Einstein's Masterwork E-Book

John Gribbin

• Herausgeber: Icon Books
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2015

Seitenzahl: 292

Beschreibung

In 1915, Albert Einstein unveiled his masterwork – a theory, in his words, 'of incomparable beauty': the General Theory of Relativity. It is sometimes overshadowed – wrongly, argues John Gribbin – by his work of 1905, the Special Theory of Relativity and E = mc≤. Just over 100 years later, the first direct detection of gravitational radiation is seen as the ultimate proof of the General Theory's accuracy. The General Theory describes the evolution of the Universe, black holes, the behaviour of orbiting neutron stars, and why clocks run slower on Earth than in space. It even suggests the possibility of time travel. In this 'beautifully written and highly accessible account of the genesis of a great theory' (Physics World), Gribbin vividly illustrates what an incomparable scientist Albert Einstein really was.

Leseprobe

Einstein’s Masterwork

Einstein’s Masterwork

1915 and the General Theory of Relativity

JOHN GRIBBIN

with MARY GRIBBIN

Published in the UK in 2015 by Icon Books Ltd, Omnibus Business Centre, 39–41 North Road, London N7 9DP email: [email protected]

Sold in the UK, Europe and Asia by Faber & Faber Ltd, Bloomsbury House, 74–77 Great Russell Street, London WC1B 3DA or their agents

Distributed in the UK, Europe and Asia by TBS Ltd, TBS Distribution Centre, Colchester Road, Frating Green, Colchester CO7 7DW

Distributed in Australia and New Zealand by Allen & Unwin Pty Ltd, PO Box 8500, 83 Alexander Street, Crows Nest, NSW 2065

Distributed in South Africa by Jonathan Ball, Office B4, The District, 41 Sir Lowry Road, Woodstock 7925

ISBN: 978-184831-852-6

Text copyright © 2015 John and Mary Gribbin

The authors have asserted their moral rights

No part of this book may be reproduced in any form, or by any means, without prior permission in writing from the publisher

Typeset in Dante by Marie Doherty

Printed and bound in the UK by Clays Ltd, St Ives plc

Contents

About the Author

Introduction

1 In the Beginning

Early life; Breaking free; Einstein and the Poly; Rejection; Rescue

2 The Annus Mirabilis

The doctoral thesis; Jiggling atoms; Particles of light; The special one

3 The Long and Winding Road

The geometry of relativity; Moving on; In the shadow of a giant; On the move; First steps; What Einstein should have known; The masterwork

4 Legacy

Black holes and timewarps; Beyond reasonable doubt; Making waves; The Universe at large

5 The Icon of Science

Personal problems; Fame; A last quantum hurrah; Exile; Spooky action at a distance; The final years

Further Reading

Endnotes

Index

List of Illustrations

1. Einstein’s mother, Pauline Einstein

2. Einstein’s father, Hermann Einstein

3. Albert as a boy, circa 1893

4. Albert and Maja Einstein

5. Marcel Grossmann, Albert Einstein, Gustav Geissler and Eugen Grossmann in Thalwil, near Zurich

6. The house in which Einstein lived in Bern, 49 Kramgasse

7. Albert with Mileva and Hans Albert

8. Albert, circa 1912

9. First Solvay Congress, Brussels, 1911

10. Albert and Elsa Einstein aboard the SS Rotterdam en route to the US, 1921

11. Eddington, Lorentz, Einstein, Ehrenfest and de Sitter, at the Leiden Observatory

The most valuable theory of my life … The theory is of incomparable beauty.

ALBERT EINSTEIN, 1915

If Einstein had not produced the Special Theory in 1905, someone else would have done so within a short time, five years or so. That is the general situation with almost all scientific advances, they are in the air; if A doesn’t make them, then B certainly will.

The General Theory is the startling exception, maybe the only one in [the 20th] century. It is agreed by the most eminent of theoretical physicists – Dirac has said so without qualification – that if Einstein had not created the General Theory [in 1915] no one else would have done so, perhaps not until now, perhaps not for generations.

C.P. SNOW, INCONVERSATIONS WITH EINSTEIN

BY ALEXANDER MOSZKOWSKI

About the Author

John Gribbin was born in 1946 in Maidstone, Kent. He studied physics at the University of Sussex and went on to complete an MSc in astronomy at the same university before moving to the Institute of Astronomy in Cambridge, to work for his PhD.

After working for the journals Nature and New Scientist, he has concentrated chiefly on writing books on everything from the Universe and the Multiverse to the history of science. His books have received science-writing awards in the UK and the US. His other biographical subjects include Erwin Schrödinger, Stephen Hawking, Richard Feynman, Galileo, Buddy Holly and James Lovelock.

Since 1993, Gribbin has been a Visiting Fellow in Astronomy at the University of Sussex.

1 In the Beginning

Early life; Breaking free; Einstein and the Poly; Rejection; Rescue

In 1905, Albert Einstein produced the most important package of ideas from any scientist since Isaac Newton. The iconic image we have of Einstein is the white-haired genius, a wise and fatherly guru, a cross between God and Harpo Marx. But in 1905 Einstein was a handsome, dark-haired young man (he celebrated his 26th birthday on 14 March that year), previously something of a ladies’ man but recently married, with a baby son. He didn’t even have a PhD at the time he published the scientific papers that made him famous.

What made Newton and Einstein so special was that they didn’t just have one brilliant idea (like, say, Charles Darwin with his theory of natural selection) but a whole variety of brilliant ideas, within a few months of one another. There were other similarities between the two great men. In 1666, Newton celebrated his 24th birthday, and although he had already obtained his degree from the University of Cambridge, for much of 1665 and 1666 he had been unable to take up a Fellowship at Trinity College because the university had been closed by an outbreak of plague. So he had been working in isolation at the family home in Lincolnshire. In 1905, the 26-year-old Einstein had already graduated from the Swiss Federal Polytechnic in Zurich, but had been unable to obtain a post at any university. So he had settled for a junior post at the patent office in Bern, working in isolation on scientific topics at home in his spare time – and also, as he later admitted, during office hours.

Especially in the theoretical sciences and mathematics, it is often true that people do their best work in their twenties, even if that work never matches the achievements of a Newton or an Einstein. But there the similarities between the two geniuses stop. Newton was a loner by choice, who made few friends and never married; although most of his great work was done in 1665–6, it was only published later, at different times, in response to pressure from colleagues who became aware of what he had achieved. Einstein was a gregarious family man, eager to get a foothold in the academic world, who knew the importance of advertising his discoveries and published them as soon as he could. It was his only chance of getting out of the patent office and into a university post. But what was the man later regarded as the greatest genius of the 20th century doing working in a patent office anyway?

Early life

Albert had been born in Ulm, in Germany, in 1879. In the summer of the following year, however, the family moved to Munich, in the south of Germany, where Albert’s father, Hermann, went into partnership with his younger brother Jakob in the booming electrical industry. Jakob had a degree from the Stuttgart Polytechnic Institute and provided the expert know-how for the business; the money to set them up came from the family of Albert’s mother, Pauline. Hermann’s role was on the administrative side, running the business. Jakob and his wife, Ida, shared a pleasant house on the outskirts of Munich with Hermann, Pauline and little Albert.

Far from showing any signs of precocious genius, little Albert was so slow to learn to speak that his parents feared that there might be something wrong with him. It wasn’t until well after his second birthday that he began talking, but when he did he used proper sentences from the start, quietly working the words out in his head and whispering them to himself before speaking out loud. In November 1881, his sister Maja was born, and she later recalled his response to her arrival, reported to her by her mother when she was old enough to understand. It seems that Albert had been told he would soon have something new to play with, and was expecting a toy; on being introduced to his baby sister, he asked: ‘Where are the wheels?’a Although brother and sister developed an affectionate bond, young Albert was prone to occasional outbursts of violent temper, when he would throw things at the nearest person – all too often, Maja. Family legend tells of the time he hit her over the head with a garden hoe, and how at the age of five he chased his first violin teacher out of the house, throwing a chair after her. But the music-loving Pauline was tough and strong-minded enough to ensure that he carried on with the violin lessons whether he liked them or not, eventually instilling in him a love of music that provided a lifelong release from the strains of his scientific work. And he had talent – much later, when he was a sixteen year old at high school in Switzerland, a school inspector would single him out for praise, reporting that ‘one student, [named] Einstein, actually sparkled [in] his emotional performance of an adagio from a Beethoven sonata.’1

The expression ‘tough love’ could have been invented to describe Pauline’s attitude to her children. When he was only four, Albert was given a guided tour of the neighbourhood by his parents, and from then on was not only allowed but encouraged to go out alone and find his way through the streets – although, unknown to the boy, they kept a distant eye on him on his first few solo expeditions. One of the first regular journeys he had to make was to school. The Einsteins were secular Jews and were unconcerned that the nearest school was Catholic, so that is where Albert received his first formal education, very much in the old-fashioned tradition of learning by rote and with strict discipline enforced by corporal punishment. Albert’s disenchantment with the school was strengthened when he was still only five years old and ill in bed. His father gave the boy a magnetic compass to relieve his boredom, and Albert became intrigued by the way in which the needle always tried to point to the north, no matter how he twisted and turned the instrument. He was fascinated by the idea of an invisible force that kept a grip on the compass needle, and baffled that none of his teachers at the school had shown him anything half as interesting. This helped to instil an early conviction that he was much better off working things out for himself than working within the system.

Albert’s stubborn insistence on finding his own way in the world led to a curious development during his years at the Catholic school. At that time, the statutes of the city of Munich required all students to receive some religious education, and although Hermann and Pauline didn’t mind Albert attending a Catholic school, they drew the line at having him indoctrinated in the Catholic faith. So, to meet their obligations they got a relative to teach Albert about the Jewish faith – as they thought, just as a matter of form. To everyone’s surprise, Albert lapped it all up and became something of a religious fanatic, observing the Jewish rituals that his parents had abandoned, refusing to eat pork and making up hymns that he would sing to himself as he walked to school in the morning. This religious phase lasted until Albert was about twelve and had been a student at the local high school (Gymnasium) for two years. His loss of faith was a direct result of his discovery of science; but that discovery owed nothing to the high school, and everything to a young medical student called Max Talmey.

Although Hermann and Pauline Einstein did not follow all the religious traditions of their nominal faith, there was one Jewish custom that they kept. At that time, there was a tradition among middle-class Jewish families of helping young students who might be struggling to make ends meet, and the Einsteins got into the habit of inviting Talmey, who came from Poland,b to dinner once a week. It was Talmey who introduced Albert, who was ten when they met, to the latest scientific ideas, discussing them with the boy as if he were an adult. Talmey lent books popularizing science to Albert, introduced him to algebra and in 1891 gave him a book about geometry. Einstein later described reading this book as the single most important factor in making him a scientist. He was gripped, fascinated by the way in which mathematical logic could be used to start from simple premises to construct truths, such as Pythagoras’ Theorem, that are absolutely true. Within a year, he had worked his own way through the entire mathematics syllabus of the high school. This rather left the school, as he saw it, as a pointless waste of time. He had also lost his faith in God and now, as a young teenager, saw religion as part of a deception played by the State in order to manipulate its people, especially the young.

Albert had made a good start to his time at the Luitpold Gymnasium, finding it easy to keep up with his peers; but although this was one of the best schools of its kind, a combination of the rigid educational system, his loss of religious faith and his discovery that he could leap ahead of the curriculum by working on his own led him to neglect his classwork. He still got good grades in mathematics, but couldn’t see the point of subjects like Classical Greek and gained a reputation as an impudent troublemaker. One family anecdote recalls that Albert’s father was summoned to the school to be told that his son was a troublemaker. When he asked what they meant, he was told ‘he sits at the back and smiles’.

The situation at school came to a head in 1894, when the family business went bust. The firm had done reasonably well in the 1880s, like many other small businesses taking advantage of the booming demand for electrical equipment such as dynamos, lighting systems and telephones. But in the classic pattern of progress following the invention of a new technology, those small businesses were now being swallowed up by large firms, or going under in the face of competition from the giants, such as Siemens and AEG. It was a lack of capital, as much as anything else, that saw the Einsteins lose out in this competition. But before matters came to a head they had gained a reputation in southern Germany and northern Italy. Italy had not gone so far down the road towards domination of the electrical industry by one or two firms, and with the encouragement of one of their Italian colleagues Hermann, Jakob and their wives decided to move to Italy to start again. There was one snag. Albert, who was now fifteen, had three years left to complete at the Gymnasium, which would ensure his admission to a good university. A family decision was made to leave him behind in Munich, staying in a boarding house but with a distant relative keeping an eye on him.

The result ought to have been predictable. Albert was lonely and miserable in Munich, and without family life to fall back on the school seemed unbearable. There was another worry. Albert had always hated the militaristic aspect of German society at the time, and as a young boy, scared by the sight and sound of marching troops, had once begged his parents to promise that he would never have to be a soldier. But the law then required every German male to undergo a period of military duty. The only escape was to leave the country and renounce his German citizenship before his seventeenth birthday; if he left later, he would be regarded as a deserter.

Breaking free

There is some confusion about how exactly Einstein engineered his escape from Munich, but this is the most likely pattern of events. He was certainly depressed and managed to persuade his doctor to provide a certificate stating that he should rejoin the family for health reasons. He also persuaded his maths teacher to provide a letter stating that Einstein had already mastered the syllabus, and there was nothing more he could teach the young man. Armed with these documents, Einstein approached the principal of the school and told him that he was leaving; the principal’s response, we are told, was that Einstein was being expelled anyway, for being a disruptive influence. The likelihood is that Einstein had carefully cultivated his role as a disruptive influence in order to ensure that he would not be asked – let alone ordered – to stay on. Whether he jumped or was pushed, there is no doubt that in the spring of 1895, just six months after being left in Munich to complete his education, Einstein turned up on the doorstep of his parents’ new home in Milan, in northern Italy.c He duly renounced his German citizenship (the declaration took effect in January 1896) and swore he would never go back to that country. By then, Einstein was living in Switzerland and set in motion the slow process of obtaining Swiss citizenship; but in those relatively free and easy days in Europe the lack of a passport did not prevent him travelling as he pleased, in particular between Switzerland and Italy. On official forms, under ‘nationality’ he simply described himself as ‘the son of German parents’.

In the summer of 1895 Einstein was sixteen, in Italy, with no responsibilities (and no prospects). Although he did some work for the family business and had vague notions of becoming a teacher of philosophy, for several months he mostly just enjoyed himself, touring the art centres of Italy, visiting the Alps and falling in love with the culture. When pressed by his father to settle down and give some thought to the future, Einstein assured Hermann that in the autumn he would take the entrance examination for the Swiss Federal Polytechnic in Zurich (often known by the initials of its German name, as the ETH). The ETH was not a great university in the mould of Heidelberg or Berlin, but a new kind of institution devoted primarily to the education of would-be teachers and engineers. The cocksure Einstein was certain he would be able to walk into an establishment with such relatively modest academic standards, and it came as a rude shock when he failed the exam. (His later claim to have failed deliberately, in order to avoid being pushed into a profession by his father, should be taken with a large pinch of salt; if that were the case, why would he have gone back and embarked on the same course a year later?)

In fact, Einstein was lucky to be allowed to take the exam. The normal age for this was eighteen, and applicants were expected to have a high school diploma; Einstein was still six months short of his seventeenth birthday and had left high school under a cloud. But the director of the ETH, Albin Herzog, recognised Einstein’s potential and offered him a lifeline. He suggested that Einstein should enrol in a Swiss secondary school in the town of Aarau, a little way outside of Zurich, to do some catching up before taking the entrance exam again in 1896. There, he could lodge in the home of Jost Winteler, a teacher at the school, and live as one of the family.

The domestic arrangements suited Einstein down to the ground. As Winteler taught Latin and Greek he was not one of Einstein’s tutors, so school did not intrude too much on daily life. One of Einstein’s cousins, Robert Koch, was a student at the school and lodging next door. And there was plenty of family life – the Wintelers had three daughters and four sons, plus a couple of other paying guests, and Einstein was soon one of the family. A classmate during this year in Aarau later described the Einstein of 1895–6, to his biographer Carl Seelig, as ‘sure of himself, his grey felt hat pushed back on his thick, black hair [striding] energetically up and down … unhampered by convention, his attitude towards the world was that of the laughing philosopher, and his witty mockery pitilessly lashed any conceit or pose.’

Mature beyond his years, Einstein clearly made a big impact on his companions – none more so than Marie Winteler, the eighteen-year-old daughter of the house, who had just completed her course as a trainee teacher and was living with her parents while waiting to start her first job. In spite of the age difference, an enormous gulf for most teenagers, the two fell in love. Both families seem to have been happy with the development, which blossomed into something like an unofficial engagement and persisted after Einstein returned to Pavia and then moved on to Zurich. But in the spring of 1897, as his own horizons broadened and he made new friends in the city, he broke off the relationship. It took some time to convince Marie that he meant it, but in the end everything was settled amicably, and the Einsteins and the Wintelers remained good friends – so much so that Einstein’s sister Maja later married Marie’s brother Paul. Anna, another of the Winteler siblings, married Michele Besso, Einstein’s best friend in Zurich and for long after his student days were over. In a letter written to Besso’s wife and son after he died in 1955, Einstein said ‘what I admired most about Michele was the fact that he was able to live so many years with one woman, not only in peace but also in constant unity, something I have lamentably failed at twice.’2

Alongside his happy relationship with the Winteler family, an active social life, music and his first experience of love, Einstein did enough work at school (where he had been allowed to join the final year group, with classmates a year older than himself) to achieve high grades in all his subjects except French, which he always struggled with. In the Swiss system, examination papers were marked on a grading scale from 1 to 6, with 6 being the top mark. Einstein’s average of 5½ was the best in his year, from the youngest pupil in the class. Although this was brought down by his French paper, which was rather generously graded between 3–4, the essay he wrote (in French) for the examination is the most interesting of the papers (which survive and can be found in The Collected Papers of Albert Einstein) because the set subject of the essay was ‘Mes Projets d’Avenir’.d Ignoring the terrible French, the essay gives us a glimpse into Einstein’s personal ambitions at the time, which seem remarkably limited in the light of what he would achieve:

If I am lucky enough to pass my examinations, I will attend the Polytechnic in Zurich. I will stay there four years to study mathematics and physics. My idea is to become a teacher in these fields of natural science and I will choose the theoretical part of these sciences.

Einstein goes on to say that this ambition is partly based on the fact that he lacks any ‘practical talent’, but also because ‘there is a certain independence in the profession of science that greatly appeals to me’. That certainly chimes with the way his life would develop. But there was already a hint of what was to come in some of the ideas Einstein did not commit to paper in 1896. He later recalled that while still a schoolboy in Aarau, he puzzled over the idea that if you could run at the speed of light, you would see a light wave standing still alongside you, frozen in time, as it were; but the laws of physics said that such a ‘time-independent wave-field’ could not exist.3 It would be nine years before he found the solution to that puzzle.

Einstein and the Poly

After passing his entrance examination for the ETH early in the summer of 1896, Einstein spent some time with his family in Italy, where the electrical business was once again in crisis. Jakob left to work for another company and ended up living comfortably in Vienna as the manager of a firm of instrument makers; Hermann tried to make another fresh start in Milan. Albert was sufficiently concerned about the prospects for this latest venture that he tried unsuccessfully to dissuade his relations from pouring more money into the scheme; but in October he had to put these family difficulties behind him as he returned to Zurich to enrol for his course.

In spite of the year spent in Aarau, Einstein was still six months short of the official age for admission, eighteen, and one of the youngest students ever admitted to the ETH. The ‘Poly’, as it was known locally, wasn’t that old itself, having been founded in 1855 as the first university-level academic institution in Switzerland (the Swiss Confederation only came into being in 1848). Since then, three universities had been established in Switzerland – in Basel, Zurich and Geneva. Unlike the Poly, which was a Federal Swiss government establishment, the universities were run by their respective cantons. Unlike the universities, initially the Poly could not award doctoral degrees; but in 1911 it was given full university status including the right to award doctorates. That hasn’t stopped it being known as the Poly right down to the present day.

At the end of the 19th century, there were just under a thousand students at the ETH. But, as its name implies, the ETH was primarily devoted to the education of engineers, not theoretical physicists, and there were just five students, including Einstein, taking the science course in his year. These included Marcel Grossmann, a model student who attended all the lectures and took detailed notes which he kept carefully for revision. Grossmann became a firm friend of Einstein, and in the long run those beautifully written notes would prove even more important to him than to Grossmann. The group also included a lone woman, Mileva Maric, a Serbian, from what was then part of the Hungarian Empire. Mileva had had to struggle with an unsympathetic family and unsupportive school system at home to make it to university in Switzerland, the only German-speaking country where women were admitted to university at that time. Indeed, Mileva was only the fifth woman to be admitted to study physics at the ETH. The other two members of the class were Jakob Ehrat, a hardworking but unspectacular student, and Louis Kollros; both, like Grossmann, were Swiss.

Like many students, Einstein enjoyed the freedom of university life to the full and didn’t worry too much about the academic side until the examinations loomed. He didn’t reckon anyone could teach him mathematics better than he could learn on his own with the aid of books, and he seldom attended the lectures, leading one of his professors, Hermann Minkowski, later famously to describe the student Einstein as a ‘lazy dog’, who ‘never bothered about mathematics at all’. In fact, Minkowski was one of the few professors at the ETH that Einstein respected, and when he did attend a lecture given by Minkowski during his final semester at the ETH, Einstein remarked to Louis Kollros that ‘this is the first lecture on mathematical physics we have heard at the Poly’.4

Cutting lectures gave Einstein plenty of time to indulge his passions for: coffee-house discussions with his friends setting the world to rights (including scientific discussions about the latest ideas in physics); the company of women (he always got on well with women, who were charmed by his manners, his music and his masculine good looks); sailing on the lake (where he always took a notebook in case the wind dropped, so that he could scribble down his ideas on physics); and music (combining this with his love of the company of women, Einstein often gave violin recitals in the homes of ladies of his acquaintance). He lived in lodgings in Zurich, getting by financially on an allowance of 100 Swiss francs a month, generously provided by one of his maternal aunts, and supplemented by a little private tuition. Out of this, he set aside 20 francs to save towards the fee he would have to pay when he was eventually awarded Swiss citizenship. On Sundays, he took lunch with the family of Michael Fleischmann, a Zurich businessman, echoing the way the Einsteins had looked after Max Talmey in Munich.

It was music that brought Einstein and his lifelong friend Michele Besso together. Besso was six years older than Einstein and already working as a mechanical engineer. They met at a house where Einstein was among the musicians entertaining a group of students and other people, an important, if informal, social activity in those days before TV, radio or recorded music. It was Besso who introduced Einstein to the work of Ernst Mach, an Austrian philosopher-physicist who had made important contributions to the scientific debate raging at the end of the 19th century concerning the reality of atoms.

From our modern perspective, it is hard to believe that only a little over a hundred years ago people were still arguing about whether or not atoms were real. But this was indeed an important debate, which would influence a great deal of Einstein’s early scientific work and become a significant feature of his annus mirabilis.

Popular accounts of the history of science often tell you that the idea of atoms goes back to the time of the Ancient Greeks, but this is only true up to a point. What is true is that the Greek philosopher Democritus, who lived in the 5th century BC, did discuss the idea that everything is made of tiny, indestructible particles moving through a void (the vacuum) and interacting with one another. But this was never more than a minority view at the time and was dismissed by most of the Ancient Greek thinkers because they could not accept the idea of the void, a genuine nothingness between atoms. The idea was revived from time to time, notably by the Frenchman Pierre Gassendi in the 17th century, but was always dismissed, for the same reason. It was only in the 19th century that a large group of scientists really began to take the idea of atoms seriously, and even then others argued against the idea.

The scientists who took the idea of atoms seriously found evidence supporting it in both chemistry and physics. In the early 1800s, John Dalton, in England, developed the idea that each element (such as hydrogen or oxygen) is made up of a different kind of atom (but with all the atoms of a particular element identical to one another), and that compound substances (such as water) are made up of molecules in which different kinds of atom join together (in this case, as H2O). As early as 1811, jumping off from these chemical discoveries, the Italian Amadeo Avogadro announced his famous hypothesis, that at a given temperature and pressure, equal volumes of gas contain the same number of particles (molecules or atoms), with the clear implication that there is nothing in the space between these particles. But his idea was ignored for decades, and there was no clear idea of the differences between atoms and molecules until the work of Avogadro’s compatriot, Stanislao Cannizaro, in the 1850s.

By then, evidence supporting the idea of molecules was coming in from the physicists. One of the most important practical applications of science in the 19th century concerned the study of heat and motion (known as thermodynamics), which was directly relevant to the application of steam power during the industrial revolution. By studying the way in which heat could be generated and how it flowed from one object to another, scientists came up with laws of thermodynamics to describe the relationship between work and energy on the scale of the kind of machinery that powered the Industrial Revolution – sometimes referred to as the ‘macroscopic’ scale. Physicists such as the Scot James Clerk Maxwell, Hermann von Helmholtz in Germany and the Austrian Ludwig Boltzmann then developed models to describe these macroscopic phenomena in terms of the accumulated effect of huge numbers of atoms and molecules bouncing around and interacting with one another like tiny, hard spheres, obeying the basic laws of mechanics discovered by Isaac Newton 200 years earlier. This behaviour of atoms and molecules at a lower level is often referred to as ‘microscopic’ behaviour, but, crucially, atoms are actually far too small to be seen by any microscope available in the 19th century.