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Chapter ten — WORLD WITHIN WORLD

 

There are seven basic shapes of crystals in nature, and a multitude of colours. The shapes have always fascinated men, as figures in space and as descriptions of matter; the Greeks thought their elements were actually shaped like the regular solids. And it is true in modern terms that the crystals in nature express something about the atoms that compose them: they help to put the atoms into families. This is the world of physics in our own century, and crystals are a first opening into that world.

Of all the variety of crystals, the most modest is the simple colourless cube of common salt; and yet it is surely one of the most important. Salt has been mined at the great salt mine at Wieliczka near the ancient Polish capital of Cracow for nearly a thousand years, and some of the wooden workings and horse-drawn machinery have been preserved from the seventeenth century. The alchemist Paracelsus may have come this way on his eastern travels. He changed the course of alchemy after ad1500 by insisting that among the elements that constitute man and nature must be counted salt. Salt is essential to life, and it has always had a symbolic quality in all cultures. Like the Roman soldiers, we still say ‘salary’ for what we pay a man, though it means ‘salt money’. In the Middle East a bargain is still sealed with salt in what the Old Testament calls ‘a covenant of salt forever’.

In one respect Paracelsus was wrong; salt is not an element in the modern sense. Salt is a compound of two elements: sodium and chlorine. That is remarkable enough, that a white fizzy metal like sodium, and a yellowish poisonous gas like chlorine, should finish up by making a stable structure, common salt. But more remarkable is that sodium and chlorine belong to families. There is an orderly gradation of similar properties within each family, sodium belongs to the family of alkali metals, and chlorine to the active halogens. The crystals remain unchanged, square and transparent, as we change one member of a family for another. For instance, sodium can certainly be replaced by potassium: potassium chloride. Similarly in the other family the chlorine can be replaced by its sister element bromine: sodium bromide. And, of course, we can make a double change: lithium fluoride, in which sodium has been replaced by lithium, chlorine by fluorine. And yet all the crystals are indistinguishable by the eye.

What makes these family likenesses among the elements? In the 1860s everyone was scratching their heads about that, and several scientists moved towards rather similar answers. The man who solved the problem most triumphantly was a young Russian called Dmitri Ivanovich Mendeleev, who visited the salt mine at Wieliczka in 1859. He was twenty-five then, a poor, modest, hardworking and brilliant young man. The youngest of a vast family of at least fourteen children, he had been the darling of his widowed mother, who drove him through science by her ambition for him.

What distinguished Mendeleev was not only genius, but a passion for the elements. They became his personal friends; he knew every quirk and detail of their behaviour. The elements, of course, were distinguished each by only one basic property, that which John Dalton had proposed originally in 1805: each element has a characteristic atomic weight. How do the properties that make them alike or different flow from that single given constant or parameter? This was the underlying problem and Mendeleev worked at this. He wrote the elements out on cards, and he shuffled the cards in a game that his friends used to call Patience.



Mendeleev wrote on his cards the atoms with their atomic weights, and dealt them out in vertical columns in the order of their atomic weights. The lightest, hydrogen, he did not really know what to do with and he sensibly left it outside his scheme. The next in atomic weight is helium, but luckily Mendeleev did not know that because it had not yet been found on earth — it would have been an awkward maverick until its sister elements were found much later.

Mendeleev therefore began his first column with the element lithium, one of the alkali metals. So it is lithium (the lightest that he knew after hydrogen), then beryllium, then boron, then the familiar elements, carbon, nitrogen, oxygen, and then as the seventh in his column, fluorine. The next element in order of atomic weights is sodium, and since that has a family likeness to lithium, Mendeleev decided this was the place to start again and form a second column parallel to the first. The second column goes on with a sequence of familiar elements: magnesium, alumin­ium, silicon, phosphorus, sulphur, and chlorine. And sure enough, they make a complete column of seven, so that the last element, chlorine, stands in the same horizontal row as fluorine.

Evidently there is something in the sequence of atomic weights that is not accidental but systematic. It is clear again as we begin the next column, the third. The next elements in order of atomic weights after chlorine are potassium, then calcium. Thus the first row so far contains lithium, sodium, and potassium, which are all alkali metals; and the second row so far contains beryllium, magnesium, and calcium, which are metals with another set of family likenesses. The fact is that the horizontal rows on this arrangement makes sense: they put families together. Mendeleev had found, or at least had found evidence for, a mathematical key among the elements. If we arrange them in order of atomic weight, take seven steps to make a vertical column, and start afresh after that with the next column, then we get family arrangements falling together in the horizontal rows.

 

So far we can follow Mendeleev’s scheme without a hitch, just as he set it out in 1871, two years after the first conception. Nothing falls out of step until the third column — and then, inevitably, the first problem. Why inevitably? Because, as you can see from the case of helium, Mendeleev did not have all the elements. Sixty-three out of the total of ninety-two were known; so sooner or later he was bound to come to gaps. And the first gap he came to was where I stopped, at the third place in the third column.

I say that Mendeleev came to a gap, but that abbreviated form of words conceals what is most formidable in his thought. At the third place in the third column Mendeleev came to a difficulty, and he solved the difficulty by interpreting it as a gap. He made that choice because the next known element, namely titanium, simply does not have the properties that would fit it there, in the same horizontal row or family with boron and aluminium. So he said, ‘There is a missing element there, and when it is found its atomic weight will put it before titanium. Opening the gap will put the later elements of the column into the right horizontal rows; titanium belongs with carbon and silicon’ — and indeed it does in the basic scheme.

The conception of the gaps or missing elements was a scientific inspiration. It expressed in practical terms what Francis Bacon had proposed in general terms long ago, the belief that new instances of a law of nature can be guessed or induced in advance from old instances. And Mendeleev’s guesses showed that induction is a more subtle process in the hands of a scientist than Bacon and other philosophers supposed. In science we do not simply march along a linear progression of known instances to unknown ones. Rather, we work as in a crossword puzzle, scanning two separate progressions for the points at which they intersect: that is where the unknown instances should lie in hiding. Men­deleev scanned the progression of atomic weights in the columns, and the family likenesses in the rows, to pinpoint the missing elements at their intersections. By doing so, he made practical predictions, and he also made manifest (what is still poorly understood) how scientists actually carry out the process of induction.

Very well: the points of greatest interest are the gaps that lie in the third and fourth columns. I will not go on building the table beyond there — except to say that when you count the gaps and go on down, sure enough, the column ends where it should, at bromine in the halogen family. There were a number of gaps, and Mendeleev singled out three. The first I have just pointed to in the third column and third row. The other two are in the fourth column, in the third and fourth rows. And of them Mendeleev prophesied that on discovery it would be found, not only that they have atomic weights that fit into the vertical progression, but that they would have those properties that are appropriate to the families in the third and fourth horizontal rows.

For instance, the most famous of Mendeleev’s forecasts, and the last to be confirmed, was the third — what he called eka-silicon. He predicted the properties of this strange and important element with great exactitude, but it was nearly twenty years before it was found in Germany, and called not after Mendeleev, but germanium. Having begun from the principle that ‘eka-silicon will have properties inter­mediate between silicon and tin’, he had predicted that it would be 5*5 times heavier than water; that was right. He predicted that its oxide would be 4-7 times heavier than water; that was right. And so on with chemical and other properties.

These forecasts made Mendeleev famous everywhere — except in Russia: he was not a prophet there, because the Tsar did not like his liberal politics. The later discovery in England of a whole new row of elements, beginning with helium, neon, argon, enlarged his triumph. He was not elected to the Russian Academy of Sciences, but in the rest of the world his name was magic.

The underlying pattern of the atoms is numerical, that was clear. And yet that cannot be the whole story; we must be missing something. It simply does not make sense to believe that all the properties of the elements are contained in one number, the atomic weight: which hides — what? The weight of an atom might be a measure of its complex­ity. If so, it must hide some internal structure, some way the atom is physically put together, which generates those properties. But, of course, as an idea that was inconceivable so long as it was believed that the atom is indivisible.

And that is why the turning-point comes in 1897, when J. J. Thomson in Cambridge discovers the electron. Yes, the atom has constituent parts; it is not indivisible, as its Greek name had implied. The electron is a tiny part of its mass or weight, but a real part, and it carries a single electric charge. Each element is characterized by the number of electrons in its atoms. And their number is exactly equal to the number of the place in Mendeleev’s table that that element occupies when hydrogen and helium are included in first and second place. That is, lithium has three electrons, beryllium has four electrons, boron has five, and so on steadily all through the table. The place in the table that an element occupies is called its atomic number, and now that turned out to stand for a physical reality within its atom — the number of electrons there. The picture has shifted from atomic weight to atomic number, and that means, essentially, to atomic structure.

That is the intellectual breakthrough with which modern physics begins. Here the great age opens. Physics becomes in those years the greatest collective work of science — no, more than that, the great collective work of art of the twentieth century.

I say ‘work of art’, because the notion that there is an underlying structure, a world within the world of the atom, captured the imagination of artists at once. Art from the year 1900 on is different from the art before it, as can be seen in any original painter of the time: Umberto Boccioni, for instance, in The Forces of a Street, or his Dynamism of a Cyclist. Modern art begins at the same time as modern physics because it begins in the same ideas.

Since the time of Newton’s Opticks, painters had been entranced by the coloured surface of things. The twentieth century changed that. Like the X-ray pictures of Röntgen, it looked for the bone beneath the skin, and for the deeper, solid structure that builds up from the inside the total form of an object or a body. A painter like Juan Gris is engaged in the analysis of structure, whether he is looking at natural forms in Still Life or at the human form in Pierrot.

The Cubist painters, for example, are obviously inspired by the families of crystals. They see in them the shape of a village on a hillside, as Georges Braque did in his Houses at L’Estaque, or a group of women as Picasso painted them in Les Demoiselles d’Avignon. In Pablo Picasso’s famous beginning to Cubist painting — a single face, the Portrait of Daniel-Henry Kahnweiler — the interest has shifted from the skin and the features to the underlying geometry. The head has been taken apart into mathematical shapes and then put together as a reconstruction, a re-creation, from the inside out.

This new search for the hidden structure is striking in the painters of Northern Europe: Franz Marc, for example, looking at the natural landscape in Deer in a Forest; and (a favourite with scientists) the Cubist Jean Metzinger, whose Woman on a Horse was owned by Niels Bohr, who collected pictures in his house in Copenhagen.

There are two clear differences between a work of art and a scientific paper. One is that in the work of art the painter is visibly taking the world to pieces and putting it together on the same canvas. And the other is that you can watch him thinking while he is doing it. (For example, Georges Seurat putting one coloured dot beside another of a different colour to get the total effect in Young Woman with a Powder Puff and Le Bec.) In both those respects the scientific paper is often deficient. It often is only analytic; and it almost always hides the process of thought in its impersonal language.

I have chosen to talk about one of the founder fathers of twentieth-century physics, Niels Bohr, because in both these respects he was a consummate artist. He had no ready-made answers. He used to begin his lecture courses by saying to his students, ‘Every sentence that I utter should be regarded by you not as an assertion but as a question’. What he questioned was the structure of the world. And the people that he worked with, when young and old (he was still penetrating in his seventies), were others who were taking the world to pieces, thinking it out, and putting it together.

He went first in his twenties to work with J. J. Thomson, and his one-time student Ernest Rutherford who, round about 1910, was the outstanding experimental physicist in the world. (Thomson and Rutherford had both been turned to science by the interest of their widowed mothers, as Mendeleev had been.) Rutherford was then a professor at Manchester University. And in 1911 he had proposed a new model for the atom. He had said that the bulk of the atom is in a heavy nucleus or core at the centre, and the electrons circle it on orbiting paths, the way that the planets circle the sun. It was a brilliant conception — and a nice irony of history, that in three hundred years the outrageous image of Copernicus and Galileo and Newton had become the most natural model for every scientist. As often in science, the incredible theory of one age had become the everyday image for its successors.

Nevertheless, there was something wrong with Ruther­ford’s model. If the atom is really a little machine, how can its structure account for the fact that it does not run down — that it is a little perpetual motion machine, and the only perpetual motion machine that we have? The planets as they move in their orbits lose energy continuously, so that year by year their orbits get smaller — a very little smaller, but in time they will fall into the sun. If the electrons are exactly like the planets, then they will fall into the nucleus. There must be something to stop the electrons from losing energy continuously. That required a new principle in physics, so as to limit the energy an electron can give out to fixed values. Only so can there be a yardstick, a definite unit which holds the electrons to orbits of fixed sizes.

Niels Bohr discovered the unit he was looking for in the work that Max Planck had published in Germany in 1900. What Planck had shown, a dozen years earlier, is that in a world in which matter comes in lumps, energy must come in lumps, or quanta, also. By hindsight that does not seems so strange. But Planck knew how revolutionary the idea was the day he had it, because on that day he took his little boy for one of those professorial walks that academics take after lunch all over the world, and said to him, ‘I have had a conception today as revolutionary and as great as the kind of thought that Newton had’. And so it was.

Now in a sense, of course, Bohr’s task was easy. He had the Rutherford atom in one hand, he had the quantum in the other. What was there so wonderful about a young man of twenty-seven in 1913 putting the two together and making the modern image of the atom? Nothing but the wonderful, visible thought-process: nothing but the effort of synthesis. And the idea of seeking support for it in the one place where it could be found: the fingerprint of the atom, namely the spectrum in which its behaviour becomes visible to us, looking at it from outside.

That was Bohr’s marvellous idea. The inside of the atom is invisible, but there is a window in it, a stained-glass window: the spectrum of the atom. Each element has its own spectrum, which is not continuous like that which Newton got from white light, but has a number of bright lines which characterize that element. For example, hydro­gen has three rather vivid lines in its visible spectrum: a red line, a blue-green line, and a blue line. Bohr explained them each as a release of energy when the single electron in the hydrogen atom jumps from one of the outer orbits to one of the inner orbits.

As long as the electron in a hydrogen atom remains in one orbit, it emits no energy. Whenever it jumps from an outer orbit to an inner orbit, the energy difference between the two is emitted as a light quantum. These emissions from many billions of atoms simultaneously are what we see as a characteristic hydrogen line. The red line is when the electron jumps from the third orbit to the second; the blue-green line when the electron jumps from the fourth orbit to the second.

Bohr’s paper On the Constitution of Atoms and Molecules became a classic at once. The structure of the atom was now as mathematical as Newton’s universe. But it contained the additional principle of the quantum. Niels Bohr had built a world inside the atom by going beyond the laws of physics as they had stood for two centuries after Newton. He returned to Copenhagen in triumph. Denmark was home for him again, a new place to work. In 1920 they built the Niels Bohr Institute in Copenhagen for him. Young men came there to discuss quantum physics from Europe, America and the Far East. Werner Heisenberg came often from Germany and was goaded into conceiving some of his crucial ideas there: Bohr would never allow anyone to stop at a half-formed idea.

It is interesting to trace the steps of confirmation of Bohr’s model of the atom, because in a way they recapitulate the life-cycle of every scientific theory. First comes the paper. In that, known results are used to support the model. That is to say, the spectrum of hydrogen in particular is shown to have lines, long known, whose positions correspond to quantum transitions of the electron from one orbit to another.

The next step is to extend that kind of confirmation to a new phenomenon: in this case, lines in the higher energy X-ray spectrum, which is not visible to the eye but which is formed in just the same way by electron leaps. That work was going on in Rutherford’s laboratory in 1913, and yielded beautiful results exactly confirming what Bohr had predicted. The man who did the work was Harry Moseley, twenty-seven years old, who did no more brilliant work because he died in the forlorn British attack at Gallipoli in 1915 — a campaign which cost, indirectly, the lives of other young men of high promise, among them that of the poet Rupert Brooke. Moseley’s work, like Mendeleev’s, sug­gested some missing elements, and one of them was discovered in Bohr’s laboratory and named hafnium, after the Latin name for Copenhagen. Bohr announced the discovery incidentally in the speech he made when accept­ing the Nobel Prize for Physics in 1922. The theme of the speech is memorable, for Bohr described in detail what he summarized almost poetically in another speech: how the concept of the quantum had

 

led gradually to a systematic classification of the types of stationary binding of any electron in an atom, offering a complete explanation of the remarkable relationships between the physical and chemical properties of the elements, as expressed in the famous periodic table of Mendeleev. Such an interpretation of the properties of matter appeared as a realization, even surpassing the dreams of the Pythagoreans, of the ancient ideal of reducing the formulation of the laws of nature to considerations of pure numbers.

 

And just at this moment, when everything seems to be going so swimmingly, we suddenly begin to realize that Bohr’s theory, like every theory sooner or later, is reaching the limits of what it can do. It begins to develop little cranky weaknesses, a kind of rheumatic pain. And then comes the crucial realization that we have not cracked the real problem of atomic structure at all. We have cracked the shell. But within that shell the atom is an egg with a yolk, the nucleus; and we have not begun to understand the nucleus.

Niels Bohr was a man with a taste for contemplation and leisure. When he won the Nobel Prize he spent the money on buying a house in the country. His taste for the arts also ran to poetry. He said to Heisenberg, ‘When it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images’. That is an unexpected thought: when it comes to atoms, language is not describing facts but creating images. But it is so. What lies below the visible world is always imaginary, in the literal sense: a play of images. There is no other way to talk about the invisible — in nature, in art, or in science.

When we step through the gateway of the atom, we are in a world which our senses cannot experience. There is a new architecture there, a way that things are put together which we cannot know: we only try to picture it by analogy, a new act of imagination. The architectural images come from the concrete world of our senses, because that is the only world that words describe. But all our ways of picturing the invisible are metaphors, likenesses that we snatch from the larger world of eye and ear and touch.

Once we have discovered that the atoms are not the ultimate building blocks of matter, we can only try to make models of how the building blocks link and act together. The models are meant to show, by analogy, how matter is built up. So, to test the models, we have to take matter to pieces, like the diamond cleaver feeling for the structure of the crystal.

The ascent of man is a richer and richer synthesis, but each step is an effort of analysis: of deeper analysis, world within world. When the atom was found to be divisible it seemed that it might have an indivisible centre, the nucleus. And then it turned out, around 1930, that the model needed a new refinement. The nucleus at the centre of the atom is not the ultimate fragment of reality either.

At twilight on the sixth day of Creation, so say the Hebrew commentators to the Old Testament, God made for man a number of tools that gave him also the gift of creation. If the commentators were alive today, they would write ‘God made the neutron’. Here it is, at Oak Ridge in Tennessee, the blue glow that is the trace of neutrons: the visible finger of God touching Adam in Michelangelo’s painting, not with breath but with power.

I must not start quite so early. Let me begin the story about 1930. At that time the nucleus of the atom still seemed as invulnerable as the atom itself had once seemed. The trouble was that there was no way it could come apart into electrical pieces: the numbers simply would not fit. The nucleus has a positive charge (to balance the electrons in the atom) equal to the atomic number. But the mass of the nucleus is not a constant multiple of the charge: it ranges from being equal to the charge (in hydrogen) to much over twice the charge in the heavy elements. That was inexplicable, so long as everyone remained convinced that all matter must be built up from electricity.

It was James Chadwick who broke with that deeply rooted idea, and proved in 1932 that the nucleus consists of two kinds of particles: not only of the electrical positive proton, but of a non-electrical particle, the neutron. The two particles are almost equal in mass, namely equal (roughly) to the atomic weight of hydrogen. Only the simplest nucleus of hydrogen contains no neutrons, and consists of a single proton.

The neutron was therefore a new kind of probe, a sort of alchemist’s flame, because, having no electric charge, it could be fired into the nuclei of atoms without suffering electrical disturbance, and change them. The modern alchemist, the man who more than anyone took advantage of that new tool, was Enrico Fermi in Rome.

Enrico Fermi was a strange creature. I did not know him until much later, because in 1934 Rome was in the hands of Mussolini, Berlin was in the hands of Hitler, and men like me did not travel there. But when I saw him in New York, later, he struck me as the cleverest man I had ever set eyes on — well, perhaps the cleverest man with one exception. He was compact, small, powerful, penetrating, very sporty, and always with the direction in which he was going as clear in his mind as if he could see to the very bottom of things.

Fermi set about shooting neutrons at every element in turn, and the fable of transmutation came true in his hands. The neutrons he used you can see streaming out of this reactor because it is what it lightly called a ‘swimming pool’ reactor, meaning that the neutrons are slowed down by water. I should give it its proper name: it is a High Flux Isotope Reactor, which has been developed at Oak Ridge, Tennessee.

Transmutation was, of course, an age-old dream. But to men like me, with a theoretical bent of mind, what was most exciting about the 1930s was that there began to open up the evolution of nature. I must explain that phrase. I began here by talking about the day of Creation, and I will do that again. Where shall I start? Archbishop James Ussher of Armagh, a long time ago, about 1650, said that the universe was created in 4004 BC. Armed as he was with dogma and ignorance, he brooked no rebuttal. He or another cleric knew the year, the date, the day of the week, the hour, which fortunately I have forgotten. But the puzzle of the age of the world remained, and remained a paradox, well into the 1900s: because, while it was then clear that the earth was many, many millions of years old, we could not conceive where the energy came from in the sun and the stars to keep them going so long. By then we had Einstein’s equations, of course, which showed that the loss of matter would produce energy. But how was the matter rearranged?

Very well: that is really the crux of energy and the door of understanding that Chadwick’s discovery opened. In 1939 Hans Bethe, working at Cornell University, for the first time explained in very precise terms the transformation of hydrogen to helium in the sun, by which a loss of mass streams out to us as this proud gift of energy. I speak of these matters with a kind of passion, because of course to me they have the quality, not of memory, but of experience. Hans Bethe’s explanation is as vivid to me as my own wedding day, and the subsequent steps that followed as the birth of my own children. Because what was revealed in the years that followed (and finally sealed in what I suppose to be the definitive analysis in 1957) is that in all the stars there are going on processes which build up the atoms one by one into more and more complex structures. Matter itself evolves. The word comes from Darwin and biology, but it is the word that changed physics in my lifetime.

The first step in the evolution of the elements takes place in young stars, such as the sun. It is the step from hydrogen to helium, and it needs the great heat of the interior; what we see on the surface of the sun are only storms produced by that action. (Helium was first identified by a spectrum line during the eclipse of the sun in 1868; that is why it was called helium, for it was not known on earth then.) What happens in effect is that from time to time a pair of nuclei of heavy hydrogen collide and fuse to make a nucleus of helium.

In time the sun will become mostly helium. And then it will become a hotter star in which helium nuclei collide to make heavier atoms in turn. Carbon, for instance, is formed in a star whenever three helium nuclei collide at one spot within less than a millionth of a millionth of a second. Every carbon atom in every living creature has been formed by such a wildly improbable collision. Beyond carbon, oxygen is formed, silicon, sulphur and heavier elements. The most stable elements are in the middle of Mendeleev’s table, roughly between iron and silver. But the process of building the elements overshoots well beyond them.

If the elements are built up one by one, why does nature stop? Why do we find only ninety-two elements, of which the last is uranium? To answer that question we have, evidently, to build elements beyond it, and to confirm that as the elements become bigger, they become more complex and tend to fall apart into pieces. When we do that, however, we are not only making new elements but are making something that is potentially explosive. The ele­ment. plutonium, which Fermi made in the first historic Graphite Reactor (we called it a ‘Pile’ in those old colloquial days) was the man-made element that demonstrated this to the world at large. In part it is a monument to the genius of Fermi; but I think of it as a tribute to the god Pluto of the underworld who gave his name to the element, for forty thousand people died at Nagasaki of the plutonium bomb there. It is one more time in the history of the world when a monument commemorates a great man and many dead, together.

I must return briefly to the mine at Wieliczka because there is a historical contradiction to be explained here. The elements are being built up in the stars constantly, and yet we used to think that the universe is running down. Why? Or how?


The idea that the universe is running down comes from a simple observation about machines. Every machine consumes more energy than it renders. Some of it is wasted in friction, some of it is wasted in wear. And in some more sophisticated machines than the ancient wooden capstans at Wieliczka, it is wasted in other necessary ways — for example, in a shock-absorber or a radiator. These are all ways in which the energy is degraded. There is a pool of inaccessible energy into which some of the energy that we put in always runs, and from which it cannot be recovered.

In 1850 Rudolf Clausius put that thought into a basic principle. He said that there is energy which is available, and there is also a residue of energy which is not accessible. This inaccessible energy he called entropy, and he formu­lated the famous Second Law of Thermodynamics: entropy is always increasing. In the universe, heat is draining into a sort of lake of equality in which it is no longer accessible.

That was a nice idea a hundred years ago, because then heat could still be thought of as a fluid. But heat is not material any more than fire is, or any more than life is. Heat is a random motion of the atoms. And it was Ludwig Boltzmann in Austria who brilliantly seized on that idea to give a new interpretation to what happens in a machine, or a steam engine, or the universe.

When energy is degraded, said Boltzmann, it is the atoms that assume a more disorderly state. And entropy is a measure of disorder: that is the profound conception that came from Boltzmann’s new interpretation. Strangely enough, a measure of disorder can be made; it is the probability of the particular state — defined here as the number of ways it can be assembled from its atoms. He put that quite precisely,

 

S = K log W;

 

S, the entropy, is to be represented as proportional to the logarithm of W, the probability of the given state (K being the constant of proportionality which is now called Boltz­mann’s constant).

Of course, disorderly states are much more probable than orderly states, since almost every assembly of the atoms at random will be disorderly; so by and large any orderly arrangement will run down. But ‘by and large’ is not ‘always’. It is not true that orderly states constantly run down to disorder. It is a statistical law, which means that order will tend to vanish. But statistics do not say ‘always’. Statistics allow order to be built up in some islands of the universe (here on earth, in you, in me, in the stars, in all sorts of places) while disorder takes over in others.

That is a beautiful conception. But there is still one question to be asked. If it is true that probability has brought us here, is not the probability so low that we have no right to be here?

People who ask that question always picture it thus. Think of all the atoms that make up my body at this moment. How madly improbable that they should come to this place at this instant and form me. Yes, indeed, if that was how it happened, it would not only be improbable — I would be virtually impossible.

But, of course, that is not how nature works. Nature works by steps. The atoms form molecules, the molecules form bases, the bases direct the formation of amino acids, the amino acids form proteins, and proteins work in cells. The cells make up first of all the simple animals, and then sophisticated ones, climbing step by step. The stable units that compose one level or stratum are the raw material for random encounters which produce higher configurations, some of which will chance to be stable. So long as there remains a potential of stability which has not become actual, there is no other way for chance to go. Evolution is the climbing of a ladder from simple to complex by steps, each of which is stable in itself.

Since this is very much my subject, I have a name for it: I call it Stratified Stability. That is what has brought life by slow steps but constantly up a ladder of increasing com­plexity — which is the central progress and problem in evolution. And now we know that that is true not only of life but of matter. If the stars had to build a heavy element like iron, or a super-heavy element like uranium, by the instant assembly of all the parts, it would be virtually impossible. No. A star builds hydrogen to helium; then at another stage in a different star helium is assembled to carbon, to oxygen, to heavy elements; and so step by step up the whole ladder to make the ninety-two elements in nature.

We cannot copy the processes in the stars as a whole, because we do not command the immense temperatures that are needed to fuse most elements. But we have begun to put our foot on the ladder: to copy the first step, from hydrogen to helium. In another part of Oak Ridge the fusion of hydrogen is attempted.

It is hard to recreate the temperature within the sun, of course — over ten million degrees centigrade. And it is still harder to make any kind of container that will survive that temperature and trap it for even a fraction of a second. There are no materials that will do; a container for a gas in this violent state can only have the form of a magnetic trap. This is a new kind of physics: plasma-physics. Its excite­ment, yes, and its importance, is that it is the physics of nature. For once, the rearrangements that man makes run, not against the direction of nature, but along the same steps which nature herself takes in the sun and in the stars.

Immortality and mortality is the contrast on which I end this essay. Physics in the twentieth century is an immortal work. The human imagination working communally has produced no monuments to equal it, not the pyramids, not the Iliad, not the ballads, not the cathedrals. The men who made these conceptions one after another are the pioneering heroes of our age. Mendeleev, shuffling his cards; J. J. Thomson, who overturned the Greek belief that the atom is indivisible; Rutherford, who turned it into a planetary system; and Niels Bohr, who made that model work. Chadwick, who discovered the neutron, and Fermi, who used it to open up and to transform the nucleus. And at the head of them all are the iconoclasts, the first founders of the new conceptions: Max Planck, who gave energy an atomic character like matter; and Ludwig Boltzmann to whom, more than anyone else, we owe the fact that the atom — the world within a world — is as real to us now as our own world.

Who would think that, only in 1900, people were battling, one might say to the death, over the issue of whether atoms are real or not. The great philosopher Ernst Mach in Vienna said, No. The great chemist Wilhelm Ostwald said, No. And yet one man, at that critical turn of the century, stood up for the reality of atoms on funda­mental grounds of theory. He was Ludwig Boltzmann, at whose memorial I pay homage.

Boltzmann was an irascible, extraordinary, difficult man, an early follower of Darwin, quarrelsome and delightful, and everything that a human being should be. The ascent of man teetered on a fine intellectual balance at that point, because had anti-atomic doctrines then really won the day, our advance would certainly have been set back by decades, and perhaps a hundred years. And not only in physics would it have been held back, but in biology, which is crucially dependent on that.

Did Boltzmann just argue? No. He lived and died that passion. In 1906, at the age of sixty-two, feeling isolated and defeated, at the very moment when atomic doctrine was going to win, he thought all was lost, and he committed suicide. What remains to commemorate him is his immortal formula,

 

S = K log W,

 

carved on his grave.

I have no phrase to match the compact and penetrating beauty of Boltzmann’s. But I will take a quotation from the poet William Blake, who begins the Auguries of Innocence with four lines:

 

To see a World in a Grain of Sand

And a Heaven in a Wild Flower

Hold Infinity in the palm of your hand

And Eternity in an hour.



 


Date: 2016-01-14; view: 791


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