by Manjit Kumar
Figure 4: Young’s two-slits experiment. At far right, the resulting interference pattern on the screen is shown
To explain the appearance of these bright and dark ‘fringes’, Young used an analogy. Two stones are dropped simultaneously and close together into a still lake. Each stone produces waves that spread out across the lake. As they do so, the ripples originating from one stone encounter those from the other. At each point where two wave troughs or two wave crests meet, they coalesce to produce a new single trough or crest. This was constructive interference. But where a trough meets a crest or vice versa, they cancel each other out, leaving the water undisturbed at that point – destructive interference.
In Young’s experiment, light waves originating from the two slits similarly interfere with each other before striking the screen. The bright fringes indicate constructive interference while the dark fringes are a product of destructive interference. Young recognised that only if light is a wave phenomenon could these results be explained. Newton’s particles would simply produce two bright images of the slits with nothing but darkness in between. An interference pattern of bright and dark fringes was simply impossible.
When he first put forward the idea of interference and reported his early results in 1801, Young was viciously attacked in print for challenging Newton. He tried to defend himself by writing a pamphlet in which he let everyone know his feelings about Newton: ‘But, much as I venerate the name of Newton, I am not therefore obliged to believe that he was infallible. I see, not with exultation, but with regret, that he was liable to err, and that his authority has, perhaps, sometimes even retarded the progress of science.’70 Only a single copy was sold.
It was a French civil engineer who followed Young in stepping out of Newton’s shadow. Augustin Fresnel, fifteen years his junior, independently rediscovered interference and much else of what Young, unknown to him, had already done. However, compared to the Englishman, Fresnel’s elegantly designed experiments were more extensive, with the presentation of results and accompanying mathematical analysis so impeccably thorough that the wave theory started to gain distinguished converts by the 1820s. Fresnel convinced them that the wave theory could better explain an array of optical phenomena than Newton’s particle theory. He also answered the long-standing objection to the wave theory: light cannot travel around corners. It does, he said. However, since light waves are millions of times smaller than sound waves, the bending of a beam of light from a straight path is very, very small and therefore extremely difficult to detect. A wave bends only around an obstacle not much longer than itself. Sound waves are very long and can easily move around most barriers they encounter.
One way to get opponents and sceptics to finally decide between the two rival theories was to find observations for which they predicted different results. Experiments conducted in France in 1850 revealed that the speed of light was slower in a dense medium such as glass or water than in the air. This was exactly what the wave of light predicted, while Newton’s corpuscles failed to travel as fast as expected. But the question remained: if light was a wave, what were its properties? Enter James Clerk Maxwell and his theory of electromagnetism.
Born in 1831 in Edinburgh, Maxwell, the son of a Scottish landowner, was destined to become the greatest theoretical physicist of the nineteenth century. At the age of fifteen, he wrote his first published paper on a geometrical method for tracing ovals. In 1855 he won Cambridge University’s Adams Prize for showing that Saturn’s rings could not be solid, but had to be made of small, broken bits of matter. In 1860 he instigated the final phase of the development of the kinetic theory of gases, the properties of gases explained by maintaining that they consisted of particles in motion. But his greatest achievement was the theory of electromagnetism.
In 1819 the Danish physicist Hans Christian Oersted discovered that an electric current flowing through a wire deflected a compass needle. A year later the Frenchman François Arago found that a wire carrying an electric current acted as a magnet and could attract iron filings. Soon his compatriot André Marie Ampère demonstrated that two parallel wires were attracted towards one another if each had a current flowing through it in the same direction. However, they repelled each other if the currents flowed in the opposite directions. Intrigued by the fact that a flow of electricity could create magnetism, the great British experimentalist Michael Faraday decided to see if he could generate electricity using magnetism. He pushed a bar magnet in and out of a helix coil of wire and found an electric current being generated. The current ceased whenever the magnet was motionless within the coil.
Just as ice, water and steam are different manifestations of H2O, Maxwell showed in 1864 that electricity and magnetism were likewise different manifestations of the same underlying phenomenon – electromagnetism. He managed to encapsulate the disparate behaviour of electricity and magnetism into a set of four elegant mathematical equations. On seeing them, Ludwig Boltzmann immediately recognised the magnitude of Maxwell’s achievement and could only quote Goethe in admiration: ‘Was it a God that wrote these signs?’71 Using these equations, Maxwell was able to make the startling prediction that electromagnetic waves travelled at the speed of light through the ether. If he was right, then light was a form of electromagnetic radiation. But did electromagnetic waves actually exist? If so, did they really travel at the speed of light? Maxwell did not live long enough to see his prediction confirmed by experiment. Aged just 48, he died from cancer in November 1879, the year Einstein was born. Less than a decade later, in 1887, Heinrich Hertz provided the experimental corroboration that ensured Maxwell’s unification of electricity, magnetism and light was the crowning achievement of nineteenth-century physics.
Hertz proclaimed in his paper outlining his investigations: ‘The experiments described appear to me, at any rate, eminently adapted to remove any doubt as to the identity of light, radiant heat, and electromagnetic wave motion. I believe that from now on we shall have greater confidence in making use of the advantages, which this identity enables us to derive both in the study of optics and electricity.’72 Ironically, it was during these very experiments that Hertz discovered the photoelectric effect that provided Einstein with evidence for a case of mistaken identity. His light-quanta challenged the wave theory of light that Hertz and everyone else thought was well and truly established. Light as a form of electromagnetic radiation had proved so successful that for physicists to even contemplate discarding it in favour of Einstein’s light-quanta was unthinkable. Many found light-quanta absurd. After all, the energy of a particular quantum of light was determined by the frequency of that light, but surely frequency was something associated with waves, not particle-like bits of energy travelling through space.
Einstein readily accepted that the wave theory of light had ‘proved itself superbly’ in explaining diffraction, interference, reflection and refraction, and that it would ‘probably never be replaced by another theory’.73 However, this success, he pointed out, rested on the vital fact that all these optical phenomena involved the behaviour of light over a period of time, and any particle-like properties would not be manifest. The situation was starkly different when it came to the virtually ‘instantaneous’ emission and absorption of light. This was the reason, Einstein suggested, why the wave theory faced ‘especially great difficulties’ explaining the photoelectric effect.74
A future Nobel laureate, but in 1906 a privatdozent at Berlin University, Max Laue wrote to Einstein that he was willing to accept that quanta may be involved during the emission and absorption of light. However, that was all. Light itself was not made up of quanta, warned Laue, but it is ‘when it is exchanging energy with matter that it behaves as if it consisted of them’.75 Few even conceded that much. Part of the problem lay with Einstein himself. In his original paper he did say that light ‘behaves’ as though it consisted of quanta. This was hardly a categorical endorsement of the quantum of light. This was because Einstein wanted something more than just a ‘heuristic point of vie
w’: he craved a fully-fledged theory.
The photoelectric effect had proved to be a battlefield for the clash between the supposed continuity of light waves and the discontinuity of matter, atoms. But in 1905 there were still those who doubted the reality of atoms. On 11 May, less than two months after he finished his quantum paper, the Annalen der Physik received Einstein’s second paper of the year. It was his explanation of Brownian motion and it became a key piece of evidence in support of the existence of atoms.76
When in 1827 the Scottish botanist Robert Brown peered through a microscope at some pollen grains suspended in water, he saw that they were in a constant state of haphazard motion as if buffeted by some unseen force. It had already been noted by others that this erratic wiggling increased as the temperature of the water rose, and it was assumed that some sort of biological explanation lay behind the phenomenon. However, Brown discovered that when he used pollen grains that were up to twenty years old they moved in exactly the same way. Intrigued, he produced fine powders of all manner of inorganic substances, from glass to a piece of the Sphinx, and suspended each of them in water. He found the same zigzagging motion in each case and realised that it could not be animated by some vital force. Brown published his research in pamphlet entitled: A Brief Account of Microscopical Observations Made in the Months of June, July, and August 1827, on the Particles Contained in the Pollen of Plants; and on the General Existence of Active Molecules in Organic and Inorganic Bodies. Others offered plausible explanations of ‘Brownian motion’, but all were sooner or later found wanting. By the end of the nineteenth century, those who believed in the existence of atoms and molecules accepted that Brownian motion was the result of collisions with water molecules.
What Einstein recognised was that the Brownian motion of a pollen grain was not caused by a single collision with a water molecule, but was the product of a large number of such collisions. At each moment, the collective effect of these collisions was the random zigzagging of the pollen grain or suspended particle. Einstein suspected that the key to understanding this unpredictable motion lay in deviations, statistical fluctuations, from the expected ‘average’ behaviour of water molecules. Given their relative sizes, on average, many water molecules would strike an individual pollen grain simultaneously from different directions. Even on this scale, each collision would result in an infinitesimal push in one direction, but the overall effect of all of them would leave the pollen unmoved as they cancelled each other out. Einstein realised that Brownian motion was due to water molecules regularly deviating from their ‘normal’ behaviour as some of them got bunched up and struck the pollen together, sending it in particular direction.
Using this insight, Einstein succeeded in calculating the average horizontal distance a particle would travel as it zigzagged along in a given time. He predicted that in water at 17°C, suspended particles with a diameter of one-thousandth of a millimetre would move on average just six-thousandths of a millimetre in one minute. Einstein had come up with a formula that offered the possibility of working out the size of atoms armed only with a thermometer, microscope and stopwatch. Three years later, in 1908, Einstein’s predictions were confirmed in a delicate series of experiments conducted at the Sorbonne by Jean Perrin, for which he received the Nobel Prize in 1926.
With Planck championing the theory of relativity, and the analysis of Brownian motion recognised as a decisive breakthrough in favour of the atom, Einstein’s reputation grew despite the rejection of his quantum theory of light. He received letters often addressed to him at Bern University, as few knew he was a patent clerk. ‘I must tell you quite frankly that I was surprised to read that you must sit in an office for 8 hours a day,’ wrote Jakob Laub from Würzburg. ‘History is full of bad jokes.’77 It was March 1908 and Einstein agreed. After almost six years he no longer wanted to be a patent slave.
He applied for a job as a mathematics teacher at a school in Zurich, stating that he would be ready and willing to teach physics as well. With his application he enclosed a copy of his thesis that had earned him, at the third attempt, a doctorate from Zurich University in 1905 and laid the groundwork for the paper on Brownian motion. Hoping it would bolster his chances, he also sent all of his published papers. Despite his impressive scientific achievements, of the 21 applicants, Einstein did not even make the short list of three.
It was at the behest of Alfred Kleiner, the professor of experimental physics at Zurich University, that Einstein tried for a third time to become a privatdozent, an unpaid lecturer, at the University of Bern. The first application was rejected because at the time he did not have a PhD. In June 1907, he failed a second time because he did not submit a habilitationsschrift – a piece of unpublished research. Kleiner wanted Einstein to fill a soon-to-be-created extraordinary professorship in theoretical physics, and being a privatdozent was a necessary stepping-stone to such an appointment. So he produced a habilitationsschrift as demanded and was duly appointed a privatdozent in the spring of 1908.
Only three students attended his first lecture course on the theory of heat. All three were friends. They had to be, since Einstein had been allocated Tuesdays and Saturdays between seven and eight in the morning. University students had the choice of whether or not to attend courses offered by a privatdozent and none were willing to get up that early. As a lecturer, then and later, Einstein was often under-prepared and made frequent mistakes. And when he did, he simply turned to the students and asked: ‘Who can tell me where I went wrong?’ or ‘Where have I made a mistake?’ If a student pointed out an error in his mathematics, Einstein would say, ‘I have often told you, my mathematics have never been up to much.’78
The ability to teach was a vital consideration for the job earmarked for Einstein. To ensure that he was up to the task, Kleiner organised to attend one of his lectures. Annoyed at ‘having-to-be-investigated’, he performed poorly.79 However, Kleiner gave him a second chance to impress and he did. ‘I was lucky’, Einstein wrote to his friend Jakob Laub. ‘Contrary to my habit, I lectured well on that occasion – and so it came to pass.’80 It was May 1909 and Einstein could finally boast that he was ‘an official member of the guild of whores’ as he accepted the Zurich post.81 Before moving to Switzerland with Mileva and five-year-old Hans Albert, Einstein travelled to Salzburg in September to give the keynote lecture to the cream of German physics at a conference of the Gesellschaft Deutscher Naturforscher und Ärtze. He went well prepared.
It was a singular honour to be asked to deliver such a lecture. It was one usually reserved for a distinguished elder statesman of physics, not someone who had just turned 30 and was about take up his first extraordinary professorship. So all eyes were on Einstein, but he seemed oblivious as he paced the podium and delivered what would turn out to be a celebrated lecture: ‘On the Development of Our Views Concerning the Nature and Constitution of Radiation’. He told the audience that ‘the next stage in the development of theoretical physics will bring us a theory of light that may be conceived of as a sort of fusion of the wave and of the emission theory of light’.82 It was not a hunch, but based on the result of an inspired thought experiment involving a mirror suspended inside a blackbody. He managed to derive an equation for the fluctuations of the energy and momentum of radiation that contained two very distinct parts. One corresponded to the wave theory of light, while the other had all the hallmarks of the radiation being composed of quanta. Both parts appeared to be indispensable, as did the two theories of light. It was the first prediction of what would later be called wave-particle duality – that light was both a particle and a wave.
Planck, who was chairing, was the first to speak after Einstein sat down. He thanked him for the lecture and then told everyone he disagreed. He reiterated his firmly held belief that quanta were necessary only in the exchange between matter and radiation. To believe as Einstein did that light was actually made up of quanta, Planck said, was ‘not yet necessary’. Only Johannes Stark stood up to support Einstein. Sa
dly, he, like Lenard, would later become a Nazi and the two of them would attack Einstein and his work as ‘Jewish Physics’.
Einstein left the Patent Office to devote more of his time to research. He was in for a rude awakening when he arrived in Zurich. The time he needed to prepare for the seven hours of lectures that he gave each week left him complaining that his ‘actual free time is less than in Bern’.83 The students were struck by the shabby appearance of their new professor, but Einstein quickly gained their respect and affection by his informal style as he encouraged them to interrupt if anything was unclear. Outside formal lectures, at least once a week he took his students along to the Café Terasse to chat and gossip until closing time. Before long he got used to his workload and turned his attention to using the quantum to solve a long-standing problem.
In 1819 two French scientists, Pierre Dulong and Alexis Petit, measured the specific heat capacity, the amount of energy needed to raise the temperature of a kilogram of a substance by one degree, for various metals from copper to gold. For the next 50 years no one who believed in atoms doubted their conclusion that ‘the atoms of all simple bodies have exactly the same heat capacity’.84 It therefore came as a great surprise when, in the 1870s, exceptions were discovered.
Imagining that the atoms of a substance oscillated when heated, Einstein adapted Planck’s approach as he tackled the specific heat anomalies. Atoms could not oscillate with just any frequency, but were ‘quantised’ – able to oscillate only with those frequencies that were multiples of a certain ‘fundamental’ frequency. Einstein came up with a new theory of how solids absorb heat. Atoms are permitted to absorb energy only in discrete amounts, quanta. However, as the temperature drops, the amount of energy the substance has decreases, until there is not enough available to provide each atom with the correct-sized quantum of energy. This results in less energy being taken up by the solid and leads to a decrease in specific heat.
