The Clockwork Universe

A Little History Of Science: The Clockwork Universe

The American Revolution (also known as the American War of Independence) in 1776, the French Revolution in 1789, and the Russian Revolution in 1917 each swiftly brought about new forms of government and a new social order. There was also a Newtonian Revolution. Fewer people have heard of the Newtonian Revolution, but it was just as important, and although it took decades rather than years to work its effect, its consequences were profound. The Newtonian Revolution described the world in which we live.

After he died in 1727, Sir Isaac continued to be a towering figure in the eighteenth century. In every field of endeavour, people wanted to be the ‘Newton’ of their subject. Adam Smith wanted to be the Newton of economics; some called William Cullen the Newton of medicine; Jeremy Bentham strove to be the Newton of social and political reform. What they all sought was a general law or principle that would glue their discipline together, just as Newton’s gravity seemed to hold the universe in its regular and stately progression through the seasons and years. As the poet Alexander Pope joked, ‘Nature, and Nature’s laws lay hid in night./ God said, Let Newton be! and all was light.’ As an Englishman, Pope might have been biased in favour of his countryman. In France, Germany and Italy, Newton cut a sizeable figure even in his own lifetime, but there were other scientific traditions that still counted. In France, Descartes’ mechanical vision of the universe remained powerful. In Germany there were squabbles over who had invented calculus, with the admirers of the philosopher G.W. Leibniz (1646–1716) insisting that Newton was less important in developing this mathematical tool than their man. In Britain, however, Newton attracted many followers, who were only too pleased to call themselves ‘Newtonians’, and who used his magnificent insights in mathematics, physics, astronomy and optics.

Gradually, however, the power of Newton’s experimental optics and laws of motion also took hold of European thought. His reputation was helped by a most unlikely advocate: the poet, novelist and man of letters Voltaire (1694–1778). Voltaire’s most famous creation was the loveable character, Candide, who featured in an adventure story. Candide lives a life of continuous disaster – everything that can go wrong does go wrong – but he never forgets his philosophy: the world that God has created must be the best possible one. So he remains cheerful, sure that what happens to him, no matter how dreadful, is for the best ‘in this best of possible worlds’. (After his horrible adventures he decides that he should have stayed at home and tended his garden: pretty good advice, actually.) Candide was a gentle dig at the philosophy of Newton’s rival in the invention of calculus, Leibniz. Voltaire was a great fan of Newton and, in fact, all things English. He spent a couple of years in England and was very impressed with the freedom of speech and thought there. (Voltaire was imprisoned at home in France for criticising the Catholic Church and the French king, so he knew how important free speech is.) He also came away from England appreciating Newton’s achievements, and he wrote a popular version of Newton’s ideas for ordinary people in French. Voltaire’s book found many readers in Europe, where everyone was discussing the ways in which Newton’s mathematics and physics made sense of the movements of the planets and stars, the daily ebb and flow of the tides, the trajectory of bullets, and of course the falling of apples.

Newton gradually acquired his towering reputation because the tools – both mathematical and physical – that he set out in his famous Principia actually worked. These tools helped mathematicians, physicists and astronomers to study a number of problems that Newton had only touched on. No work of science is ever the last word, and so it was with Newton’s. Many individuals were happy for Newton to be the giant on whose shoulders they could stand. And in many instances, he did help them see further.

Let’s look at three examples: the causes of the tides, the shape of the earth, and the number and orbits of the planets in the solar system.

There are low and high tides: a low tide is when the sea is ‘out’ and you have to walk a lot further before you can have a swim, and a high tide is when the sea is ‘in’ and it’s washing away your sand- castles. The tides have a regular, daily pattern, and knowing about them was important for sailors, who might need a high tide to get the ship into harbour.

Aristotle had drawn a connection between the tides and the moon. After it became common to believe that the earth actually moves, some compared the tides with the waves you can make in a bucket of water by tilting it to and fro. For Newton, gravity was the key. He argued that the moon’s ‘gravitational pull’ is greatest when the moon is closest to the earth. (Like the earth revolving around the sun, the moon revolves around the earth in an ellipse, so the distances between the earth and moon vary regularly.) The gravity of the moon attracts the water in the oceans towards it. As the earth revolves, an area of sea will become nearer to, and then further away from, the moon, and so the increasing and decreasing force of gravity helps raise and lower the oceans in the regular fashion that we can see. This explains the high and low tides. Newton was right to think that the tides illustrated gravity in action.

Later Newtonians refined the master’s calculations. The Swiss doctor Daniel Bernoulli (1700–82) offered a closer analysis of tides in 1740. He was much more interested in mathematics, physics and navigation than in medicine, and he also helped explain how strings vibrate (as when you strum a guitar) and how pendulums swing (as in grandfather clocks). He improved the design of ships, too. At the medical school in Basel, he used Newtonian mechanics to look at things such as the way our muscles contract and shorten to make our limbs move. His work on tides was in response to a question set by the Academy of Sciences in Paris, which offered a prize for the best answer – learned societies often did this.

Bernoulli shared the prize with several others, each helping to explain why tides behave as they do, and including, in their explanations, the effect of the gravitational pull of the sun as well. When two things, like the earth and the moon, attract each other, the mathematics is relatively simple. In the real world, the sun, planets and other things having mass complicate the picture, and the mathematics becomes much more difficult.

The Paris Academy of Sciences was also involved with a second major question of Newtonianism: was the earth a round ball? It was easy to see that it wasn’t completely smooth, like a table tennis ball – there were mountains and valleys. But was it basically round?

Newton had said no, since he had shown that the force of gravity at the equator was slightly different from the force of gravity in northern Europe. He knew this by experiments with a pendulum.

The swing of a pendulum is influenced by the force of the earth’s gravity; the stronger the gravity, the faster the pendulum moves, and so it takes a shorter amount of time for it to complete its to-and- fro cycle. Sailors had measured how far the pendulum swung in exactly one second, and the distance was slightly shorter at the equator. This difference told Newton that the distance to the centre of the earth was slightly greater at the equator. If the earth were a perfect ball, it would be the same distance everywhere from the surface to the centre. Consequently, Newton said that the earth was actually flattened at the poles – as if it had been squashed from top to bottom – and it bulged a bit at the equator. He thought this shape had been created by the earth’s rotation on its north–south axis when it was still very new and cooling from its fluid state. Newton hinted that this meant that the earth was older than 6,000 years, but he never revealed how old he thought the earth really was.

When Newton’s work was being debated in France during the 1730s, many French scientists refused to believe that the earth had this imperfect shape. So Louis XV, King of France, sent out two expeditions, one to Lapland, near the Arctic Circle, and one to Peru, near the equator – an expensive way to test a simple fact.

What the two expeditions did was to measure the precise length of one degree of latitude at these two locations. Latitude is a measure of the north–south axis of the earth, with the equator being zero degrees, the North Pole +90 degrees and the South Pole –90 degrees. (It takes 360 degrees to go around the globe completely.) You can see the lines of latitude drawn from side to side across a map of the world. If the earth were perfectly round, each degree of latitude would be the same. The Lapland expedition returned first (they hadn’t had to travel so far) but when the Peru group came back, after nine years, it was shown that the degree of latitude in Lapland was longer than the one in Peru, exactly as predicted by Newton’s model. These results helped raise Newton’s reputation in continental Europe.

Astronomers all over Europe were looking at the stars and planets in an attempt to predict how they moved, and therefore where they would be observed each evening (or each year). These predictions became ever more precise, as more and more observations were done, and as the mathematical analysis of their movements became more accurate.

Building bigger telescopes enabled astronomers to see further into space, and then to discover new stars, and even new galaxies. One of the most important of these stargazers was a refugee to England from Germany, William Herschel (1738–1822). Herschel was a musician, but his passion was looking at the heavens. One night, in 1781, he noticed a new object, which was not a star. At first he thought it was probably a comet and he described it to a local group in Bath, where he lived.

His observation attracted the attention of others, and it quickly became clear that Herschel had discovered a new planet. It was eventually named Uranus, after a character in Greek mythology.

This discovery changed Herschel’s life and enabled him to devote himself entirely to astronomy. King George III, whose family had also come from Germany, took an interest in Herschel’s work. George helped Herschel build the world’s largest telescope, and eventually to come to live near Windsor, where one of the royal castles was located. So devoted was Herschel to looking at the heavens, that when he moved to Windsor he arranged his life so that he need not miss a single night’s observations. In all his work, Herschel was helped by his sister Caroline (1750–1848), who was also an expert astronomer. Herschel’s son John (1792–1871) also continued his father’s work, making it a family business.

William Herschel not only looked at stars, planets and other heavenly bodies, but he also thought deeply about what he was seeing. Since he had the best telescopes of his time, he could see further. He produced catalogues of stars that were much larger and more accurate than ever before. He realised that our galaxy, the Milky Way, was not the only galaxy in the universe, and he puzzled long and hard about what were called ‘nebulae’, areas in the sky that appeared as fuzzy white blotches. A few of these can sometimes be seen on a clear night with the naked eye, but Herschel’s telescope revealed many more of these blotchy areas. The Milky Way begins to look fuzzy as we peer at its more distant points, and astronomers had assumed that nebulae were simply clusters of stars. Herschel showed that some of them probably are, but that others were enormous areas of gaseous clouds swirling around in deep space. In addition, by looking at ‘double stars’, pairs of stars close to each other (well, it’s ‘close’ considering the distances we are talking about), he showed that the behaviour of these stars could be explained by gravitational attraction: Newton’s gravity was shown to extend even into the outer reaches of space.

Newton’s laws of gravity and of motion, along with his mathematical analysis of force (power), acceleration (increasing speed), and inertia (the tendency to keep moving in a straight line), became the guiding principles for natural philosophers during the eighteenth century. No one did more to show how much these principles could explain than the Frenchman, Pierre Simon de Laplace (1749–1827). Laplace worked with Lavoisier, whom we’ll meet in Chapter 20, but, unlike his unlucky friend, Laplace came through the French Revolution unharmed. Admired by Napoleon, he was a leading figure in French science for half a century. Laplace used Newton’s laws of motion and his mathematical tools to show that the things one could see in the sky could be understood, and that future movements of planets, stars, comets and asteroids could be predicted with accuracy. He developed a theory of how our solar system, with the sun and its planets, could have been born millions of years ago from a vast explosion, with the sun throwing off great chunks of hot gases that gradually cooled to form the planets (and their moons). He called this the ‘nebular hypothesis’, and he offered some very complicated mathematical calculations to show that it might have happened that way. Laplace was describing a version of what we now call the Big Bang, although physicists today know a great deal more about this than Laplace could have known.

Laplace was so impressed with the power of Newton’s laws of motion that he believed that if we could only know where every particle in the universe was at a given moment, we could predict the running of the whole universe to the ends of time. He realised that it was not possible to do this. What he meant was that the laws of matter and motion were such that the whole universe really did work like a very well-made clock, and that it kept perfect time. His vision of a clockwork universe served scientists for a century after him.