Boltzmanns Atom

The Great Debate That Launched A Revolution In Physics

David Lindley

• Publisher: Free Press
• Year: 2015
• ISBN:
  9781501142673
• Topic: History
• Subtopic: Science History
• Index: History

In 1900 many eminent scientists did not believe atoms existed, yet within just a few years the atomic century launched into history with an astonishing string of breakthroughs in physics that began with Albert Einstein and continues to this day. Before this explosive growth into the modern age took place, an all-but-forgotten genius strove for forty years to win acceptance for the atomic theory of matter and an altogether new way of doing physics. Ludwig Boltz-mann battled with philosophers, the scientific establishment, and his own potent demons. His victory led the way to the greatest scientific achievements of the twentieth century.Now acclaimed science writer David Lindley portrays the dramatic story of Boltzmann and his embrace of the atom, while providing a window on the civilized world that gave birth to our scientific era. Boltzmann emerges as an endearingly quixotic character, passionately inspired by Beethoven, who muddled through the practical matters of life in a European gilded age.Boltzmann's story reaches from fin de siècle Vienna, across Germany and Britain, to America. As the Habsburg Empire was crumbling, Germany's intellectual might was growing; Edinburgh in Scotland was one of the most intellectually fertile places on earth; and, in America, brilliant independent minds were beginning to draw on the best ideas of the bureaucratized old world.Boltzmann's nemesis in the field of theoretical physics at home in Austria was Ernst Mach, noted today in the term Mach I, the speed of sound. Mach believed physics should address only that which could be directly observed. How could we know that frisky atoms jiggling about corresponded to heat if we couldn't see them? Why should we bother with theories that only told us what would probably happen, rather than making an absolute prediction? Mach and Boltzmann both believed in the power of science, but their approaches to physics could not have been more opposed. Boltzmann sought to explain the real world, and cast aside any philosophical criteria. Mach, along with many nineteenth-century scientists, wanted to construct an empirical edifice of absolute truths that obeyed strict philosophical rules. Boltzmann did not get on well with authority in any form, and he did his best work at arm's length from it. When at the end of his career he engaged with the philosophical authorities in the Viennese academy, the results were personally disastrous and tragic. Yet Boltzmann's enduring legacy lives on in the new physics and technology of our wired world.Lindley's elegant telling of this tale combines the detailed breadth of the best history, the beauty of theoretical physics, and the psychological insight belonging to the finest of novels.

CHAPTER 1

---

A Letter from Bombay

Lessons in Obscurity

ON DECEMBER 11, 1845, A LENGTHY MANUSCRIPT arrived in the London offices of the Royal Society, the highest scientific association in Great Britain. The author of this work hoped his essay might be published in the Society’s august Philosophical Transactions, and the manuscript, by standard practice, was duly sent to a couple of experts for evaluation of its worth. “Nothing but nonsense” was the verdict of one of these eminent reviewers. The other allowed that the paper demonstrated “much skill and many remarkable accordances with the general facts,” but concluded nevertheless that the ideas were “entirely hypothetical” and, in the end, “very difficult to admit.”

On these recommendations, the manuscript was never published. Worse still, the author, one John James Waterston, never found out what had happened. Waterston was living at the time in Bombay, teaching navigation and gunnery to naval cadets employed by the East India Company. Born and educated in Edinburgh, he spent his life working as a civil engineer and teacher, retiring from his position in India in 1857 to return to Scotland, where he lived modestly on his savings and continued to dabble in science: astronomy, chemistry, and physics. He was known during his lifetime, if at all, as one of the numerous amateurs of Victorian science, working in isolation, contributing from time to time ideas that were more or less sound but of no great consequence.

His rejected manuscript of 1845 embodied Waterston’s one truly innovative and profound piece of work, but it was ahead of its time. Only by a few years, admittedly, but that was enough to ensure its unhappy reception by the experts of the Royal Society. Waterston proposed that any gas consisted of numerous tiny particles—he called them molecules—bouncing around and colliding with each other. He showed that the energy of motion in these particles corresponded to the temperature of the gas, and that the incessant impacts of the particles on the walls of the container gave rise to the effect commonly known as pressure. There was more: Waterston calculated the “elasticity” of gases (their ability to flow, roughly speaking) from his model, and he made the subtle observation that in a mixture of different gases all the tiny particles would, on average, have the same energy, so that heavier molecules would move more slowly than lighter ones. He was not right in every detail, but his general arguments and suppositions have survived the test of time. Waterston’s fundamental idea, that a gas is made of tiny, colliding particles whose microscopic behavior produces the measurable properties of the gas as a whole, was exactly right.

Waterston’s calculations were somewhat rough and ready, and his proofs were not quite solid. It may have been these deficiencies that led to the rejection of his paper—that, and the fact that his name was unknown. It was certainly not revolutionary, in the middle of the 19th century, to suggest that gases consisted of tiny particles. The terms atom and molecule were known in scientific circles, although they designated objects whose true nature was unclear. Even the idea that the motion and collision of these particles had something to do with temperature and pressure was not altogether new. The Royal Society, admirably consistent, had in fact rejected a very similar proposal some 25 years earlier. The author of this earlier attempt was John Herapath, another unsung amateur of Victorian science and engineering. His work was by no means as sophisticated as Waterston’s, but he had the right general idea: heat equals the motion of atoms or molecules. He wrote up his ideas in 1820 and sent them to the Royal Society. The chemist Humphrey Davy, then president of the society, declined to publish the paper. Though he was not unsympathetic to atomic thinking, Davy found Herapath’s calculations unconvincing, and in truth, Herapath was confused about the mechanics of atomic collisions and came up with an incorrect formula for the temperature of a gas. Still, Herapath succeeded in getting accounts of his work published in other scientific journals, where they were roundly ignored by the scientific community of that age.

Waterston knew of Herapath’s work, and of his erroneous formula for temperature, but neither of these two men, it appears, was aware that the atomic picture of a gas was close to a century old by the time they came to it. In 1738 Daniel Bernoulli, one of an extended Swiss clan of Bernoullis that made notable contributions to both mathematics and physics, succeeded in deriving theoretically a relationship between the pressure exerted by a gas and the energy of vibration of the supposed atoms within it. His theory attracted little attention, and was soon forgotten.

Bernoulli’s was the first modern atomic or molecular model of a gas. He explained pressure in terms of atomic motion, but not temperature, largely because the nature of heat itself was quite mysterious in Bernoulli’s day. Even so, neither he nor Herapath nor Waterston can take any credit for the idea of atoms themselves. They were the inheritors of a centuries-old tradition in natural philosophy according to which everything in the universe is composed fundamentally of minute, indivisible objects. The word atom is of Greek origin, meaning “uncuttable,” and it is from ancient Greece that the idea itself descends.

Knowledge of the atomic hypothesis from ancient times is owed largely to the survival of a long poem called De Rerum Natura (On the Nature of Things) by the Roman writer Lucretius. The names of both this poem and its author had faded into oblivion in the centuries after the fall of Rome, but a church official traveling around the monasteries of France and Germany in the 13th century happened across a copy (not an original) and brought it back to the Vatican in 1417. Manuscripts dating back to the 9th or 10th century were subsequently rediscovered and found to be substantially the same as the Vatican copy. From these versions descend all modern editions of De Rerum Natura. Its author, Titus Lucretius Carus, lived from about 95 to 55 B.C. The six books of his great opus lay out a philosophical reflection on life as well as an exposition of a scientific hypothesis. It is fiercely atheistic. It enjoyed a good deal of renown in its time, but was later attacked by the Emperor Augustus in his attempt to restore some of the faded glory of the declining Roman world by reviving the ancient pre-Christian religion.

Lucretius derived his atheism from his adherence to what can be called, with the benefit of two millennia of hindsight, an atomic theory of the natural world. For example:

clothes hung above a surf-swept shore

grow damp; spread in the sun they dry again.

Yet it is not apparent to us how

the moisture clings to the cloth, or flees the heat.

Water, then, is dispersed in particles,

atoms too small to be observable.

In other words, a wet garment has atoms (we would now say molecules) of water clinging to its fabric; heat drives the atoms off, and thus dries the material. An atomic theory of clothes drying seems to be some way from disproving the existence of deities, but Lucretius goes on to observe that the atoms have no volition, and instead move willy-nilly:

For surely the atoms did not hold council, assigning

order to each, flexing their keen minds with

questions of place and motion and who goes where.

But shuffled and jumbled in many ways, in the course

of endless time they are buffeted, driven along,

chancing upon all motions, combinations.

At last they fall into such an arrangement

as would create this universe . . .

Examined closely, Lucretius says, the range and variety of all the familiar phenomena of the world about us arise from invisible atoms zipping aimlessly this way and that. No need for gods to direct events, or inspire actions and consequences. On the other hand, Lucretius’s vision seems to leave little room for human decision or free will either. If the universe takes its course because atoms are following their random paths, then neither gods nor human beings have any control over their destinies; what will happen, will happen, and there is nothing anyone can do to change it.

This is a bleak form of atheism, implying what is nowadays called determinism, meaning that what happens in the future is wholly determined by what has happened in the past. To Lucretius and his followers this view was nevertheless a liberation. In their day the gods were fickle, cruel, and capricious, more inclined to pranks and practical jokes than to love or compassion. The citizens of Rome decidedly did not wish for a god to enter their lives. To believe, as Lucretius insisted, that there were no gods, and that the world proceeded for good or ill quite indifferent to human desires, was by contrast to achieve a measure of repose through calm acceptance. Even death was not to be feared: when the atoms of one’s soul and body were forever dispersed, there could be no sensation, no pain. Compared to being taunted or tortured for all eternity by frivolous, merciless gods, that was indeed a blessing.

In his philosophy, based on atomism, Lucretius found a reason to give up the struggle against blind fate, and to live instead with equanimity in the world as it was. He lived in the time of Julius Caesar, when the Roman republic was failing. Tyrants, wayward generals, and corrupt politicians would thereafter take over. Peace was to be found in withdrawing as far as possible from the vicissitudes of life. Whether Lucretius was able to live according to his own recommendation is doubtful. He suffered periods of insanity or mental disturbance, and killed himself when he was about 40 years old. In a story handed down by St. Jerome, Lucretius was so much and so often wrapped in thought that his wife grew resentful, and to restore marital relations secretly gave him a love potion. Unfortunately, the potion was stronger than necessary, drove him mad, and thus impelled him to suicide. Tennyson wrote a poem about the poet and described the reasons for his wife’s unhappiness:

Yet often when the woman heard his foot

return from pacings in the field, and ran

to greet him with a kiss, the master took

small notice, or austerely, for—his mind

half-buried in some weightier argument,

or fancy-borne perhaps on the rise

and long roll of the hexameter—he past

to turn and ponder those three hundred scrolls

left by the Teacher, whom he held divine.

This Teacher, the man by the contemplation of whose scrolls Lucretius earned his wife’s displeasure, was the philosopher Epicurus, whose name survives in the notion of putting pleasure foremost among one’s goals in life. A contemporary critic sniped that the ideal Epicurean way of life consisted of “eating, drinking, copulation, evacuation, and snoring,” but there was more to it than that. Epicurus aimed for what might better be called contentedness, which meant freedom from pain and satiation of one’s desires rather than any sort of unbridled hedonistic pleasure seeking.

To Epicurus, the greatest fear in life was the fear of death, or rather the fear of an unendurable afterlife that nevertheless had to be endured. As Lucretius reports, Epicurus employed the notion of atoms to argue that death was the final release from suffering, to be regretted, perhaps, but not feared. Lucretius differed from his teacher in one significant way: he went from atomism to atheism, but Epicurus still believed in the gods, and found the determinism of the atomic philosophy not to his taste. For that reason he introduced what seems now a rather odd idea:

When the atoms are carried straight down through the void

by their own weight, at an utterly random time

and a random point in space they swerve a little,

only enough to call it a tilt in motion.

Lucretius goes on to indicate that these “swerves” in the motion of atoms are what cause the atoms to cluster together or collide or otherwise interact in ways that can produce natural phenomena. The main point, however, was apparently to get around strict determinism by allowing atoms to alter their trajectories spontaneously, without any immediate cause. Perhaps this restores free will, or the ability of the gods to meddle, but it strikes the modern reader as an “unscientific” addition to the theory.

It was, indeed, Epicurus’s own ill-considered addition. He did not dream up the notion of atoms, but got them from a still earlier source, in the writings of the Greek philosopher Democritus, and his teacher, Leucippus.

Of Leucippus little is known except that he flourished and taught in the years following 440 B.C. in what is now Turkey. His pupil, Democritus, lived from about that time until 371 B.C., mostly in northern Greece, and whether the beginnings of atomism should properly be credited to him or to Leucippus is impossible to say, since the latter’s teaching is preserved only in the former’s writings. Nevertheless, between the two of them, they put together what we can easily—perhaps too easily—see as the first intimation of a recognizably modern theory of atoms. They proposed that there exists a void, and in this void atoms move about, always in motion. Atom and void are all there is. The atoms come in a variety of distinct types and are indivisible; they band together in different ways to create the tangible and visible ingredients of the world.

To Democritus it was evident that there could be no up or down in an infinite void, and he therefore proposed that atoms move endlessly in all directions, changing course only when they ran into each other. But this implies determinism: once the atoms are off and running, their courses are fixed. There is still room for a deity at the beginning—a prime mover, an uncaused cause, or some other extraphysical influence that sets the atoms up and pushes them off in certain directions—but once that’s done, determinism takes over. Does this mean there is no free will or volition? That the future is completely determined by the past? That question has haunted atomic theory, indeed physics in general, since the time of Democritus, and haunts us still today.

What distinguished Leucippus and Democritus from most of their contemporaries, and from almost all of the thinkers who followed them over the next two millennia, was that they were mainly interested in trying to understand how the world worked. Other philosophers began to focus their attention not so much on the universe as on the position of human beings in the universe, the extent to which human beings could know or understand the world around them, and how humans ought to behave. Thus arose the numerous brands of philosophy that have concerned themselves with the nature of knowledge and thought, and with the ethics and morality of human behavior. Religious philosophers took for granted that the universe has a purpose, and that humans have a purpose within it, which they may aspire to or fall away from. Leucippus and Democritus were, by contrast, scientists, aiming to understand as dispassionately as possible what is out there. Since their time, science and philosophy have become separate and frequently combative disciplines.

Atomic theory, with its implicit atheism and determinism, lost the favor of philosophical thinkers for a long period. But it crops up from time to time, for example in the writings of Isaac Newton:

It seems probable to me that God in the beginning form’d matter in solid, massy, hard, impenetrable, movable particles, of such sizes and figures and with such other properties, and in such proportion to space, as most conduced to the end for which he form’d them.

Whether from personal belief or caution, Newton is careful to cede to God the responsibility of creating atoms in the first place. But how, if at all, is this statement an advance on anything that Democritus (through Epicurus and then Lucretius) had said two thousand years earlier? Newton lists the attributes that atoms must or might have, but then concludes, quite circularly, that the properties and behavior are such “as most conduce” to the effects they need to generate. What atoms do, in other words, is whatever they need do in order to produce the phenomena of the natural world. Neither Democritus nor Newton is able to say how, in any specific sense, atoms behave so as to generate physical effects. In the absence of any such elaboration, atomism was bound to remain an appealing but speculative picture rather than a truly scientific theory.

By contrast there were, from the earliest times, plausibly scientific criticisms of the atomic philosophy. One objection that arose in Democritus’s time was later taken up with enthusiasm by Aristotle: how could atoms move constantly, without let-up, for all time? In Aristotelian mechanics, inferred from direct observation, moving objects came to a halt unless something intervened to keep them moving. You had to keep kicking a rock to keep it rolling. What, therefore, kept atoms moving?

Once Newton came along with his laws of motion, this argument lost much of its force. Newton directly contradicted Aristotle: objects keep moving, in straight lines, until something stops them. The kicked rock rumbles to a halt because the impacts it suffers sap its energy.

The other knock against atomism was that the atoms moved around in empty space, a void, and many philosophers had satisfied themselves that a void was impossible. Their reasoning, briefly, was that for anything to exist, it must have a name that referred to something rather than nothing, and since nothing by definition could not have such a name, it could not therefore exist. This argument, we would now say, is the result of a philosophical confusion between the name of a thing and the thing itself, but it took philosophers a long time to sort that one out. If indeed they have, even now.

Democritus answered these objections in essence by refusing to answer them. He simply asserted that atoms exist and that they move incessantly in the void. He didn’t attempt to provide any proof of these statements, but regarded them instead as assumptions from which he and the other atomists sought to explain what they saw in the world about them.

This attitude is strikingly modern and scientific. As Democritus saw it, you have to start somewhere. You make an assumption and explore the consequences. This is exactly what scientists continue to do today, and the fact that a certain assumption leads to all kinds of highly successful predictions and expl...

Table of contents

• Cover
• Introduction
• Chapter 1: A Letter from Bombay
• Chapter 2: Invisible World
• Chapter 3: Dr. Boltzmann of Vienna
• Chapter 4: Irreversible Changes
• Chapter 5: “You Will Not Fit In”
• Chapter 6: The British Engagement
• Chapter 7: “It’s Easy to Mistake a Great Stupidity for a Great Discovery”
• Chapter 8: American Innovations
• Chapter 9: The Shock of the New
• Chapter 10: Beethoven in Heaven
• Chapter 11: Annus Mirabilis, Annus Mortis
• Postscript
• Acknowledgments
• Bibliography and Notes
• Index
• Copyright