Counting in the Dark

With a mane of brilliant gray hair, large and penetrating eyes, a beatific smile, prolific interests in science, literature, and the arts, and a name linked to Albert Einstein—Satyendra Nath Bose was a legend in his own lifetime. In 1924 from Dacca, which was the capital of Bangladesh but essentially nowhere in the scientific world, he wrote a brilliant paper that confirmed Einstein’s contested view of the photon.¹ It showed that photons are not ordinary particles but strange entities that tend to flock together following a different kind of particle statistics. Einstein read the paper and, bolstered by this unexpected vindication of his idea, applied Bose’s method to ideal gases, laying the foundations of the quantum theory of gases. The new statistics came to be known as Bose–Einstein statistics. Indeed, Bose had not realized that his observations were truly original.² Abraham Pais, a physicist and biographer of Einstein, noted that “there had been no such successful shot in the dark since [Max] Planck introduced the quantum in 1900.”³ Bose’s paper was the last of the four revolutionary publications that completed the old quantum theory and led to the new quantum mechanics, the others being those of Planck in 1900, Einstein in 1905, and Niels Bohr in 1913.⁴

Bose was born on January 1, 1894, in Calcutta, the capital of British India. After London, it was seen as the second city of the empire on which the sun never set. At the time, an awakening of national pride was evident in the ongoing Bengal Renaissance movement, which had been spearheaded by Raja Ram Mohan Roy beginning in the late eighteenth century. A galaxy of brilliant and rebellious men appeared on the scene, embracing Western learning and science from an essentially Indian standpoint. Bose’s family was drawn into that movement, and his father, Surendranath, was inspired to set up his own chemical and pharmaceutical industry. It soon spurred an accompanying political movement. The unrest was becoming uncomfortable for the British and, in 1905, when Bose was only eleven, Lord Curzon, the British viceroy, divided Bengal into two parts. The partition sparked off widespread protests, touching the lives of many a young man. Bose’s father instructed his only son not to get involved in the political movement or attend any musical events. He obeyed the first instruction but quietly disobeyed the second.

Bose’s mathematical abilities first became evident when he was in the upper classes in school. His mathematics teacher once gave him 110 out of 100 marks on a class test. He had answered all the questions correctly and, in some cases, showed more than one method to get to the answer. The teacher predicted that Bose would one day be known as a great mathematician.

Bose subsequently joined the prestigious Presidency College, where his professors included the physicist-cum-botanist Jagadish Chandra Bose, discoverer of microwaves and a pioneer in plant electrophysiology, and the chemist Prafulla Chandra Ray, known for his work with mercurous nitrite and as a great teacher, historian, industrialist, and philanthropist. Among Bose’s classmates was Meghnad Saha who came from a poor family in East Bengal, now Bangladesh, and went on to do pioneering work in astrophysics. Saha was the first to apply the Bohr theory of atoms to calculate the temperature, pressure, and chemical composition of stars from the degree of ionization of the atoms near their surface. This work provided an explanation for why the stars seemed to have completely different chemical compositions depending on their size and temperature.

Bose and Saha became great friends. They studied mathematics together and were eventually appointed assistant lecturers in physics at the newly established University College of Science and Technology in Calcutta, founded in 1914. The pair had learned German, French, and English so that they could study the papers that were being written by Planck, Einstein, and other European scientists.

A momentous event in physics occurred following the total solar eclipse of May 29, 1919, when Arthur Eddington observed the deflection of starlight passing near the sun. His observations vindicated Einstein’s prediction for the gravitational bending of light. After this event, Bose and Saha translated all of Einstein’s and Hermann Minkowski’s papers from German into English. These were published by the University of Calcutta in 1920 in a volume entitled The Principle of Relativity, with an introduction by Prasanta Chandra Mahalanobis, a friend of Bose and Saha who would go on to become a pioneer in statistics in India. These were the first translations of Einstein’s papers into English.

Bose and Saha wrote their first research paper together on the equation of state for real gases.⁵ Saha then went abroad to work with Ralph Fowler in England, where he would further develop his theory of thermal ionization. Bose joined the newly established University of Dacca as a Reader in Physics. It was while teaching quantum theory in Dacca that he first noticed a logical problem in all known derivations of the Planck law of blackbody radiation. The problem was further accentuated when Saha drew his attention to Wolfgang Pauli’s derivation of the law, which had just appeared in print.⁶ It presented a conjectured probability of electron-photon scattering that depended on both the initial and final states, something that appeared crazy at the time. Bose was grappling with this problem sometime between late 1923 and early 1924 when he hit upon his great idea. He succeeded in deriving the Planck formula free of such logical difficulties by treating blackbody radiation as a gas of photons with a new statistics. Unable to get his paper published in the Philosophical Magazine, he sent it to Einstein with a humble request to have it translated into German and published in a reputable German journal. Einstein was, of course, delighted at this unexpected confirmation of his photon idea, albeit adapted by Bose to take account of its correct statistics. Einstein translated the paper himself and got it published in Zeitschrift für Physik with a translator’s footnote: “In my opinion Bose’s derivation signifies an important advance. The method used here gives the quantum theory of an ideal gas as I will work out elsewhere.”⁷

Thus began the writing of Einstein’s seminal papers on the new statistics. In communications to the Prussian Academy in Berlin on July 10, 1924, January 8, 1925, and January 29, 1925, he extended Bose’s method to ideal gases and predicted the Bose–Einstein condensates, a form of ultracold matter that would not be observed until seventy years later.⁸

The discovery merits an account in more detail.

The Story of Bose Statistics

On the afternoon of Sunday, October 7, 1900, Heinrich Rubens had tea with Planck and told him about the latest experimental data on the blackbody spectrum that he and Ferdinand Kurlbaum had obtained. After Rubens left, Planck set about finding a mathematical formula that would fit the data. He succeeded with his formula,

$\textit{ρ}(v,t) = \big(\frac{8πv^2 dv}{c^3}\big) \big(\frac{hv}{e \frac{hv}{kT} -1} \big) ,$

incorporating the new fundamental constant h with the dimension of action. It agreed with the classical Rayleigh–Jeans law and the empirically established Wien’s law, but only in the low- and high-frequency limits and not in the intermediate range. It became clear that the interpolating formula, which fit the data accurately across the entire spectrum, could not be deduced from classical theory. Clearly, some theoretical justification for it was required. Planck tried very hard and finally, as “an act of desperation … to obtain a positive result, under any circumstance and at whatever cost,” he introduced the concept of irreducible packets, or quanta, of energy for the material in the oven walls, not in the radiation itself.⁹ In mid-December 1900, he presented a statistical derivation involving a distribution W of the energy quanta among the hypothetical wall resonators. It had no more justification than that it gave the desired result. In 1907 he wrote:

I am not seeking the meaning of the quantum of action [light-quanta] in the vacuum but rather in places where absorption and emission occur, and [I] assume that what happens in the vacuum is rigorously described by Maxwell’s equations.¹⁰

Einstein had appeared on the scene in 1905. With his background in thermodynamics and statistical mechanics, and taking into account Boltzmann’s equation for entropy S = klnW, he was aware of the shaky foundations of Planck’s derivation of his law. Suspecting that the law implied a nonclassical, corpuscular nature of radiation itself, he used Wilhelm Wien’s results on the entropy of radiation to calculate the volume dependence of the entropy of thermal radiation. He drew the revolutionary conclusion that “[m]onochromatic radiation of low density (within the range of validity of Wien’s radiation formula) behaves thermodynamically as if it consisted of mutually independent energy quanta [emphasis added] of magnitude Rßv / N.”¹¹ The factor Rßv / N equals hv. Thus was born the idea of light quanta, now called photons. Einstein applied this principle to three empirically known phenomena: the Stokes rule in photoluminescence, the photoelectric effect, and the ionization of gases by ultraviolet light. Among these, the application to photoelectricity has drawn the most public attention as it eventually led Einstein to a Nobel Prize.

But Einstein’s idea of mutually independent energy quanta had its own problem. Władysław Natanson, as well as Paul Ehrenfest and Heike Kamerlingh Onnes, showed that it clashed with the Planck law, and therefore with Planck’s distribution W, which required indistinguishable and correlated quanta, not mutually independent quanta.¹²

Most physicists were skeptical of the light-quantum hypothesis even after Robert Millikan’s detailed work on the photoelectric effect verifying Einstein’s simple equation. Millikan himself remarked in his 1916 paper, “Yet the semi-corpuscular theory by which Einstein arrived at this equation seems at present to be wholly untenable.”¹³ The main problem was how to account for the well-established wave properties of radiation in terms of light quanta. The prejudice was so strong that even Planck, Rubens, Walther Nernst, and Emil Warburg, who were keen to bring Einstein to Berlin, felt compelled to write to the Prussian Ministry of Education:

That he may sometimes have missed the target in his speculations, as, for example, in his theory of light-quanta, cannot really be held against him. For in the most exact of natural sciences every innovation entails risk.¹⁴

Bohr, too, was opposed to the light-quantum idea and avoided using it in his 1913 paper on the atomic model.¹⁵ Following Planck quite closely, he introduced transitions between the stationary states of the atom giving rise to absorption or emission of classical radiation whose frequencies were determined by the relation v = (E₁ – E₂)/h. Contrary to what is usually stated in textbooks, he made no mention of light quanta.

Strong experimental evidence in favor of light quanta eventually emerged in 1923 from the Compton effect. The classical wave theory of radiation failed to explain the observed shifts in the wavelength of the scattered x-rays. Observation clearly pointed toward elementary processes of energy transfer between light quanta and the electrons in the atoms.

Although empirical evidence in favor of the light-quantum hypothesis was mounting, its theoretical basis remained unsatisfactory on three counts. First, there was a fundamental conflict between the statistical independence of Einstein’s light quanta and the Planck law. Second, there was no logically satisfactory derivation of the Planck law despite several attempts by leading physicists, including Planck himself, as well as Einstein, Ehrenfest, Pauli, and Peter Debye.¹⁶ All these attempts, ingenious as they were, suffered from one drawback. In all of them, the first factor in the Planck law, 8πv²dv / c³, was always taken from classical electrodynamics to be the number of modes of vibration of radiation in unit volume. These authors deduced the second factor in different ways by postulating ad hoc rules for different elementary processes. Third, all these attempts, except that of Debye, used Planck’s hypothesis that quantization was restricted to the exchange of energy between radiation and matter, but the Compton effect had shown that radiation itself consists of energy quanta.

In 1924, Bose solved all these problems in one stroke by deriving the full Planck law, including the first factor, from quantum theory. He accomplished this by extending Planck’s method of quantization of material resonators to radiation itself. The first factor, apart from a factor of 2, then emerged as the number of irreducible cells in the phase space of the photon—i.e., the number of quantum states of the photon—and hence the number of possible arrangements of a photon. Thus, the quantum states of the photon are distinguished only by the number of photons in each state. This fact immediately implies that photons, not merely hypothetical resonators in the walls, are indistinguishable. The entire physics becomes transparent.

On June 4, 1924, Bose wrote to Einstein,

I have ventured to send you the accompanying article for your perusal and opinion. I am anxious to know what you think of it. You will see that I have tried to deduce the coefficient (8πv²/c³) in Planck’s law independent of the classical electrodynamics, only assuming that the ultimate elementary regions in Phase space have the content h³.¹⁷

Einstein, in a letter to Ehrenfest dated July 12, wrote, “The Indian Bose has given a beautiful derivation of Planck’s law including the constant 8πv²/c³.”¹⁸

Nonetheless, his derivation of the first factor had to be supplemented by a factor of 2 due to the two states of polarization of light, which were not wholly quantum mechanical. Einstein observed in a postcard to Bose dated July 2,

Dear Colleague,
I have translated your work and communicated it to Zeitschrift für Physik for publication. It signifies an important step forward and I liked it very much. Factually, I find your objections against my work not correct. For Wien’s displacement law does not assume the wave (undulation) theory and Bohr’s correspondence principle is not at all applicable. However, this does not matter. You are the first to derive the factor quantum theoretically, even though because of the polarization factor 2 not wholly rigorously. It is a beautiful step forward.

With friendly greetings,
Yours,
A. Einstein¹⁹

Many years after this exchange, I spoke with Bose regarding the factor of 2 in his derivation. I had gone to meet him one afternoon and found him in an introspective mood. He was reminiscing about his meetings and conversations with Einstein in Berlin during 1925. Suddenly he said to me that he would like to tell me something confidential that I must never divulge to anyone. He got up, closed the doors, and shut the windows. I was in great suspense. He sat down and told me the following story. “You know,” he said,

my deduction of the Planck law had a factor of 2 missing. So I proposed that it came from the fact that the photon had a spin, and that it can spin either parallel or antiparallel to its direction of motion. That would give the additional factor of 2. But the old man [meaning Einstein] crossed it out and said it was not necessary to talk about spin, the factor of 2 comes from the two states of polarization of light.

Then he smiled mischievously and said to me rhetorically, “I can understand a spinning particle, but what is the meaning of the polarization of a particle?”

I was stunned! I immediately said to him,

Sir, when photon spin was eventually discovered, why didn’t you tell Einstein that you had discovered it already in 1924? No doubt a person like Einstein would have stood by you and you would have surely won a Nobel Prize!

He looked at me calmly and said, “How does it matter who discovered it?” And then with a sense of triumph, he said, “It has been discovered, hasn’t it!”

That was Bose.

Much later, around 1993 when we were preparing for the Bose centenary, while browsing old journals in the library of the Indian Association for the Cultivation of Science, I chanced upon a 1931 paper by Chandrasekhara Venkata Raman and Suri Bhagavantam in the Indian Journal of Physics with the title, “Experimental Proof of the Spin of the Photon.” I was intrigued and started reading it. I was simply amazed by what it contained:

In his well-known derivation of the Planck radiation formula from quantum statistics, Prof. S. N. Bose obtained an expression for the number of cells in phase-space occupied by the radiation, and found himself obliged to multiply it by a numerical factor 2 in order to derive from it the correct number of possible arrangements of the quantum in unit volume. The paper as published did not contain a detailed discussion of the necessity for the introduction of this factor, but we understand from a personal communication by Prof. Bose that he envisaged the possibility of the quantum possessing besides energy hv and linear momentum hv/c also an intrinsic spin or angular momentum ±h/2π round an axis parallel to the direction of its motion. The weight factor 2 thus arises from the possibility of the spin of the quantum being either right-handed or left-handed, corresponding to the two alternative signs of the angular momentum. There is a fundamental difference between this idea, and the well-known result of classical electrodynamics to which attention was drawn by [John Henry] Poynting and more fully developed by [Max] Abraham that a beam of light may in certain circumstances possess angular momentum. … Thus, according to the classical field theory, the angular momentum associated with a quantum of energy is not uniquely defined, while according to the view we are concerned with in the present paper, the photon has always an angular momentum having a definite numerical value of a Bohr unit with one or other of the two possible alternative signs.²⁰

Their experiment conclusively showed that Bose’s view was the correct one and provided the first experimental measurement of the photon spin. This fact is hardly known to scientists and historians of science.

I was beside myself with joy! But at the same time I was puzzled by the great secrecy with which Bose had confided the story. After all, Raman had already published it way back in 1931. Did Bose forget about Raman’s paper? Surely that could not be the case, for how could anyone forget such a dramatic justification of one’s revolutionary idea? And Bose had a prodigious memory. Was it that Raman did not inform Bose of his results? That also seems unlikely. In any case, since then, I have had no compunction in breaking my pledge not to divulge the story. It is important for the history of science that it becomes widely known.

Incidentally, I tried very hard to get a copy of the original paper in English that Bose sent to Einstein. I wanted to verify what exactly was written about the factor of 2. The Einstein archives do not have it, although the cover letter and Einstein’s response mentioning this puzzle are there. Bose himself never bothered to keep a copy.

Be that as it may, it could hardly have been foreseen at that time that a short paper, only about four pages long, without a single reference, would eventually have profound influence across a vast spectrum of physics.

Bosons in Particle Physics

One of the first effects of Bose’s publication was that the British physicist Paul Dirac coined the word boson for the class of quantum particles that follow Bose–Einstein statistics. Aside from bosons, there is only one other class of quantum particles: fermions, which were discovered by Dirac independently of Enrico Fermi. Bosons and fermions follow two types of quantum statistics: the Bose–Einstein statistics and the Fermi–Dirac statistics, respectively. Since the original idea for the statistics of quantum particles came from Bose, Dirac chose to name the particles following Bose–Einstein statistics bosons. In his modesty, he named the other type fermions. These appellations appeared for the first time in Dirac’s classic monograph The Principles of Quantum Mechanics.²¹

It turns out that bosons have intrinsic spins that are nℏ, with n = 0, 1, 2, … ; fermions have spins that are (n + 1/2)ℏ. This is known as the spin-statistics theorem. A crucial difference between bosons and fermions is that, while any number of identical bosons can occupy the same quantum state, two or more identical fermions cannot occupy the same quantum state. The clannish behavior of bosons is responsible for Bose–Einstein condensation, and the standoffish behavior of fermions, expressed through the Pauli exclusion principle, is responsible for the fact that we cannot cross one finger through another—that is, the hardness of matter.

The fundamental building blocks of the universe can only be bosons and fermions. According to the Standard Model of particle physics, leptons—which are the electrons, the muons, the tauons, the neutrinos, and their antiparticles—and quarks and their antiparticles are all fermions. The quantum excitations of the fields that mediate interactions among them are all bosons. Examples include the photon, which mediates electromagnetic interactions; the W^± and Z, which mediate weak interactions such as radioactivity; and gluons, which bind quarks to form the hadrons, such as neutrons, protons, and pions.

There is one more fundamental particle that the Standard Model requires to generate the masses of leptons, which would otherwise be massless like the photon and fly away at the speed of light, making it impossible for atoms to form in the universe. That particle is a spin-0 boson. It was named the Higgs boson after Peter Higgs of the University of Edinburgh, though several other physicists proposed such a particle at more or less the same time as Higgs in 1964. It took nearly half a century and a multibillion-dollar particle accelerator, the Large Hadron Collider at CERN, to find it.

The much-hyped result was finally announced on July 4, 2012, by CERN’s director general Rolf-Dieter Heuer. He simply said, “I think we have it,” to a large audience who had queued all night to gather in the seminar room where Higgs and François Englert were also present. Higgs and Englert shared the 2013 Nobel Prize for their work.

Bosons in Cosmology

The Higgs boson was intrinsic to understanding of how lepton mass was generated in the Big Bang. In 1964, Arno Penzias and Robert Wilson, working with the Holmdel Horn Antenna at the Bell Labs in Princeton, accidentally discovered cosmic microwave background radiation, which was strong evidence in favor of a hot early universe, as implicated in the Big Bang theory, and against the rival steady-state theory. For this landmark discovery, Penzias and Wilson were awarded the 1978 Nobel Prize in Physics. It turns out that, according to precision observations carried out in 1994 by the Far Infrared Absolute Spectrophotometer aboard the Cosmic Background Explorer satellite, cosmic microwave background radiation has a pure Planck spectrum, signaling that it is blackbody radiation in thermal equilibrium at a temperature of 2.7K.

It was precisely the spectrum of blackbody radiation measured in labs in the last few years of the nineteenth century that led Planck to discover quantum theory in 1900. And it was this Planck spectrum that led Bose to discover the new statistics in 1924.

Bose–Einstein Condensates

At first, Bose’s new statistics seemed outlandish to everyone except Einstein, who immediately understood its importance. Bose’s method of counting the quantum states of radiation showed that photons of a given frequency were indistinguishable. That implied that photons could not be continuously tracked, which is suggestive of a spread-out wavelike character. Einstein realized at once that such a fundamental character could not be true of radiation alone; it must be true of matter as well. He calculated the fluctuations in the number density of particles in very small volumes of a Bose gas. He found two terms: one that would be expected from the particle nature of matter, and another surprising term that implied a wavelike character. At once, he recollected having seen a doctoral thesis written by a young French scholar named Louis de Broglie, in which the possibility of matter waves was proposed in analogy with the dual nature of radiation. Einstein seems to have initially reserved his judgment on de Broglie’s idea, but now, with his own calculations based on a Bose gas, he realized that there was more than mere analogy in the wavelike character of gases.²² He then began writing a series of papers in which he explained Bose’s counting method and its implications for material gases. Einstein described the importance of associating de Broglie waves with a material gas using the formula λ = h/mv for the wavelength of matter, and proposed molecular beam experiments to test the wavelike nature of matter. He also concluded that, at very low temperatures below a critical point, all the material particles of a Bose gas would condense to the ground state of the system, without any attractive force, only by virtue of their statistical property.²³ Due to very low temperatures, their wavelengths would increase (λ ~ h/$\sqrt{2mkT}$). These wavelengths would overlap with each other to such an extent that they would lose their individual identities and form one huge, wavelike entity unlike anything known at the time—a bizarre quantum state of matter. This came to be known as the Bose–Einstein condensate.

It was not until seven decades later that Bose–Einstein condensates could be produced in a lab. Physicists had to wait for the development of extremely delicate laser cooling and evaporative cooling techniques before they could produce cold atoms near absolute zero. Eventually, on June 5, 1995, the first gaseous condensate was produced by Eric Cornell and Carl Wieman at the University of Colorado at Boulder in the NIST–JILA lab. It was produced in a gas of rubidium atoms cooled to 170 nanokelvins, a mere whisker above absolute zero. Soon after, Wolfgang Ketterle and his group at MIT produced a Bose–Einstein condensate in a gas of sodium atoms. All three researchers were awarded the 2001 Nobel Prize in Physics for their discovery. According to the Nobel committee, the three scientists “caused atoms to ‘sing in unison.’”²⁴

The latest paper on Bose–Einstein condensates appeared in Nature in June 2020. It is entitled, “Observation of Bose–Einstein Condensates in an Earth-Orbiting Research Lab.”²⁵ The purpose of the study was to overcome the effects of gravity on a large collection of atoms by placing them in a microgravity environment. Such a condition is realized in an Earth-orbiting satellite that is in free fall. This elongates the free-fall time of the atoms released from the trap, overcoming terrestrial limitations.

Superfluidity and Superconductivity

Although Bose–Einstein condensates were first directly observed in 1995, indirect evidence for them had been accumulating ever since the discovery of superfluidity and superconductivity. A superfluid is a fluid with zero viscosity that can flow through narrow tubes without any loss of kinetic energy. Pyotr Kapitsa and John Allen discovered the phenomenon in 1938. It occurs in two isotopes of helium—helium-3 and helium-4—when they are cooled to temperatures close to absolute zero and liquefied. Superfluidity can produce various exotic states of matter that are believed to occur in astrophysics, high energy physics, and some theories of quantum gravity.

Superfluidity is a manifestation of Bose–Einstein condensation. It occurs in helium-4 whose atoms have integer spin and are therefore bosons that can condense below a critical temperature. Superfluidity in helium-3 occurs at much lower temperatures than in helium-4 because helium-3 atoms are fermions and two of them must pair up to form composite bosons that can then condense. David Lee, Douglas Osheroff, and Robert Richardson won the 1996 Nobel Prize for their discovery of superfluidity in helium-3. In 2003, Anthony Leggett won the same prize for developing the quantum mechanical theory of superfluidity of helium-3 based on its bosonic character after pairing.

Superconductivity occurs in certain materials below a critical temperature. At such temperatures, they suddenly lose all their electrical resistance and expel magnetic flux, in what is known as the Meissner effect. An electrical current can flow through a superconducting wire loop endlessly without a power source, as Kammerlingh Onnes discovered in 1911. It is not perfect conductivity, as one might think, and classical physics cannot explain it. The first microscopic quantum mechanical theory of superconductivity was proposed by John Bardeen, Leon Cooper, and Robert Schrieffer in 1957. In their theory, known as the BCS (Bardeen–Cooper–Schrieffer) theory, superconductivity occurs via Bose–Einstein condensation of a pair of electrons of opposite momentum forming a composite boson of integer spin by interacting through an exchange of phonons. This process is analogous to how superfluidity occurs in helium-3. In 1972, Bardeen, Cooper, and Schrieffer were all awarded the Nobel Prize in Physics for this work.²⁶

Bosons, Fermions, and Supersymmetry

The fact that there are two classes of fundamental building blocks, bosons and fermions, rather than just one, has prompted physicists searching for unified theories of particles to propose a relationship between the two. This has become known as supersymmetry. If such a symmetry exists, it would bring the standoffish fermions and the clannish bosons together within the fold of a single family and would imply the existence of a lot of undiscovered particles. The latter could provide an elegant solution to many problem areas in the Standard Model. In supersymmetry, each boson and fermion would have an associated particle, termed a superpartner, in the other class. An electron, for example, which is a fermion, would have a superpartner called a selectron, its bosonic partner. In perfectly supersymmetric theories, each pair of superpartners would have the same mass and internal quantum numbers, except for their spin.

But if such superpartners existed, they would have been found long ago. As a result, it has been conjectured that perhaps supersymmetry is softly broken, allowing superpartners to differ in mass. Such theories, if true, would solve important problems such as setting an upper bound on the Higgs boson mass and alleviating the hierarchy problem that arises from the enormously different scales in the theory. The hope is that the reason physicists are still confronted by these problems in the Standard Model is perhaps because so far only half of the picture has been in sight.

To date, there is no experimental evidence that supersymmetry exists or that alternative extensions of the current models might be more probable. Particle accelerators specifically designed to study physics beyond the Standard Model are required. The latest trends from the upgraded Large Hadron Collider have cast considerable gloom in some camps of supersymmetry searchers.²⁷

Bose in Europe

Citing Einstein’s appreciative postcard of July 2, 1924, Bose applied to the University of Dacca for a two-year study leave to visit European laboratories. His request was promptly granted. Bose’s first port of call was Paris, where he arrived on October 18. He put up at 17 rue du Sommerard in the Latin Quarter, a haven for Indian scholars. Bose’s main interest was in visiting leading European laboratories to learn firsthand the latest techniques, particularly in radiochemistry and x-ray crystallography, practices far removed from his theoretical studies in quantum theory. His fame preceded his arrival in Paris, and so access was never an issue. But what transpired at his first meeting with Marie Curie was somewhat of a surprise. Carrying a letter of introduction from Paul Langevin, who was familiar with his work, Bose went to meet Curie with the intention of learning to work with radioactivity. In his own words,

I was allowed entry to her small chamber. The great elderly lady sat there, dressed in black. I could recognize her from pictures of her that I had seen. I handed her the letter of introduction. She greeted me affectionately and said that there was no way she could disregard a recommendation from such a person. You will certainly get an opportunity to work with me, she said. But not right now, after three or four months. Get to know the language, otherwise you will find it difficult to work in the laboratory. You are in no hurry, I presume.

She spoke at ease in chaste English for about ten minutes. I had no opportunity to tell her that I knew a French of sorts already. I had been at it for the last ten years at home. I came away resigned to carrying out her instructions.²⁸

Bose spent the next six months learning x-ray crystallography and spectroscopy in the laboratory of Maurice de Broglie, the elder brother of Louis de Broglie. He then returned to Curie’s Radium Institute and worked there for a few months.

His next destination was Berlin, where he arrived in October 1925. He sent a message to Einstein on October 8 seeking an appointment, but Einstein was not in Berlin at the time, and so they did not meet until his return. They met frequently thereafter and had wide-ranging discussions on physics and other contemporary issues of interest. They had a difference of opinion regarding the probability of interaction between matter and radiation, Einstein believing that spontaneous emission of radiation was an intrinsic property of atoms, while Bose saw it as a consequence of the new statistics.

Einstein gave Bose a letter of introduction, which helped him gain the necessary privileges to borrow books from the university library and to attend the physics colloquium. He also had the opportunity to meet important scientific figures, such as Fritz Haber, Otto Hahn, Herman Mark, Lise Meitner, Michael Polanyi, Richard von Mises, and Eugene Wigner.

Bose described the excitement in Berlin at that time. In a letter to Jacqueline Zadoc-Kahn, a physicist in Paris, he wrote:

Everybody (every physicist) seems to be quite excited in Berlin, about the way things have been going on with physics, first on the 28th last [October], [Werner] Heisenberg spoke in the colloquium about his theory, then in the last colloquium, there was a long lecture on the recent hypothesis of the spinning electron (perhaps you have heard about it). Everybody is quite bewildered and there is going to be very soon a discussion of [Erwin] Schrödinger’s papers. Einstein seems quite excited about it. The other day coming from the colloquium, we suddenly found him jumping, in the same compartment where we were, and forthwith he began to talk excitedly about the things we have just heard. He has to admit that it seems a tremendous thing, considering the lot of things which these new theories correlate and explain, but he is very much troubled by the unreasonableness of it all. We were all silent, but he talked almost all the time, unconscious of the interest and wonder that he is exciting in the minds of other passengers.²⁹

Back to Dacca

Shortly after his return to the University of Dacca, Bose was appointed professor, head of the Department of Physics, and dean of the Faculty of Science. He set about using the knowledge of experimental science that he acquired in Europe to improve higher education and scientific research in his country, redesigning the laboratories and initiating work in x-ray crystallography, spectroscopy, and crystal magnetism. He also worked extensively in chemistry, advising the doctoral students of his friend Jnan Chandra Ghosh, who worked on strong electrolytes and was often away from campus. Instead of plunging into theoretical chemistry, for which he was well equipped, Bose preferred to get his hands dirty, synthesizing and analyzing chemicals of contemporary practical importance. The inspiration possibly came from his father’s small chemical works and his teacher Ray, the founder of the Indian chemical industry. Bose set up a small chemistry lab and encouraged students to synthesize emetine, sulfa drugs, and other drugs. Much of this research was never published and the few papers that did appear hardly ever carried his name.³⁰

Bose was a polymath whose office at the University of Dacca turned into a center for free-flowing discussions on topics ranging from physics, chemistry, mathematics, and statistics to literature, history, linguistics, and much more. In his spare time, he would work out difficult mathematical problems. According to Kariamanikkam Srinivasa Krishnan, who had worked with Raman to discover the Raman effect, and who later joined the University of Dacca, “Dr. Bose finds his pleasure in complex problems. His enthusiasm dies once he solves them. He throws the proofs in the waste-paper basket, never bothering to send them to any journal.”³¹ Legend has it that doctoral students would come when Bose was not around and collect these discarded proofs to use in their own doctoral theses.

Return to Calcutta

The 1940s saw an upsurge in the Indian independence movement. The partition of Bengal into West Bengal and East Bengal, with Dacca as its capital, was imminent. In 1945, Bose left Dacca with a heavy heart to become the Khaira Professor of Physics at the University College of Science in Calcutta. He worked there until his retirement in 1956.

In Calcutta, too, Bose devoted his working time to experimental science rather than theoretical physics. He set up an x-ray laboratory and encouraged organic chemists to determine molecular structures through x-ray analysis. He also worked on thermoluminescence and developed a novel rapid-scanning technique to study the changing thermoluminescence spectra. This opened up fresh avenues for research in rapid continuous scanning. He reported the results from these studies in 1954 at the Third General Assembly of the International Union of Crystallography in Paris.

Bose also designed a special powder camera and a differential thermal analyzer for analyzing the structure of clay minerals collected from different parts of India. The results were published by his students, A. K. Bose and Purnima Sengupta, in Nature during 1954.³² These efforts may not carry the stamp of his genius, but they show his dedication to building up a sound scientific culture in the country.

A persistent lament among his countryfolk is that a man of Bose’s genius could have contributed much more to science. There is also some residual discontent that he was denied the Nobel Prize while so many others got it simply by proving he was right. Lev Landau, a great Russian physicist and a Nobel laureate himself, proposed a genius scale to rank the smartest physicists of the twentieth century up to 1968. It was a logarithmic scale in which scientists he put in class 1 (rank 0.5) contributed ten times more, in his estimation, than those in class 2. There were five classes. He put Einstein, of course, on top of class 1. He put those who developed quantum mechanics in the same class, where Bose also figures. Landau put himself in the next class.³³

In the early 1950s, Bose suddenly returned to theoretical physics, and particularly to Einstein’s unified field theories, with great enthusiasm. He wrote five papers—four of them in French—in less than two years, solving difficult mathematical problems.³⁴ These were his last scientific papers. Although they were all published in well-known international journals, none of them figures in a 2014 review of unified field theories.³⁵ In 1955, Bose was looking forward to meeting Einstein again and discussing some new ideas with him during the international conference to celebrate fifty years of relativity in Berne. The conference was to be held in July, but Einstein passed away in April. Bose was working on a new paper when news of Einstein’s death reached him. According to eyewitnesses, he was silent for a while and then tore up the paper and threw it into the wastepaper basket.

Inspired by Rabindranath Tagore, a poet who had in 1913 become the first non-European to win the Nobel Prize, Bose devoted considerable time to promoting science in his mother tongue. In 1948, he set up Bangiya Bijnan Parishad, an institution for the popularization of scientific knowledge.

After his retirement from the University College of Science in 1956, Bose was appointed vice chancellor of Visva-Bharati University, the institution founded in 1921 by Tagore. Bose served there for only three years, after which he was appointed National Professor of Physics in 1959. He was also given the Indian government’s second highest civilian award, the Padma Vibhushan, in 1954 and was sworn in as a nominated member of parliament, in the upper house, Rajya Sabha.

Bose’s contribution to quantum theory was only formally recognized by foreign academies in 1958, after Dirac happened to visit Calcutta in 1954 and found that Bose had not yet been elected a fellow of the Royal Society, London. Dirac went back to England and pursued the matter.

There is an amusing story about Dirac’s visit to Calcutta. He arrived with his wife, and Bose went with some of his students to meet them at the railway station. After alighting from the train, they were taken to Bose’s car and ushered into the back seat while Bose and his students crowded into the front seat. When Dirac, one of the founders of Fermi–Dirac statistics, politely invited some students to come to the back seat, Bose quipped, “We believe in Bose statistics.”

Bose passed away on February 4, 1974. To perpetuate his memory, the Government of India established the S. N. Bose National Centre for Basic Sciences in Calcutta in 1986. As a fellow physicist, Binay Malkar, once observed, “As long as there is light in this universe, there will be Bosons everywhere.”³⁶