobel Prize in Physics in 1923, recalled his own days as a student in New York during the 1890s. He was constantly ridiculed by other students for his devotion to “a ‘finished,’ yes, a ‘dead subject,’ like physics.” Why not work in a more interesting field that was going somewhere?[34]
Others, however, were much more cautious. It was true that the nineteenth century had made significant advances in the field of physics —above all in developing mechanical models to explain many aspects of the natural world. Yet enigmas and anomalies remained. Some observations just didn’t fit neatly into the best theories of that age. The question was this: Were those enigmas and anomalies simply intellectual irritations that would soon be resolved? Or were they really signs that the existing scientific consensus was wrong and needed radical revision? Nobody really knew.
The historian Thomas Kuhn developed the idea of a “paradigm shift” —a radical change in the way in which scientists see our world.[35] He saw this kind of shift in the Copernican revolution of the sixteenth century, in which the view that the sun and planets revolved around the Earth was displaced by the very different view that the Earth was another planet revolving around the sun. Yet Kuhn’s interest lay mainly in the way in which a dominant paradigm collapsed and gave way to something new. A tipping point was reached. It was realized that the old way of thinking just couldn’t cope with the anomalies, opening the way to new ways of thinking that could make sense of these otherwise puzzling observations.
Let’s look at one of these anomalies that troubled physicists at the end of the nineteenth century. Technically, this is known as the “advance of the perihelion of Mercury.”
The Curious Behavior of the Planet Mercury
Newton’s theory of planetary motion triumphantly explained the way the planets orbited the sun on the basis of his theory of universal gravitation and the laws of motion. It was widely seen as an intellectual marvel of the eighteenth century. The astronomer Johannes Kepler had early identified three basic laws of planetary motion. Yet these were simply summaries of the way the planets orbited around the sun. They did not explain why they behaved in this way. Newton’s theory of gravity provided a robust and persuasive explanation of these observations, showing that planetary orbits reflected something deeper and more fundamental about our universe.
Newton’s theory faced a major challenge with the discovery of the planet Uranus in March 1781. Although Uranus is actually visible to the naked eye, it had hitherto been assumed to be a star on account of the planet’s faint image and its slow orbit around the sun. Once this “star” was recognized as a planet, its motion was studied carefully. It was found that the orbit of this new planet did not fit what was predicted on the basis of Newtonian mechanics. So what was wrong? Did the anomalous behavior of Uranus reveal a flaw in Newton’s theory? Might Newtonianism have to be abandoned?
Yet astronomers quickly realized that there might be another explanation, which involved modifying Newton’s theory, not abandoning it. What if there was an unknown planet beyond Uranus, whose gravitational pull distorted the orbit of Uranus? The calculations of the French astronomer Urbain Le Verrier and others suggested where this planet might be found. In 1846, the planet Neptune was observed. The anomalous behavior of Uranus was thus resolved without abandoning or modifying Newton’s basic ideas. Many scientists of the nineteenth century saw the discovery of Neptune as confirming the reliability of Newtonianism.
Yet another planetary anomaly emerged during the later nineteenth century —this time concerning the small planet Mercury. Like all the planets, Mercury orbited the sun in an ellipse. The point at which it was closest to the sun —known as the perihelion —was discovered to move by a tiny, but observable, amount each year.[36] Why?
In 1859, Le Verrier, having successfully predicted the location of Neptune by calculating the impact of its gravitational field on the orbit of Uranus, proposed that this puzzling phenomenon could be explained by the gravitational pull of the other planets on Mercury.[37] His calculations suggested that most of this change could be explained in this way, but not all of it. One possible explanation of this discrepancy was the existence of a hitherto unknown planet of roughly half the mass of Mercury positioned closer to the sun. This would explain the observations on the basis of Newton’s theory of gravity. This sparked a search for the proposed planet, which Le Verrier named Vulcan. It was never found.[38] At the end of the nineteenth century, the curious behavior of Mercury remained unexplained. What caused it?
On November 18, 1915, Albert Einstein reported to the Prussian Academy that the advancing perihelion of Mercury was explained precisely and persuasively by his new general theory of relativity. His new way of seeing the world had resolved this long-standing problem —along with many others. We therefore turn to consider the many new ideas developed by Einstein, beginning with the remarkable series of four articles published in 1905 that established his reputation as one of the most significant scientific thinkers of his age —despite the fact that he was working as a clerk in the patent office in the Swiss city of Bern, not as a research scientist at a leading Swiss university or scientific research institution. In what follows, we shall consider Einstein’s early scientific career and focus on those four scientific papers that marked him out as stamped with that elusive quality of genius.
[21] For the science, see Kragh, Conceptions of Cosmos, 46–65.
[22] McKie and de Beer, “Newton’s Apple.”
[23] See Chapman, England’s Leonardo.
[24] Epstein, “Voltaire’s Myth of Newton.”
[25] Newton, Principia, 507.
[26] See the argument of Curry, “Losing Faith.”
[27] Sklar, Space, Time, and Spacetime, 162.
[28] Einstein, “Ernst Mach,” 102.
[29] Von Soldner, “Ueber die Ablenkung eines Lichtstrals von seiner geradlinigen Bewegung.”
[30] For a very readable account of what we know about black holes, see Susskind, The Black Hole War.
[31] Maxwell, The Scientific Papers, vol. 2, 244.
[32] Michelson, “Some of the Objects and Methods of Physical Science,” 15.
[33] Newcomb, “The Place of Astronomy among the Sciences,” 69–70.
[34] Millikan, Autobiography, 269–70.
[35] See especially Kuhn, The Structure of Scientific Revolutions.
[36] This “precession of the perihelion” of Mercury takes place at the rate of 574 arcseconds (0.159 degree) per century.
[37] Le Verrier, “Théorie du mouvement de Mercure.”
[38] For the background, see Baum and Sheehan, In Search of Planet Vulcan.