The Universe Within (3 page)

Again we return to late sixteenth- and early seventeenth-
­
century Renaissance Italy, where Galileo Galilei took the first steps towards founding the field of physics. He realized that mathematics, when used in conjunction with careful experiments and accurate measurements, could provide a powerful description of the real world. Mathematics allows us to form conceptions of the world far beyond our everyday experience, to delve deeply into our models of reality, and to search for contradictions in our descriptions, which often suggest new phenomena. But in the end, the only true test of the correctness or falsity of our ideas is, as Galileo first fully appreciated, experiment and observation.

So, through a combination of logical reasoning, observation, and painstaking experiment, Galileo developed physics as a new, universal discipline. His experiments with soot-blackened balls rolling on inclined planes, and his observations of the moons of Jupiter and the phases of Venus, provided the vital clues to ruling out the ancient Ptolemaic picture, in which the Earth lay at the centre of the universe, and establishing instead a Copernican universe with the sun at the centre of the solar system. That was the first step on the path to a Newtonian universe.

Galileo was a prodigious inventor: of a geometrical compass, a water clock, a new type of thermometer, telescopes, and microscopes, all the instruments that allowed him to accurately observe and measure the world. He risked his life in pursuit of his ideas. His notion of universal mathematical laws of motion, which could be uncovered by reason, was very threatening to religious authority. When his observations supported the Copernican, heliocentric picture of the solar system and directly contradicted the views of the Catholic Church, he was tried by the Inquisition and was forced to recant and then to live under house arrest for the rest of his life. He used the period of his imprisonment to write his final masterpiece,
Two New Sciences
, which laid the ground for Newton's theory of mechanics. These achievements inspired Albert Einstein to call Galileo “the father of modern physics — indeed of modern science.”
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The combination of mathematical theory and real experience, pioneered by Galileo, drove the development of every modern technology, from electronics to construction engineering, from lasers to space travel. And it opened up the universe to our understanding, from far below the size of an atom right up to the entire visible cosmos. To be sure, there are still great gaps in our knowledge. But when we look at how rapidly and how far physics has come since Galileo, who can say what its future limits are?

· · ·

MY OWN ATTRACTION TO
maths and physics began when I was about seven years old. Upon my father's release from prison in 1966, he realized he was in serious danger of rearrest. So he escaped across the border with Botswana and made his way overland to Kenya. After a considerable delay, my mother, my two older brothers, and I were granted permission to join him, under the condition that we never return to South Africa. However, as a refugee, my father had no passport and could not obtain employment. Neighbouring Tanzania, under President Julius Kambarage Nyerere, was far more strongly committed to supporting the struggle against apartheid. So, after a brief stay in Nairobi, we were granted asylum in Tanzania and moved to Dar es Salaam, the country's largest city.

I was sent to a government school, where I had a wonderful Scottish teacher named Margaret Carnie. She encouraged me to undertake many scientific activities, like making maps of the school, building electric motors, and playing around with equations. She was passionate about teaching, extraordinarily supportive and not at all prescriptive, and she gave me a lot of freedom. Most of all, she believed in me.

When I was ten, we moved to London, England, just in time to see the Apollo 11 lunar landing and watch Neil Armstrong step onto the moon. Who could ever forget the picture of Earth as a gorgeous blue marble floating above the moon's horizon? We were swept up in the moment and filled with optimism for the future.

It was the end of the sixties, and space was suddenly the coolest thing around. It's hard to convey the sense of the excitement, how the space program bound together people from all walks of life and every political opinion. It symbolized a certain spirit — ambitious and aglow with the crazy idea of using technology to fling a climbing rope up to the cosmos.

Equally as enthralling as the moon landing was the drama of Apollo 13, only one year later. Imagine you're 320,000 kilometres from home, out in the void of deep space, and you hear a loud bang. “Houston, we have a problem . . .” One of two main oxygen tanks had exploded, leaking precious oxygen into space over the next two hours. The three astronauts crowded into the only lifeboat they had: the little lunar explorer capsule, which had nowhere near the fuel they needed to get back to Earth. The drama was incredible. There were daily bulletins on TV. All over the world, people were biting their nails. How could the astronauts possibly survive?

NASA
's engineers came up with a fantastic solution. They used the moon's gravity to pull them towards it, then slingshot the little pod around its dark side and back to Earth. A few days later, there the astronauts were, their hot little tin can dive-bombing into the Pacific, where they were fished out and then, incredibly, waving to us from the TV, gaunt, unshaven, but alive. Everyone survived. It was pure magic.

The trajectory for this manoeuvre was computed using the equations discovered by the founder of the field we now call theoretical physics, and also one of the most capable mathematicians of all time: Isaac Newton.

Newton, like Galileo, was an outsider. He came from an ordinary background but possessed an extraordinary mind. He was deeply religious but highly secretive about his beliefs. And understandably so, since, for example, he passionately rejected the idea of the Holy Trinity while spending the duration of his scientific career at Trinity College in Cambridge. Newton seems also to have been motivated to a large degree by mysticism — he wrote far more on interpretations of the Bible and on the occult than he ever did on science. The famous economist John Maynard Keynes studied Newton's private papers, a box of which he had acquired at auction, and came to this conclusion: “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.”
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Newton spent most of his early scientific years on alchemy, researching transmutation (turning base elements into gold) and trying to find the elixir of life. None of these efforts were successful; he seems to have succeeded only in poisoning himself with mercury. This poisoning may have contributed to a nervous breakdown he is believed to have suffered around the age of fifty-one, after which he largely gave up doing serious science.

Newton's mathematical researches were his magic that worked. He searched for mathematical formulae that would describe the motion of objects on Earth and the planets in space. He found spectacularly simple and successful answers. In the late sixteenth century, a series of very accurate measurements of the motions of celestial bodies were made by the astronomer Tycho Brahe from the world's greatest observatory of the time, Uraniborg in Denmark. Brahe's protégé, German mathematician and astronomer Johannes Kepler, had successfully modelled the data with some ingenious empirical rules. It fell to Newton to develop Galileo's insights into a complete mathematical theory.

BEFORE GALILEO, COPERNICUS HAD
pioneered the idea that the Earth was not the centre of the universe. The prevailing wisdom, tracing back to Aristotle and Ptolemy, held that the sun, moon, and planets moved around the Earth carried on a great interlocking system of celestial spheres, which could be carefully arranged to fit the observations. Aristotle claimed that it was just in the Earth's nature not to move. Earthly bodies followed earthly laws, and celestial bodies obeyed celestial laws.

Newton's point of view was quite different: his law of gravitation was the first step on a path towards “unification,” a single, neat set of mathematical laws describing all of physical reality. It was the most far-reaching idea, that exactly the same laws should apply everywhere — on Earth, in the solar system, right across the cosmos. Newton's law of gravitation states that the gravitational force of attraction between two objects depends only on their masses and how far apart they are. The more massive the object, the more strongly it attracts and is attracted. The farther apart two objects are, the weaker the force of attraction between them.

In order to work out the consequences of this law of gravity, Newton had to develop a theory of forces and motion. It required a whole new type of mathematics, called “calculus.” Calculus is the study of continuous processes, such as the motion of an object whose position is given as a function of time. The velocity measures the rate of change of the object's position, and the acceleration tells you the rate of change of the velocity. Both are calculated over infinitesimally small times, so calculus implicitly rests on a notion of infinitely small quantities. Once he had developed it, Newton's theory had applications well beyond gravity or the solar system. It predicts how
any
collection of objects will move when
any
set of forces acts upon it.

In describing the motion of objects, Newton's starting point was an idealization. How would an object behave if it were released in empty space, with nothing else around it? To be specific, picture a hockey puck floating all alone in an absolute void that stretches to infinity. Let's ignore gravity, or any other forces. What would you expect the puck to do? If it was all alone, and there was nothing nearby to measure its position from, how could you tell if it was moving?

Now imagine a second hockey puck, also floating freely in the void. Picture two tiny people, each of them standing on one of the pucks and seeing the other puck some way off. What do they see? And how will each puck move?

Newton's answer was simple. According to the view from either puck, the other puck will move in a straight line and at a constant speed, forever. If you imagine more and more pucks, with none more special than any other, then according to every puck's viewpoint, every other puck will move in the same way. This was Newton's first law of motion: in the absence of forces, the velocity of any object remains constant.

Let us come back down to earth, to a perfectly smooth, slippery ice rink. The world's greatest Zamboni has just gone over it. Imagine a puck sliding along the ice in a perfectly straight line. But now you skate alongside it and push it with your stick. Push on its side and the trajectory will curve; push behind it and you can speed it up. Newton's second law describes both effects in one equation: force equals mass times acceleration.

Finally, when you push on anything — the puck, another person, or the side of the rink — it pushes back at you equally hard. This is described by Newton's third law, which says that for every force there is always an equal and opposite force.

Newton's three laws are simple but incredibly powerful. They describe everything known about motion prior to the twentieth century. In combination with his law of gravitation, they explain how the force due to the sun's gravity pulls the planets inwards — just as a string pulls on a whirling stone — and bends the motion of the planets into orbit around it. According to Newton's third law, just as the string pulls in the stone or the sun pulls the Earth around it, the stone pulls the string out and the Earth pulls back on the sun, causing the sun's position to wobble back and forth slightly as the Earth goes around it. The same effect is now used to search for planets in orbit around other stars: the slight wobble in a distant star's position causes a tiny modulation in the colour of the light we receive, which can be detected. More familiar is the effect of the moon's gravitational pull on the water in Earth's oceans, which is responsible for the tides.

Implicit within these laws was the idea, dating back to Galileo, that it is only the
relative
positions and motions of objects that really matter. Galileo pointed out that a person travelling in the hold of a ship, which is sailing steadily along, simply cannot tell from watching anything inside the ship — for example, a fly buzzing around — whether the ship is moving. Today we experience the same thing when we sit in an aircraft moving at 1,000 kilometres per hour and yet everything feels just as if we are at home in our living room.

In our ice-rink world, we can see the same effect. Imagine two pucks that happen to be sliding along the ice exactly parallel to each other and moving at the same speed. From either puck's point of view, the other is not moving. However, from a third puck's point of view, both would be moving in straight lines at the same velocity. In this ice-rink world, all that really matters are the
relative
positions and
motions of the objects. Because Newton's laws never mention a velocity, the point of view of any puck moving at any constant velocity is equally valid. All such observers agree on forces and accelerations, and they would all agree that Newton's laws are valid.

The idea that the same laws of motion apply for any observer moving at a constant velocity was very important. It explained how it can be that we are moving rapidly through space around the sun without feeling any effect. Our orbital speed is huge — around 30 kilometres per second — but, as Galileo realized, it is imperceptible to us because everything around us on the surface of the Earth is travelling right alongside us, with exactly the same enormous velocity. Today we know that the sun is moving, at an even more fantastical speed of 250 kilometres per second, around our galaxy, and that our galaxy, the Milky Way, is moving at a yet greater speed of 600 kilometres per second through the universe. We are actually space travellers, but because Newton's laws do not care about our velocity, we don't feel a thing!