Quantum

by Manjit Kumar

  James Clerk Maxwell, the nineteenth century’s greatest theoretical physicist, had warned as early as 1871 against such complacency: ‘This characteristic of modern experiments – that they consist principally of measurements – is so prominent, that the opinion seems to have got abroad that in a few years all the great physical constants will have been approximately estimated, and that the only occupation which will be left to men of science will be to carry on these measurements to another place of decimals.’13 Maxwell pointed out that the real reward for the ‘labour of careful measurement’ was not greater accuracy but the ‘discovery of new fields of research’ and ‘the development of new scientific ideas’.14 The discovery of the quantum was the result of just such a ‘labour of careful measurement’.

  In the 1890s some of Germany’s leading physicists were obsessively pursuing a problem that had long vexed them: what was the relationship between the temperature, the range of colours, and the intensity of light emitted by a hot iron poker? It seemed a trivial problem compared to the mystery of X-rays and radioactivity that had physicists rushing to their laboratories and reaching for their notebooks. But for a nation forged only in 1871, the quest for the solution to the hot iron poker, or what became known as ‘the blackbody problem’, was intimately bound up with the need to give the German lighting industry a competitive edge against its British and American competitors. But try as they might, Germany’s finest physicists could not solve it. In 1896 they thought they had, only to find within a few short years that new experimental data proved that they had not. It was Max Planck who solved the blackbody problem, at a cost. The price was the quantum.

  PART I

  THE QUANTUM

  ‘Briefly summarized, what I did can be described as simply an act of desperation.’

  —MAX PLANCK

  ‘It was as if the ground had been pulled out from under one, with no firm foundation to be seen anywhere, upon which one could have built.’

  —ALBERT EINSTEIN

  ‘For those who are not shocked when they first come across quantum theory cannot possibly have understood it.’

  —NIELS BOHR

  Chapter 1

  THE RELUCTANT REVOLUTIONARY

  ‘A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it’, wrote Max Planck towards the end of his long life.1 Bordering on cliché, it could easily have served as his own scientific obituary had he not as an ‘act of desperation’ abandoned ideas that he had long held dear.2 Wearing his dark suit, starched white shirt and black bow tie, Planck looked the archetypal late nineteenth-century Prussian civil servant but ‘for the penetrating eyes under the huge dome of his bald head’.3 In characteristic mandarin fashion he exercised extreme caution before committing himself on matters of science or anything else. ‘My maxim is always this,’ he once told a student, ‘consider every step carefully in advance, but then, if you believe you can take responsibility for it, let nothing stop you.’4 Planck was not a man to change his mind easily.

  His manner and appearance had hardly changed when to students in the 1920s, as one recalled later, ‘it seemed inconceivable that this was the man who had ushered in the revolution’.5 The reluctant revolutionary could scarcely believe it himself. By his own admission he was ‘peacefully inclined’ and avoided ‘all doubtful adventures’.6 He confessed that he lacked ‘the capacity to react quickly to intellectual stimulation’.7 It often took him years to reconcile new ideas with his deep-rooted conservatism. Yet at the age of 42, it was Planck who unwittingly started the quantum revolution in December 1900 when he discovered the equation for the distribution of radiation emitted by a blackbody.

  All objects, if hot enough, radiate a mixture of heat and light, with the intensity and colour changing with the temperature. The tip of an iron poker left in a fire will start to glow a faint dull red; as its temperature rises it becomes a cherry red, then a bright yellowish-orange, and finally a bluish-white. Once taken out of the fire the poker cools down, running through this spectrum of colours backwards until it is no longer hot enough to emit any visible light. Even then it still gives off an invisible glow of heat radiation. After a time this too stops as the poker continues to cool and finally becomes cold enough to touch.

  It was the 23-year-old Isaac Newton who, in 1666, showed that a beam of white light was woven from different threads of coloured light and that passing it through a prism simply unpicked the seven separate strands: red, orange, yellow, green, blue, indigo, and violet.8 Whether red and violet represented the limits of the light spectrum or just those of the human eye was answered in 1800. It was only then, with the advent of sufficiently sensitive and accurate mercury thermometers, that the astronomer William Herschel placed one in front of a spectrum of light and found that as he moved it across the bands of different colours from violet to red, the temperature rose. To his surprise it continued to rise when he accidentally left the thermometer up to an inch past the region of red light. Herschel had detected what was later called infrared radiation, light that was invisible to human eyes from the heat that it generated.9 In 1801, using the fact that silver nitrate darkens when exposed to light, Johann Ritter discovered invisible light at the other end of the spectrum beyond the violet: ultraviolet radiation.

  The fact that all heated objects emit light of the same colour at the same temperature was well known to potters long before 1859, the year that Gustav Kirchhoff, a 34-year-old German physicist at Heidelberg University, started his theoretical investigations into the nature of this correlation. To help simplify his analysis, Kirchhoff developed the concept of a perfect absorber and emitter of radiation called a blackbody. His choice of name was apt. A body that was a perfect absorber would reflect no radiation and therefore appear black. However, as a perfect emitter its appearance would be anything but black if its temperature was high enough for it to radiate at wavelengths from the visible part of the spectrum.

  Kirchhoff envisaged his imaginary blackbody as a simple hollow container with a tiny hole in one of its walls. Since any radiation, visible or invisible light, entering the container does so through the hole, it is actually the hole that mimics a perfect absorber and acts like a blackbody. Once inside, the radiation is reflected back and forth between the walls of the cavity until it is completely absorbed. Imagining the outside of his blackbody to be insulated, Kirchhoff knew that if heated, only the interior surface of the walls would emit radiation that filled the cavity.

  At first the walls, just like a hot iron poker, glow a deep cherry-red even though they still radiate predominantly in the infrared. Then, as the temperature climbs ever higher, the walls glow a bluish-white as they radiate at wavelengths from across the spectrum from the far infrared to the ultraviolet. The hole acts as a perfect emitter since any radiation that escapes through it will be a sample of all the wavelengths present inside the cavity at that temperature.

  Kirchhoff proved mathematically what potters had long observed in their kilns. Kirchhoff’s law said that the range and intensity of the radiation inside the cavity did not depend on the material that a real blackbody could be made of, or on its shape and size, but only on its temperature. Kirchhoff had ingeniously reduced the problem of the hot iron poker: what was the exact relationship between the range and intensity of the colours it emitted at a certain temperature to how much energy is radiated by a blackbody at that temperature? The task that Kirchhoff set himself and his colleagues became known as the blackbody problem: measure the spectral energy distribution of blackbody radiation, the amount of energy at each wavelength from the infrared to the ultraviolet, at a given temperature and derive a formula to reproduce the distribution at any temperature.

  Unable to go further theoretically without experiments with a real blackbody to guide him, Kirchhoff nevertheless pointed physicists in the right direction. He told them that the distribution being inde
pendent of the material from which a blackbody was made meant that the formula should contain only two variables: the temperature of the blackbody and the wavelength of the emitted radiation. Since light was thought to be a wave, any particular colour and hue was distinguished from every other by its defining characteristic: its wavelength, the distance between two successive peaks or troughs of the wave. Inversely proportional to the wavelength is the frequency of the wave – the number of peaks, or troughs, that pass a fixed point in one second. The longer the wavelength, the lower the frequency and vice versa. But there was also a different but equivalent way of measuring the frequency of a wave: the number of times it jiggled up and down, ‘waved’, per second.10

  Figure 1: The characteristics of a wave

  The technical obstacles in constructing a real blackbody and the precision instruments needed to detect and measure the radiation ensured that no significant progress was made for almost 40 years. It was in the 1880s, when German companies tried to develop more efficient light bulbs and lamps than their American and British rivals, that measuring the blackbody spectrum and finding Kirchhoff’s fabled equation became a priority.

  The incandescent light bulb was the latest in a series of inventions, including the arc lamp, dynamo, electric motor, and telegraphy, fuelling the rapid expansion of the electrical industry. With each innovation the need for a globally agreed set of units and standards of electrical measurement became increasingly urgent.

  Two hundred and fifty delegates from 22 countries gathered in Paris, in 1881, for the first International Conference for the Determination of Electrical Units. Although the volt, amp and other units were defined and named, no agreement was reached on a standard for luminosity and it began to hamper the development of the most energy-efficient means of producing artificial light. As a perfect emitter at any given temperature, a blackbody emits the maximum amount of heat, infrared radiation. The blackbody spectrum would serve as a benchmark in calibrating and producing a bulb that emitted as much light as possible while keeping the heat it generated to a minimum.

  ‘In the competition between nations, presently waged so actively, the country that first sets foot on new paths and first develops them into established branches of industry has a decisive upper hand’, wrote the industrialist and inventor of the electrical dynamo, Werner von Siemens.11 Determined to be first, in 1887 the German government founded the Physikalisch-Technische Reichsanstalt (PTR), the Imperial Institute of Physics and Technology. Located on the outskirts of Berlin in Charlottenburg, on land donated by Siemens, the PTR was conceived as an institute fit for an empire determined to challenge Britain and America. The construction of the entire complex lasted more than a decade, as the PTR became the best-equipped and most expensive research facility in the world. Its mission was to give Germany the edge in the appliance of science by developing standards and testing new products. Among its list of priorities was to devise an internationally recognised unit of luminosity. The need to make a better light bulb was the driving force behind the PTR blackbody research programme in the 1890s. It would lead to the accidental discovery of the quantum as Planck turned out to be the right man, in the right place, at the right time.

  Max Karl Ernst Ludwig Planck was born in Kiel, then a part of Danish Holstein, on 23 April 1858 into a family devoted to the service of Church and State. Excellence in scholarship was almost his birthright. Both his paternal great-grandfather and grandfather had been distinguished theologians, while his father became professor of constitutional law at Munich University. Venerating the laws of God and Man, these duty-bound men of probity were also steadfast and patriotic. Max was to be no exception.

  Planck attended the most renowned secondary school in Munich, the Maximilian Gymnasium. Always near the top of his class, but never first, he excelled through hard work and self-discipline. These were just the qualities demanded by an educational system with a curriculum founded on the retention of enormous quantities of factual knowledge through rote learning. A school report noted that ‘despite all his childishness’ Planck at ten already possessed ‘a very clear, logical mind’ and promised ‘to be something right’.12 By the time he was sixteen it was not Munich’s famous taverns but its opera houses and concert halls that attracted the young Planck. A talented pianist, he toyed with the idea of pursuing a career as a professional musician. Unsure, he sought advice and was bluntly told: ‘If you have to ask, you’d better study something else!’13

  In October 1874, aged sixteen, Planck enrolled at Munich University and opted to study physics because of a burgeoning desire to understand the workings of nature. In contrast to the near-militaristic regime of the Gymnasiums, German universities allowed their students almost total freedom. With hardly any academic supervision and no fixed requirements, it was a system that enabled students to move from one university to another, taking courses as they pleased. Sooner or later those wishing to pursue an academic career took the courses by the pre-eminent professors at the most prestigious universities. After three years at Munich, where he was told ‘it is hardly worth entering physics anymore’ because there was nothing important left to discover, Planck moved to the leading university in the German-speaking world, Berlin.14

  With the creation of a unified Germany in the wake of the Prussian-led victory over France in the war of 1870–71, Berlin became the capital of a mighty new European nation. Situated at the confluence of the Havel and the Spree rivers, French war reparations allowed its rapid redevelopment as it sought to make itself the equal of London and Paris. A population of 865,000 in 1871 swelled to nearly 2 million by 1900, making Berlin the third-largest city in Europe.15 Among the new arrivals were Jews fleeing persecution in Eastern Europe, especially the pogroms in Tsarist Russia. Inevitably the cost of housing and living soared, leaving many homeless and destitute. Manufacturers of cardboard boxes advertised ‘good and cheap boxes for habitation’ as shanty towns sprung up in parts of the city.16

  Despite the bleak reality that many found on arriving in Berlin, Germany was entering a period of unprecedented industrial growth, technological progress, and economic prosperity. Driven largely by the abolition of internal tariffs after unification and French war compensation, by the outbreak of the First World War Germany’s industrial output and economic power would be second only to the United States. By then it was producing over two-thirds of continental Europe’s steel, half its coal, and was generating more electricity than Britain, France and Italy combined. Even the recession and anxiety that affected Europe after the stock market crash of 1873 only slowed the pace of German development for a few years.

  With unification came the desire to ensure that Berlin, the epitome of the new Reich, had a university second to none. Germany’s most renowned physicist, Herman von Helmholtz, was enticed from Heidelberg. A trained surgeon, Helmholtz was also a celebrated physiologist who had made fundamental contributions to understanding the workings of the human eye after his invention of the ophthalmoscope. The 50-year-old polymath knew his worth. Apart from a salary several times the norm, Helmholtz demanded a magnificent new physics institute. It was still being built in 1877 when Planck arrived in Berlin and began attending lectures in the university’s main building, a former palace on Unter den Linden opposite the Opera House.

  As a teacher, Helmholtz was a severe disappointment. ‘It was obvious,’ Planck said later, ‘that Helmholtz never prepared his lectures properly.’17 Gustav Kirchhoff, who had also transferred from Heidelberg to become the professor of theoretical physics, was so well prepared that he delivered his lectures ‘like a memorized text, dry and monotonous’.18 Expecting to be inspired, Planck admitted ‘that the lectures of these men netted me no perceptible gain’.19 Seeking to quench his ‘thirst for advanced scientific knowledge’, he stumbled across the work of Rudolf Clausius, a 56-year-old German physicist at Bonn University.20

  In stark contrast to the lacklustre teaching of his two esteemed professors, Planck was immediately enthralled by Claus
ius’ ‘lucid style and enlightening clarity of reasoning’.21 His enthusiasm for physics returned as he read Clausius’ papers on thermodynamics. Dealing with heat and its relationship to different forms of energy, the fundamentals of thermodynamics were at the time encapsulated in just two laws.22 The first was a rigorous formulation of the fact that energy, in whatever guise, possessed the special property of being conserved. Energy could neither be created nor destroyed but only converted from one form to another. An apple hanging from a tree possesses potential energy by virtue of its position in the earth’s gravitational field, its height above the ground. When it falls, the apple’s potential energy is converted into kinetic energy, the energy of motion.

  Planck was a schoolboy when he first encountered the law of the conservation of energy. It struck him ‘like a revelation’ he said later, because it possessed ‘absolute, universal validity, independently from all human agency’.23 It was the moment he caught a glimpse of the eternal, and from then on he considered the search for absolute or fundamental laws of nature ‘as the most sublime scientific pursuit in life’.24 Now Planck was just as spellbound reading Clausius’ formulation of the second law of thermodynamics: ‘Heat will not pass spontaneously from a colder to a hotter body.’25 The later invention of the refrigerator illustrated what Clausius meant by ‘spontaneously’. A refrigerator needed to be plugged into an external supply of energy, in this case electrical, so that heat could be made to flow from a colder to a hotter body.