Chapter seven — THE MAJESTIC CLOCKWORK

When Galileo wrote the opening pages of the Dialogue on the Great World Systems about 1630, he said twice that Italian science (and trade) was now in danger of being overtaken by northern rivals. How true a prophecy that was. The man that he had most in mind was the astronomer Johannes Kepler who came to Prague in the year 1600 at the age of twenty-eight and spent his most productive years there. He devised the three laws that turned the system of Copernicus from a general description of the sun and the planets into a precise, mathematical formula.

First, Kepler showed that the orbit of a planet is only roughly circular: it is a broad ellipse in which the sun is slightly off centre, at one focus. Second, a planet does not travel at constant speed: what is constant is the rate at which the line joining the planet to the sun sweeps out the area lying between its orbit and the sun. And third, the time that a particular planet takes for one orbit — its year — increases with its (average) distance from the sun in a quite exact way.

That was the state of affairs when Isaac Newton was born in 1642, that Christmas Day. Kepler had died twelve years earlier, Galileo in that year. And not only astronomy but science stood at a watershed: the coming of a new mind that saw the crucial step from the descriptions that had done duty in the past to the dynamic, causal explanations of the future.

By the year 1650, the centre of gravity of the civilized world had shifted from Italy to Northern Europe. The obvious reason is that the trade routes of the world were different since the discovery and exploitation of America. No longer was the Mediterranean what its name implies, the middle of the world. The middle of the world had shifted north as Galileo had warned, to the fringe of the Atlantic. And with a different trade came a different political outlook, while Italy and the Mediterranean were still ruled by autocracies.

New ideas and new principles now moved forward in the Protestant seafaring nations of the north, England and the Netherlands. England was becoming Republican and Puri­tan. Dutchmen came over the North Sea to drain the English fens; the marshes became solid land. A spirit of independence grew in the flat vistas and the mists of Lincolnshire, where Oliver Cromwell recruited his Ironsides. By 1650 England was a republic which had cut off the head of its reigning monarch.

When Newton was born at his mother’s house in Woolsthorpe in 1642, his father had died some months earlier. In a little while his mother married again, and Newton was left in the care of a grandmother. He was not exactly a homeless boy, and yet from that time he shows none of the intimacy that parents give. All his life he makes’ the impression of an unloved man. He never married. He never seems to have been able to flow out in that warmth which makes achievement a natural outcome of thought honed in the company of other people. On the contrary, Newton’s achievements were solitary, and he always feared that others would steal them from him as (perhaps he thought) they had stolen his mother. We hear almost nothing of him at school or as an undergraduate.

The two years after Newton graduated at Cambridge, 1665 and 1666, were years of Plague, and he spent the times when the University was closed at home. His mother was widowed and back at Woolsthorpe. Here he struck his vein of gold: mathematics. Now that his notebooks have been read, it is clear that Newton had not been well taught, and that he proved most of the mathematics he knew for himself. Then he went on to original discovery. He invented fluxions, what we now call the calculus. Newton kept fluxions as his secret tool; he discovered his results with it, but he wrote them out in conventional mathematics.

Here Newton also conceived the idea of universal gravitation, and at once tested it by calculating the motion of the moon round the earth. The moon was a powerful symbol for him. If she follows her orbit because the earth attracts her, he reasoned, then the moon is like a ball (or an apple) that has been thrown very hard: she is falling towards the earth, but is going so fast that she constantly misses it — she keeps on going round because the earth is round. How great must the force of attraction be?

I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centres about which they revolve; and thereby compared the force requisite to keep the moon in her orb with the force of gravity at the surface of the earth; and found them answer pretty nearly.

The understatement is characteristic of Newton; his first rough calculation had, in fact, given the period of the moon close to its true value, about 27 1/4 days.

When the figures come out right like that, you know as Pythagoras did that a secret of nature is open in the palm of your hand. A universal law governs the majestic clockwork of the heavens, in which the motion of the moon is one harmonious incident. It is a key that you have put into the lock and turned, and nature has yielded in numbers the confirmation of her structure. But, if you are Newton, you do not publish it.

When he went back to Cambridge in 1667, Newton was made a Fellow of his college, Trinity. Two years later his professor resigned the chair of mathematics. It may not have been explicitly in favour of Newton, as used to be thought, but the effect was the same — Newton was appointed. He was then twenty-six.

Newton published his first work in optics. It was conceived like all of his great thought ‘in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention’. Newton was not at home but had gone back to Trinity College, Cambridge, for a short interval when the Plague slackened.

It is odd to find that a man whom we regard as the master of explanation of the material universe should have begun by thinking about light. There are two reasons for that. First of all, this was a mariner’s world, in which the bright minds of England were occupied with all the problems that arose from seafaring. Men like Newton did not think of themselves as doing technical research, of course — that would be too naive an explanation of their interest. They were drawn to the topics that their important elders argued about, as young men have always been. The telescope was a salient problem of the time. And indeed, Newton was first aware of the problem of colours in white light when he was grinding lenses for his own telescope.

But of course, there is beneath this a more fundamental reason. Physical phenomena consist always of the interac­tion of energy with matter. We see matter by light; we are aware of the presence of light by the interruption by matter. And that thought makes up the world of every great physicist, who finds that he cannot deepen his understanding of one without the other.

In 1666 Newton began to think about what caused the fringes at the edge of a lens, and looked at the effect by simulating it by a prism. Every lens at its edge is a little prism. Now of course the fact that the prism gives you , coloured light is a commonplace at least as old as Aristotle. But, alas, so were the explanations of the time, because they made no analysis of quality. They simply said the white light comes through the glass, and it is darkened a little at the thin end, so it only becomes red; it is darkened a little more where the glass is thicker, and becomes green; it is darkened a little more where the glass is thickest, so it becomes blue. Marvellous! for the whole account explains absolutely nothing, yet sounds very plausible. The obvious thing that it does not explain, as Newton pointed out, was self-evident the moment he let the sunlight in through a chink to pass through his prism. It was this: the sun comes in as a circular disc, but it comes out as an elongated shape. Everybody knew that the spectrum was elongated; that also had been known for a thousand years in some way to those who cared to look. But it takes a powerful mind like Newton to break his head on explaining the obvious. And Newton said that the obvious is that the light is modified; the light is physically separated.

That is a fundamentally new idea in scientific explana­tion, quite inaccessible to his contemporaries. Robert Hooke argued with him, every kind of physicist argued with him; until Newton got so bored with all the arguments that he wrote to Leibniz,

I was so persecuted with discussions arising from the publi­cation of my theory of light that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow.

From that time on he really refused to have anything to do with debate at all — and certainly with the debaters like Hooke. He would not publish his book on optics until 1704, a year after Hooke died, having warned the president of the Royal Society:

I intend to be no farther solicitous about matters of Philosophy and therefore I hope you will not take it ill if you find me never doing anything more in that kind.

But let us begin at the beginning, in Newton’s own words. In the year 1666

I procured me a Triangular glass-Prisme, to try therewith the celebrated Phaenomenaof Colours. And in order thereto having darkened my chamber, and made a small hole in my window — shuts, to let in a convenient quantity of the Suns light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colours produced thereby; but after a while applying my self to consider them more circumspectly, I became surprised to see them in an oblong form; which, according to the received laws of Refraction, I expected should have been circular.

And I saw . . . that the light, tending to [one] end of the Image, did suffer a Refraction considerably greater than the light tending to the other. And so the true cause of the length of that Image was detected to be no other, then that Light consists of Rays differently refrangible, which, without any respect to a difference in their incidence, were, according to their degrees of refrangibility, transmitted towards divers parts of the wall.

The elongation of the spectrum was now explained; it was caused by the separation and fanning out of the colours. Blue is bent or refracted more than red, and that is an absolute property of the colours.

Then I placed another Prisme ... so that the light . . . might pass through that also, and he again refracted before it arrived at the wall. This done, I took the first Prisme in my hand and turned it to and fro slowly about its Axis, so much as to make the several parts of the Image . . . successively pass through . . . that I might observe to what places on the wall the second Prisme would refract them.

When any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retained its colour, notwithstanding my utmost endeavours to change it.

With that, the traditional view was routed; for if light were modified by glass, the second prism should produce new colours, and turn red to green or blue. Newton called this the critical experiment. It proved that once the colours are separated by refraction, they cannot be changed any further.

I have refracted it with Prismes, and reflected with it Bodies which in Day-light were of other colours; I have intercepted it with the coloured film of Air interceding two compressed plates of glass; transmitted it through coloured Mediums, and through Mediums irradiated with other sorts of Rays, and diversly terminated it; and yet could never produce any new colour out of it.

But the most surprising, and wonderful composition was that of Whiteness. There is no one sort of Rays which alone can exhibit this. ‘Tis ever compounded, and to its composition are requisite all the aforesaid primary Colours, mixed in a due proportion. I have often with Admiration beheld, that all the Colours of the Prisme being made to converge, and thereby to be again mixed, reproduced light, intirely and perfectly white.

Hence therefore it comes to pass, that Whiteness is the usual colour of Light; for, Light is a confused aggregate of Rays indued with all sorts of Colors, as they are promiscuously darted from the various parts of luminous bodies.

That letter was written to the Royal Society shortly after Newton was elected a Fellow in 1672. He had shown himself to be a new kind of experimenter, who understood how to form a theory and how to test it decisively against alternatives. He was rather proud of his achievement.

A naturalist would scarce expect to see ye science of those colours become mathematicall, and yet I dare affirm that there is as much certainty in it as in any other pan of Opticks.

Newton had begun to have a reputation in London as well as in the University; and a sense of colour seems to spread into that metropolitan world, as if the spectrum scattered its light across the silks and spices the merchants brought to the capital.

The palette of painters became more varied, there was a taste for richly coloured objects from the East, and it became natural to use many colour words. This is very clear in the poetry of the time. Alexander Pope, who was sixteen when Newton published the Opticks, was surely a less sensuous poet than Shakespeare, yet he uses three or four times as many colour words as Shakespeare, and uses them about ten times as often. For instance, Pope’s description of fish in the Thames,

The bright-ey’d Perch with Fins of Tyrian Dye,

The Majestic Clockwork

The silver Eel, in shining Volumes roll’d,

The yellow Carp, in Scales bedrop’d with Gold,

Swift Trouts, diversify’d with Crimson Stains,

would be inexplicable if we did not recognize it as an exercise in colours.

A metropolitan reputation meant, inevitably, new contro­versies. Results that Newton outlined in letters to London scientists were bandied about. That was how there began, after 1676, a long and bitter dispute with Gottfried Wilhelm Leibniz about priority in the calculus. Newton would never believe that Leibniz, a powerful mathematician himself, had conceived it independently.

Newton thought of retiring altogether from science into his cloister at Trinity. The Great Court was a spacious setting for a scholar in comfortable circumstances; he had his own small laboratory and his own garden. In Neville’s Court Wren’s great library was being built. Newton sub­scribed £40 to the fund. It seemed that he might look forward to a donnish life devoted to private study. But, in the end, if he refused to bustle among the scientists in London, they would come to Cambridge to put their arguments to him.

Newton had conceived the idea of a universal gravitation in the Plague year of 1666 and had used it, very success­fully, to describe the motion of the moon round the earth. It seems extraordinary that in nearly twenty years that followed he should have made almost no attempt to publish anything about the bigger problem of the motion of the earth round the sun. The stumbling block is uncertain, but the facts are plain. Only in 1684 did there arise in London an argument between Sir Christopher Wren, Robert Hooke and the young astronomer Edmond Halley, as a result of which Halley came to Cambridge to see Newton.

After they had been some time together, the doctor [Halley] asked him what he thought the curve would be that would be described by the planets, supposing the force of attraction towards the sun to be reciprocal to the square of their distance from it. Sir Isaac replied immediately that it would be an ellipsis. The doctor, struck with joy and amazement, asked him how he knew it. ‘Why,’ saith he, ‘I have calculated it.’ Whereupon Dr Halley asked him for his calculation without any further delay. Sir Isaac looked among his papers but could not find it, but he promised him to renew it, and then to send it him.

It took three years, from 1684 to 1687, before Newton wrote out the proof, and it came out as long as — well, in full, as long as the Principia. Halley nursed, wheedled, and even financed the Principia, and Samuel Pepys accepted it as president of the Royal Society in 1687.

As a system of the world, of course, it was sensational from the moment it was published. It is a marvellous description of the world subsumed under a single set of laws. But much more, it is also a landmark in scientific method. We think of the presentation of science as a series of propositions, one after another, as deriving from the mathematics of Euclid. And so it does. But it is not until Newton turned this into a physical system, by changing mathematics from a static to a dynamic account, that modern scientific method really begins to be rigorous.

And we can see in the book actually where the stumbling blocks were that kept him from pushing on after the orbit of the moon had come out so well. For instance, I am convinced that it is because he could not solve the problem at Section 12 on ‘How does a sphere attract a particle?’ At Woolsthorpe he had calculated roughly, treating the earth and the moon as particles. But they (and the sun and the planets) are large spheres; can the gravitational attraction between them be accurately replaced by an attraction between their centres? Yes, but only (it turned out, ironically) for attractions that fall off as the square of the distance. And in that we see the immense mathematical difficulties that he had to overcome before he could publish.

When Newton was challenged on such questions as ‘You have not explained why gravity acts’, ‘You have not explained how action at a distance could take place’, or indeed ‘You have not explained why rays of light behave the way they do’, he always answered in the same terms: ‘I do not make hypotheses’. By which he meant, ‘I do not deal in metaphysical speculation. May down a law, and derive the phenomena from it’. That was exactly what he had said in his work on optics, and exactly what had not been understood by his contemporaries as a new outlook in optics.

Now if Newton had been a very plain, very dull, very matter-of-fact man, all that would be easily explicable. But I must make you see that he was not. He was really a most extraordinary, wild character. He practised alchemy. In secret, he wrote immense tomes about the Book of Revel­ation. He was convinced that the law of inverse squares was really already to be found in Pythagoras. And for such a man, who in private was full of these wild metaphysical and mystical speculations, to hold this public face and say, ‘I make no hypotheses’ — that is an extraordinary expression of his secret character. William Wordsworth in The Prelude has a vivid phrase,

Newton, with his prism and silent face,

which sees and says it exactly.

Well, the public face was very successful. Of course, Newton could not get promotion in the University, because he was a Unitarian — he did not accept the doctrine of the Trinity, with which scientists in his time were tempera­mentally ill at ease. Therefore he could not become a parson, therefore he could not possibly become the Master of a College. So, in 1696, Newton went to London to the Mint. In time he became Master of the Mint. After Hooke’s death he accepted the Presidency of the Royal Society in 1703. He was knighted by Queen Anne in 1705. And to his death in 1727 he dominated the intellectual landscape of London. The village boy had made good.

The sad thing is that I think he had made good not by his own standards, but only by the standards of the eighteenth century. The sad thing is that it was that society whose criterion he accepted, when he was willing to be a dictator in the councils of the Establishment and count that success.

An intellectual dictator is not a sympathetic figure, even when he has risen from humble beginnings. Yet in his private writings, Newton was not so arrogant as he seems in his public face, so often and so variously represented.

To explain all nature is too difficult a task for any one man or even for any one age. ‘Tis much better to do a little with certainty, and leave the rest for others that come after you, than to explain all things.

And in a more famous sentence he says the same thing less precisely but with a hint of pathos.

I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, while the great ocean of truth lay all undiscovered before me.

By the time Newton was in his seventies, little real scientific work was done in the Royal Society. England under the Georges was preoccupied with money (these are the years of the South Sea Bubble), with politics, and with scandal. In the coffee houses, nimble businessmen floated com­panies to exploit fictitious inventions. Writers poked fun at scientists, in part from spite, and in part from political motives, because Newton was a bigwig in the government establishment.

In the winter of 1713 a group of disgruntled Tory writers formed themselves into a literary society. Until Queen Anne died the next summer, it met often in the rooms in St James’s Palace of her physician, Dr John Arbuthnot. The society was called the Scriblerus Club, and set out to ridicule the learned societies of the day. Jonathan Swift’s attack on the scientific community in the third book of Gulliver’s Travels rose out of their discussions. The group of Tories, who later helped John Gay to satirize the government in The Beggar’s Opera, also helped him in 1717 to write a play Three Hours After Marriage. There the butt of the satire is a pompous, ageing scientist under the name of Dr Fossile. Here are some typical scenes from the play between him and an adventurer, Plotwell, who is having an affair with the lady of the house.

Fossile: I promis’d Lady Longfort my eagle-stone. The poor lady is like to miscarry, and ‘tis well I thought on’t. Hah! Who is here! I do not like the aspect of the fellow. But I will not be over censorious.

Plotwell: Illustrissime domine, huc adveni —

Fossile: Illustrissime domine — non usus sum loquere Latinam — If you cannot speak English, we can have no lingual conversation.

Plotwell: I can speak but a little Englise. I have great deal heard of de fame of de great luminary of all arts and sciences, de illustrious doctor Fossile. I would make commutation (what do you call it), I would exchange some of my tings for some of his tings.

The first topic of fun, naturally, is alchemy; the technical jargon is quite correct throughout.

Fossile: Pray, Sir, what university are you of?

Plotwell: De famous university of Cracow . . .

Fossile: . . . But what Arcana are you master of, Sir?

Plotwell: See dere, Sir, dat box de snuff.

Fossile: Snuff-box.

Plotwell: Right. Snuff-box. Dat be de very true gold.

Fossile: What of that?

Plotwell: Vat of dat? Me make dat gold my own self, of de lead of de great church of Cracow.

Fossile: By what operations?

Plotwell: By calcination; reverberation; purification; sublima­tion; amalgumation; precipitation; volitilization.

Fossile: Have a care what you assert. The volitilization of gold is not an obvious process . . .

Plotwell: I need not acquaint de illustrious doctor Fossile, dat all de metals be but unripe gold.

Fossile: Spoken like a philosopher. And therefore there should be an act of parliament against digging of lead mines, as against felling young timber.

The scientific references come quick and fast now: to the troublesome problem of finding the longitude at sea, to the invention of fluxions or the differential calculus,

Fossile: I am not at present dispos’d for experiments.

Plotwell: ... Do you deal in longitudes, Sir?

Fossile: I deal not in impossibilities. I search only for the grand elixir.

Plotwell: Vat do you tink of de new metode of fluxion?

Fossile: I know no other but by mercury.

Plotwell: Ha, ha. Me mean de fluxion of de quantity.

Fossile: The greatest quantity I ever knew was three quarts a day.

Plotwell: Be dere any secret in the hydrology, zoology, mineralogy, hydraulicks, acausticks, pneumaticks, logarithmatechny, dat you do want de explanation of?

Fossile: This is all out of my way.

It seems irreverent to us that Newton should have been subject to satire in his lifetime, and subject to serious criticism too. But the fact is that every theory, however majestic, has hidden assumptions, which are open to challenge and, indeed, in time will make it necessary to replace it. And Newton’s theory, beautiful as an approxi­mation to nature, was bound to have the same defect. Newton confessed it. The prime assumption he made is this: that he said at the outset, ‘I take space to be absolute’. By that he meant that space is everywhere flat and infinite as it is in our own neighbourhood. And Leibniz criticized that from the outset, and rightly. After all, it is not even probable in our own experience. We are used to living locally in a flat space, but as soon as we look in the large at the earth, we know it not to be so overall.

The earth is spherical; so that the point at the North Pole can be sighted by two observers oil the equator who are far apart, yet each of whom says, ‘I am looking due North’. Such a state of affairs is inconceivable to an inhabitant of a flat earth, or one who believes that the earth is as flat overall as it seems to be near him. Newton was really behaving like a flat-earther on a cosmic scale: sailing out into space with his foot-rule in one hand and his pocket — watch in the other, mapping space as if it were everywhere as it is here. And that is not necessarily so.

It is not even as if space has to be spherical everywhere — that is, must have a positive curvature. It might well be that space is locally lumpy and undulating. We can conceive of a kind of space that has saddle-points in it, over which massive bodies slide in some directions more easily than in others. The motions of the heavenly bodies must still be the same, of course — we see them and our explanations must fit them. But the explanations would then be different in kind. The laws that govern the moon and the planets would be geometrical and not gravitational.

At that time they were all speculations far in the future, and even if they had been uttered, the mathematics of the day could not cope with them. But thoughtful and philo­sophic minds were aware that, in laying out space as an absolute grid, Newton had given an unreal simplicity to our perception of things. In contrast, Leibniz had said the prophetic words, ‘I hold space to be something purely relative, as time is’.

Time is the other absolute in Newton’s system. Time is crucial to mapping the heavens: we do not know in the first place how far away the stars are, only at what moment they pass across our line of sight. So the mariner’s world called for the perfection of two sets of instruments: telescopes and clocks.

First, then, improvements in the telescope. They were now centred in the new Royal Observatory at Greenwich. The ubiquitous Robert Hooke had planned that when he was rebuilding London with Sir Christopher Wren after the Great Fire. The sailor trying to fix his position — longitude and latitude — off a remote shore from now on would compare his readings of the stars with those at Greenwich. The meridian of Greenwich became the fixed mark in every sailor’s storm-tossed world: the meridian, and Greenwich Mean Time.

Second as an essential aid to fixing a position was the improvement of the clock. The clock became the symbol and the central problem of the age, because Newton’s theories could only be put to practical use at sea if a clock could be made to keep time on a ship. The principle is simple enough. Since the sun rounds the earth in twenty — four hours, each of the 360 degrees of longitude occupies four minutes of time. A sailor who compares noon on his ship (the highest position of the sun) with noon on a clock that keeps Greenwich time therefore knows that every four minutes of difference place him one degree further away from the Greenwich meridian.

The government offered a prize of £20,000 for a timekeeper that would prove itself accurate to half a degree on a voyage of six weeks. And the London clock-makers (John Harrison, for instance) built one ingenious clock after another, designed so that their several pendulums should, between them, correct for the lurch of the ship.

These technical problems set off a burst of invention, and established the preoccupation with time that has dominated science and our daily lives ever since. A ship indeed is a kind of model of a star. How does a star ride through space, and how do we know what time it keeps? The ship is a starting point for thinking about relative time.

The clock-makers of the day were aristocrats among workmen, as the master-masons had been in the Middle Ages. It is a nice reflection that the clock as we know it, the pacemaker strapped to our pulse or the pocket dictator of modern life, had since the Middle Ages fired the skill of craftsmen too, in a leisurely way. In those days the early clock-makers wanted, not to know the time of day, but to reproduce the motions of the starry heavens.

The universe of Newton ticked on without a hitch for about two hundred years. If his ghost had come to Switzerland any time before 1900, all the clocks would have chimed hallelujah in unison. And yet, just after 1900 in Berne, not two hundred yards from the ancient clock — tower, a young man came to live who was going to set them all by the ears: Albert Einstein.

Time and light first began to go awry just about this time. It was in 1881 that Albert Michelson carried out an experiment (which he repeated with Edward Morley six years later) in which he fired light in different directions, and was taken aback to find that however the apparatus moved, always he came out with the same speed of light. That was quite out of keeping with Newton’s laws. And it was that small murmur at the heart of physics which first set scientists agog and questioning, about 1900.

It is not certain that the young Einstein was quite up-to — date about this. He had not been a very attentive university student. But it is certain that by the time he went to Berne he had already asked himself, years earlier as a boy in his teens, what our experience would look like seen from the point of view of light.

The answer to the question is full of paradox, and that makes it hard. And yet, as with all paradox, the hardest part is not to answer but to conceive the question. The genius of men like Newton and Einstein lies in that: they ask transparent, innocent questions which turn out to have catastrophic answers. The poet William Cowper called Newton a ‘childlike sage’ for that quality, and the descrip­tion perfectly hits the air of surprise at the world that Einstein carried in his face. Whether he talked about riding a beam of light or falling through space, Einstein was always full of beautiful, simple illustrations of such prin­ciples, and I shall take a leaf out of his book. I go to the bottom of the clocktower, and get into the tram he used to take every day on his way to work as a clerk in the Swiss Patent Office.

The thought that Einstein had had in his teens was this: ‘What would the world look like if I rode on a beam of light?’ Suppose this tram were moving away from that clock on the very beam with which we see what the clock says. Then, of course, the clock would be frozen. I, the tram, this box riding on the beam of light would be fixed in time. Time would have a stop.

Let me spell that out. Suppose the clock behind me says ‘noon’ when I leave. I now travel 186,000 miles away from it at the speed of light; that ought to take me one second. But the time on the clock, as I see it, still says ‘noon’, because it takes the beam of light from the clock exactly as long as it has taken me. So far as the clock as I see it, so far as the universe inside the tram is concerned, in keeping up with the speed of light I have cut myself off from the passage of time.

That is an extraordinary paradox. I will not go into its implications, or others that Einstein was concerned with. I will just concentrate on this point: that if I rode on a beam of light, time would suddenly come to an end for me. And that must mean that, as I approach the speed of light (which is what I am going to simulate in this tram), I am alone in my box of time and space, which is more and more departing from the norms round me.

Such paradoxes make two things clear. An obvious one: there is no universal time. But a more subtle one: that experience runs very differently for the traveller and the stay-at-home — and so for each of us on his own path. My experiences within the tram are consistent: I discover the same laws, the same relations between time, distance, speed, mass and force, that every other observer discovers. But the actual values that I get for time, distance, and so on, are not the same that the man on the pavement gets.

That is the core of the Principle of Relativity. But the obvious question is ‘Well, what holds his box and mine together?’ The passage of light: light is the carrier of information that binds us. And that is why the crucial experimental fact is the one that puzzled people since 1881: that when we exchange signals, then we discover that information passes between us always at the same pace. We always get the same value for the speed of light. And then naturally time and space and mass must be different for each of us, because they have to give the same laws for me here in the tram and for the man outside, consistently — yet the same value for the speed of light.

Light and the other radiations are signals that spread out from an event like ripples through the universe, and there is no way in which news of the event can move outwards faster than they do. The light or the radio wave or the X — ray is the ultimate carrier of news or messages, and forms a basic network of information which links the material universe together. Even if the message that we want to send is simply the time, we cannot get it from one place to another faster than the light or the radio wave that carries it. There is no universal time for the world, no signal from Greenwich by which we can set our watches without getting the speed of light inextricably tied up in it.

In this dichotomy, something has to give. For the path of a ray of light (like the path of a bullet) does not look the same to a casual bystander as to the man who fired it on the move. The path looks longer to the bystander; and therefore the time that the light takes on its path must seem longer to him, if he is to get the same value for its speed.

Is that real? Yes. We know enough now about cosmic and atomic processes to see that at high speeds that is true. If I were really travelling at, say, half the speed of light, then what I have been making three minutes and a little on my watch, Einstein’s tram-ride, would be half a minute longer for the man on the pavement.

We will take the tram up towards the speed of light to see what the appearances look like. The relativity effect is that things change shape. (There are also changes in colour, but they are not due to relativity.) The tops of the buildings seem to bend inwards and forwards. The buildings also seem crowded together. I am travelling horizontally, so horizontal distances seem shorter; but the heights remain the same. Cars and people are distorted in the same way: thin and tall. And what is true for me looking out is true for the man outside looking in. The Alice in Wonderland world of relativity is symmetrical. The observer sees the tram crushed together: thin and tall.

Evidently this is an altogether different picture of the world from that which Newton had. For Newton, time and space formed an absolute framework, within which the material events of the world ran their course in imperturbable order. His is a God’s eye view of the world: it looks the same to every observer, wherever he is and however he travels. By contrast, Einstein’s is a man’s eye view, in which what you see and what I see is relative to each of us, that is, to our place and speed. And this relativity cannot be removed. We cannot know what the world is like in itself, we can only compare what it looks like to each of us, by the practical procedure of exchanging messages. I in my tram and you reading this can share no divine and instant view of events — we can only communi­cate our own views to one another. And communication is not instant; we cannot remove from it the basic time-lag of all signals, which is set by the speed of light.

The tram did not reach the speed of light. It stopped, very decently, near the Patent Office. Einstein got off, did a day’s work, and often of an evening stopped at the Café Bollwerk. The work at the Patent Office was not very taxing. To tell the truth, most of the applications now look pretty idiotic: an application for an improved form of pop gun; and application for the control of alternating current, of which Einstein wrote succinctly, ‘It is incorrect, inaccurate, and unclear’.

In the evenings at the Cafe Bollwerk he would talk a little physics with his colleagues. He would smoke cigars and drink coffee. But he was a man who thought for himself. He went to the heart of the question, which is ‘How in fact do, not physicists but human beings, communicate with one another? What signals do we send from one to another? How do we reach knowledge?’ And that is the crux of all his papers, this unfolding of the heart of knowledge, almost petal by petal.

So the great paper of 1905 is not just about light or, as its title says, The Electrodynamics of Moving Bodies. It goes on in the same year to a postscript saying energy and mass are equivalent, E=mc2. To us, it is remarkable that the first account of relativity should instantly entail a practical and devastating prediction for atomic physics. To Einstein, it is simply a part of drawing the world together; like Newton and all scientific thinkers, he was in a deep sense a unitarian. That comes from a profound insight into the processes of nature herself, but particularly into the rela­tions between man, knowledge, nature. Physics is not events but observations. Relativity is the understanding of the world not as events but as relations.

Einstein looked back to those years with pleasure. He said to my friend Leo Szilard many years after, ‘They were the happiest years of my life. Nobody expected me to lay golden eggs’. Of course, he did go on laying golden eggs: quantum effects, general relativity, field theory. With them came the confirmation of Einstein’s early work, and the harvest of his predictions. In 1915 he predicted, in the General Theory of Relativity, that the gravitational field near the sun would cause a glancing ray of light to bend inwards — like a distortion of space. Two expeditions sent by the Royal Society to Brazil and the west coast of Africa tested the prediction during the eclipse on 29 May 1919. To Arthur Eddington, who was in charge of the African expedition, his first measurement of the photographs taken there always stayed in his memory as the greatest moment in his life. Fellows of the Royal Society rushed the news to one another; Eddington by telegram to the mathematician Littlewood, and Littlewood in a hasty note to Bertrand Russell,

Dear Russell:

Einstein’s theory is completely confirmed. The predicted displacement was 1“.72 and the observed value 1".75 :1: 0.6.

Yours J.E.L.

Relativity was a fact, in the special theory and the general. E=mc² was confirmed in time, of course. Even the point about clocks running slow was singled out at last by an inexorable fate. In 1905 Einstein had written a slightly comic prescription for an ideal experiment to test it.

If there are two synchronized clocks at A and if one of these is moved along a closed curve with constant velocity v until it returns to A, which we suppose to take t seconds, then the latter clock on arriving at A will have lost 1/2 t (v/c )2 seconds by comparison with the clock which has remained stationary. We conclude from this that a clock fixed at the Earth’s equator will run slower by a very small amount than an identical clock fixed at one of the Earth’s poles.

Einstein died in 1955, fifty years after the great 1905 paper. But by then one could measure time to a thousand millionth of a second. And therefore it was possible to look at that odd proposal to ‘think of two men on earth, one at the North Pole and one at the Equator. The one at the Equator is going round faster than the one at the North Pole; therefore his watch will lose’. And that is just how it turned out.

The experiment was done by a young man called H. J. Hay at Harwell. He imagined the earth squashed flat into a plate, so that the North Pole is at the centre and the equator runs round the rim. He put a radio-active clock on the rim and another at the centre of the plate and let it turn. The clocks measure time statistically by counting the number of radio-active atoms that decay. And sure enough, the clock at the rim of Hay’s plate keeps time more slowly than the clock at the centre. That goes on in every spinning plate, on every turntable. At this moment, in every revolving gramophone disc, the centre is ageing faster than the rim with every turn.

Einstein was the creator of a philosophical more than a mathematical system. He had a genius for finding philo­sophical ideas that gave a new view of practical experience. He did not look at nature like a God but like a pathfinder, that is, a man inside the chaos of her phenomena who believed that there is a common pattern visible in them all if we look with fresh eyes. He wrote in The World as I See It:

We have forgotten what features in the world of experience caused us to frame (pre-scientific) concepts, and we have great difficulty in representing the world of experience to ourselves without the spectacles of the old-established conceptual inter­pretation. There is the further difficulty that our language is compelled to work with words which are inseparably connected with those primitive concepts. These are the obstacles which confront us when we try to describe the essential nature of the pre-scientific concept of space.

So in a lifetime Einstein joined light to time, and time to space; energy to matter, matter to space, and space to gravitation. At the end of his life, he was still working to seek a unity between gravitation and the forces of electricity and magnetism. That is how I remember him, lecturing in the Senate House at Cambridge in an old sweater and carpet slippers with no socks, to tell us what kind of a link he was trying to find there, and what difficulties he was running his head against.

The sweater, the carpet slippers, the dislike of braces and socks, were not affectations. Einstein seemed to express, when one saw him, an article of faith from William Blake: ‘Damn braces: Bless relaxes’. He was quite unconcerned about worldly success, or respectability, or con­formity; most of the time he had no notion of what was expected of a man of his eminence. He hated war, and cruelty, and hypocrisy, and above all he hated dogma - except that hate is not the right word for the sense of sad revulsion that he felt; he thought hate itself a kind of dogma. He refused to become president of the state of Israel because (he explained) he had no head for human problems. It was a modest criterion, which other presidents might adopt; there would not be many survivors.

It is almost impertinent to talk of the ascent of man in the presence of two men, Newton and Einstein, who stride like gods. Of the two, Newton is the Old Testament god; it is Einstein who is the New Testament figure. He was full of humanity, pity, a sense of enormous sympathy. His vision of nature herself was that of a man being in the presence of something god-like, and that is what he always said about nature. He was fond of talking about God: ‘God does not play at dice,’ ‘God is not malicious’. Finally Niels Bohr one day said to him, ‘Stop telling God what to do’. But that is not quite fair. Einstein was a man who could ask immensely simple questions. And what his life showed, and his work, is that when the answers are simple too, then you hear God thinking.

Date: 2016-01-14; view: 811