When theoretical Physics wandered into the quantum realm about a century past, it was as though they were feeling about in the dark, using mathematics as a probe. There has been, in this branch of discovery, a loss for words. It took time before the name, ‘quantum’, was settled upon. ‘Spin’ is arguably a misnomer, and a misleading one at that. Any wonder, when a word such as ‘quantum’ (specific quantity, in this case, of vibrancy!) has to be employed to describe what we take to be solid, steady matter?

‘Spin’ in the quantum sense is not spin, just as solid matter in quantum terms is not solid matter!

Matter is not simple. Atomic constituents are not cricket balls in a heap. Given that light is a component of matter– matter can be induced to absorb and emit light photons – and photonics is the premier information medium — !! It could almost be contended that matter is mathematics! It has now been shown that four quantum numbers are needed to describe matter. Yet only three numbers are necessary to locate something in space! Something called spin was required to solve matter. Without it, atoms would not be stable. But what is it?

‘Status’ is possibly a better term than ‘spin’? Dismiss conventional thoughts!

Below are extracts from a lucid account of the topic by W.H. Cropper, *Great Physicists*, Oxford Uni. Press, 2001. Find specific references to ‘spin’, plus background to Quantum Physics.

**Blackbody Radiation (p. 232)**

Max Planck’s story as an unenthusiastic revolutionary began in about 1895 in Berlin, with Planck established as a theoretical physicist and concerned with the theory of the light and heat radiation emitted by special high-temperature ovens known in physical parlance as “blackbodies.” Formally, a blackbody is an object that emits its own radiation when heated, but does not reflect incident radiation. These simplifying features can be built into an oven enclosure by completely surrounding it with thick walls except for a small hole through which radiation escapes and is observed.

The colour of radiation emitted by blackbody (and other) ovens depends in a familiar way on how hot the oven is: at 550°C it appears dark red, at 750°C bright red, at 900°C orange, at 1000°C yellow, and at 1200°C and beyond, white. This radiation has a remarkably universal character: in a blackbody oven whose walls are equilibrated with the radiation they contain, the spectrum of the colour depends exclusively on the oven’s temperature. No matter what is in the oven, a uniform colour is emitted that changes only if the oven’s temperature is changed. A theory that partly accounted for these fundamental observations had been derived by Kirchoff in 1859.

To Planck there were unmistakable signs here of “something absolute,” that sublime presence he had pursued in his thermodynamic studies. The blackbody oven embodied an idealised, yet experimentally accessible, instance of radiation interacting with matter. Blackbody theoretical work had been advancing rapidly because the experimental methods for analysing blackbody spectra–that is, the rainbow of emitted colours–had been improving rapidly. The theory visualised a balanced process of energy conversions between the thermal energy of the blackbody oven’s walls and radiation energy contained in the oven’s interior. By the time Planck started his research, the blackbody radiation problem had developed into a theoretical tree with some obviously ripening plums.

Planck first did what theoreticians usually do when they are handed accurate experimental data: he derived an empirical equation to fit the data. His guide in this effort was a thermodynamic connection between the entropy and the energy of the blackbody radiation field. He defined two limiting and extreme versions of the energy–entropy relation, and then guessed that the general connection was a certain linear combination of the two extremes. In this remarkably simple way, Planck arrived at a radiation formula that did everything he wanted. The formula so accurately reproduced the blackbody data gathered by his friends Heinrich Rubens and Ferdinand Kurlbaum that it was more accurate then the spectral data themselves: “The finer the methods of measurements used,” Planck tells us, “the more accurate the formula was found to be.”

**The Unfortunate h**

Max Born, one of the generation of theoretical physicists that followed Planck and helped build the modern edifice of quantum theory on Planck’s foundations, looked on the deceptively simple manoeuvres that led Planck to his radiation formula as “one of the most fateful and significant interpolations ever made in the history of physics; it reveals an almost uncanny physical intuition.” Not only was the formula a simple and accurate empirical one, useful for checking and correlating spectral data; it was *the* radiation formula, the final authoritative *law* governing blackbody radiation. And as such it could be used as the basis for a theory–even, as it turned out, a revolutionary one. Without hesitation, Planck set out in pursuit of that theory: “On the very day when I formulated the (radiation law),” he writes, “I began to devote myself to the task of investing it with true physical meaning.”

As he approached this problem, Planck was once again inspired by “the muse entropy,” as the science historian Martin Klein puts it. “If there is a single concept that unifies the long and fruitful scientific career of Max Planck,” Klein continues, “it is the concept of entropy.” Planck had devoted years to studies of entropy and the second law of thermodynamics, and a fundamental entropy-energy relationship had been crucial in the derivation of his radiation law. His more ambitious aim now was to find a theoretical entropy-energy connection applicable to the blackbody problem.

As mentioned in chapter 13, Ludwig Boltzmann interpreted the second law of thermodynamics as “probability law.” If the relative probability or disorder for the state of a system was *W*, he concluded, then the entropy *S *of the system in that state was proportional to the logarithm of *W*,

*S* ln*W*

In a deft mathematical stroke, Planck applied this relationship to the blackbody problem by writing

*S* =* k*ln*W *(1)

For the total entropy of the vibrating molecules – Planck called them “resonators”–in the blackbody oven’s walls; *k* is a universal constant and *W* measures disorder. Although Boltzmann is often credited with inventing the entropy equation (1), and *k* is now called “Boltzmann’s constant,” Planck was first to recognise the fundamental importance of both the equation and the constant.

Planck came to this equation with reluctance. It treated entropy in the statistical manner that had been developed by Boltzmann. Boltzmann’s theory taught the lesson that conceivably–but against astronomically unfavourable odds–any macroscopic process can reverse and run in the unnatural, entropy-decreasing direction, contradicting the second law of thermodynamics. Boltzmann’s quantitative techniques even showed how to calculate the incredibly unfavourable odds. Boltzmann’s conclusions seemed fantastic to Planck, but by 1900 he was becoming increasingly desperate, even reckless, in his search for an acceptable way to calculate the entropy of the blackbody resonators. He had taken several wrong directions, made a fundamental error in interpretation, and exhausted his theoretical repertoire. No theoretical path of his previous acquaintance led where he was certain he had to arrive eventually–at a derivation of his empirical radiation law. As a last resort, he now sided with Boltzmann and accepted the probabilistic version of entropy and the second law.

For Planck, this was an “act of desperation,” as he wrote later to a colleague. “By nature I am peacefully inclined and reject all doubtful adventures,” he wrote, “but by then I had been wrestling unsuccessfully for six years (since 1894) with this problem of equilibrium between radiation and matter and I knew that this problem was of fundamental importance to physics; I also knew the formula that expresses the energy distribution in normal spectra [his empirical radiation law]. A theoretical interpretation* had* to be found at any cost, no matter how high.”

The counting procedure Planck used to calculate the disorder *W* in equation (1) was borrowed from another one of Boltzmann’s theoretical techniques. He considered–at least as a temporary measure–that the total energy of the resonators was made up of small *indivisible* “elements,” each one of magnitude . It was then possible to evaluate *W* as a count of the number of ways a certain number of energy elements could be distributed to a certain number of resonators, a simple combinatorial calculation long familiar to mathematicians.

The entropy equation (1), the counting procedure based on the device of the energy elements, and a standard entropy-energy equation from thermodynamics, brought Planck almost–but not quite-to his goal, a theoretical derivation of his radiation law. One more step had to be taken. His argument would not succeed unless he assumed that the energy of the elements was proportional to the frequency with which the resonators vibrated, v, or

= hv (2)

with *h* a proportionality constant. If he expressed the sizes of the energy elements this way, Planck could at last derive his radiation law and use the blackbody data to calculate numerical values for his two theoretical constants *h* and *k*.

This was Planck’s theoretical route to his radiation law, summarised in a brief report to the German Physical Society in late 1900. Planck hoped that he had in hand at last the theoretical plum he had been struggling for, a general theory of the interaction of radiation with matter. But he was painfully aware that to reach the plum he had ventured far out on a none-too-sturdy theoretical limb. He had made use of Boltzmann’s statistical entropy calculation–an approach that was still being questioned. And he had modified the Boltzmann technique in ways that modern commentators have found questionable. Abraham Pais, one of the best of the recent chroniclers of the history of quantum theory, says that Planck’s adaption of the Boltzmann method “was wild”.

Even wilder was Planck’s use of the energy elements in his development of the statistical argument. His procedure required the assumption that energy, at least the thermal energy possessed by the material resonators, had an inherent and irreducible graininess embodied in the quantities. Nothing in the universally accepted literature of classical physics gave the slightest credence to this idea. The established doctrine — to which Planck had previously adhered as faithfully as anyone–was that energy of all kinds existed in a continuum. If a resonator or anything else changed its energy, it did so through continuous values, not in discontinuous packets, as Planck’s picture suggested.

In Boltzmann’s hands, the technique of allocating energy in small particle-like elements was simply a calculational trick for finding probabilities. In the end, Boltzmann managed to restore the continuum by assuming that the energy elements were very small. Naturally, Planck hoped to avoid conflict with the classical continuum doctrine by taking advantage of the same strategy. But to his amazement, his theory would not allow the assumption that the elements were arbitrarily small; the constant *h* in equation (2) could not be given a zero value.

Planck hoped that the unfortunate *h*, and the energy structure it implied, were unnecessary artefacts of his mathematical argument, and that further theoretical work would lead to the result he wanted with less drastic assumptions. For about eight years, Planck persisted in the belief that the classical viewpoint would eventually triumph. He tried to “weld the (constant) *h* somehow into the framework of the classical theory. But in the face of all such attempts this constant showed itself to be obdurate.” Finally Planck realised that his struggles to derive the new physics from the old had, after all, failed. But to Planck this failure was “thorough enlightenment… I now knew for a fact that (the energy elements) … played a far more significant part in physics than I had originally been inclined to suspect, and this recognition made me see clearly the need for introduction of totally new methods of analysis and reasoning in the treatment of atomic problems.”

The physical meaning of the constant *h* was concealed, but Planck did not have much trouble extracting important physical results from the companion constant *k*. By appealing to Boltzmann’s statistical calculation of the entropy of an ideal gas, he found a way to use his value of *k* to calculate Avogradro’s number, the number of molecules in a standard or molar quantity of any pure substance. The calculation was a far better evaluation of Avogadro’s number than any other available at the time, but that superiority was not recognised until much later. Planck’s value of Avogradro’s number also permitted him to calculate the electrical charge on an electron, and this result, too, was superior to those derived through contemporary measurements.

These results were as important to Planck as the derivation of his radiation law. They were evidence of the broader significance of his theory, beyond the application to his blackbody radiation. “If the theory is at all correct,” he wrote at the end of his 1900 paper, “all of these relations should be not approximately, but absolutely, valid.” In the calculation of Avogadro’s number and the electronic charge, Planck could feel that his theory had finally penetrated “to something absolute.”

In part because of Planck’s own sometimes ambivalent efforts, and in part because of the efforts of a new, less inhibited scientific generation, Planck’s theory stood firm, energy discontinuities included. But the road to full acceptance was long and tortuous. Even the terminology was slow to develop. Planck’s energy “elements” eventually became energy “quanta,” although the Latin word “quantum,” meaning quantity, had been used earlier by Planck in another context. Not until about 1910 did Planck’s theory, substantially broadened by the work of others, have the distinction of its formal name, “quantum theory.”

Einstein’s Energy Quanta (Photons) (p. 236)

One of the few perceptive readers of Planck’s early quantum theory papers was the junior patent examiner in Bern, Albert Einstein. To Einstein, the postulation of the energy elements was vivid and real, if appalling, “as if the ground had been pulled from under one, with no firm foundation seen anywhere upon which one could have built.” As it happened, the search for a “firm foundation” occupied Einstein for the rest of his life. But even without finding a satisfying conceptual basis, Einstein managed to discover a powerful principle that carried the quantum theory forward in its next great step after Planck’s work. He presented his theory in one of the papers published during his “miraculous year” of 1905.

Planck was cautious in his use of the quantum concept. For good reason, considering its radical implications, he had hesitated to regard the quantum as a real entity. And he was careful not to infer anything concerning the radiation field, partly light and partly heat radiation, contained in the blackbody oven’s interior. The energy quanta of which he spoke belonged to his resonator model of the vibrating molecules in the oven’s walls. Einstein, in one of his 1905 papers, and in several subsequent papers, presented the “heuristic” viewpoint that real quanta existed and that they were to be found, at least in certain experiments, as constituents of light and other kinds of radiation fields. He stated his position with characteristic clarity and boldness: “In accordance with the assumption to be considered here, the energy of a light ray….. is not continuously distributed over an increasing space but consists of a finite number of energy quanta which are localised in space, which move without dividing, and which can only be produced and absorbed as complete units.”

Although it was hedged with the adjective “heuristic,” the picture Einstein presented was attractively simple: the energy contained in radiation fields, particularly light, was not distributed continuously but was localised in particle-like entities. Einstein called these particles of radiation “energy quanta”; in modern usage, complicated by the changing fortunes of Einstein’s theory, they are called “photons.”

Einstein developed his concept of photons in a variety of short, clever arguments written somewhat in the style of Planck’s 1900 paper. The entropy concept and fundamental equations from thermodynamics again opened the door to the quantum realm. Entropy equations for a radiation field make the field look like an ideal gas containing a large but finite number of independent particles. Each of these radiation particles – photons, in modern parlance – carried an amount of energy given by one of Planck’s energy elements *hv*, with *v* now representing a radiation frequency. If there are *N* photons, the total energy is

*E = Nhv*

Einstein drew from this equation the conclusion that the radiation field, like the ideal gas, contains *N* independent particles, the photons, and that the energy of an individual photon is

*E* ε = — = hv*N*

No doubt Einstein was convinced by this reasoning, but it is not certain that anyone else in the world shared his convictions. The year was 1905. Planck’s quantum postulate was still generally ignored, and Einstein had now applied it to light and other forms of radiation, a step Planck himself was unwilling to take for another ten years. What bothered Planck, and anyone else who read Einstein’s 1905 paper, was that the concept of light in particulate form had not been taken seriously by physicists for almost a century. The optical theory prevailing then, and throughout most of the nineteenth century, pictured light as a succession of wave fronts bearing some resemblance to the circular waves made by a pebble dropped into still water. It had been assumed ever since the work of Thomas Young and Augustin Fresnel in the early nineteenth century that light waves accounted for the striking interference pattern of light and dark bands generated when two specially prepared light beams are brought together. Other optical phenomena, particularly refraction and diffraction, were also simply explained by the wave theory of light.

One hundred years after Young’s first papers, Albert Einstein was rash enough to suggest that there might be some heuristic value in returning to the observation once proposed by Newton, that light can behave like a shower of particles. Einstein had found particles of light in his peculiar use of the quantum postulate. And, more important, he also showed in one of his 1905 papers that experimental results offered impressive evidence for the existence of particles of light, in astonishing contradiction to previous experiments that stood behind the seemingly impregnable wave theory.

The most important experimental evidence cited by Einstein concerned the “photoelectric effect,” in which an electric current is produced by shining ultra violet light on a fresh metal surface prepared in a vacuum. In the late 1890’s and early 1900’s, this photoelectric current was studied by Philipp Lenard (the same Lenard who later conceived a rabid, anti-Semitic hatred for Einstein, and worked furiously in the ultimately successful campaign to drive Einstein from Germany). Lenard discovered that the current emitted by the illuminated “target” metal consists of electrons whose kinetic energy can accurately be measured, and that the emitted electrons acquire their energy from the light beam shining on the metallic surface. If the classical viewpoint is taken–that light waves beat on the metallic surface like ocean waves, and that electrons are disturbed like pebbles on a beach -it seems necessary to assume that each electron receives more energy when the illumination is more intense, when the waves strike with more total energy. This, however is not what Lenard found; in 1902, he discovered that, although the total number of electrons dislodged from the metallic surface per second increases in proportion to the intensity of the illumination, the individual electron energies are independent of the light intensity.

Einstein showed that this puzzling feature of the photoelectric effect is comprehensible once the illumination in the experiment is understood to be a collection of particle-like photons. He proposed a simple mechanism for the transfer of energy from the photons to the electrons of the metal: “According to the concept that the incident light consists of [photons] of magnitude *hv*… one can conceive of the ejection of electrons by light in the following way. [Photons] penetrate the surface layer of the body [the metal], and their energy is transformed, at least in part, into kinetic energy of electrons. The simplest way to imagine this is that a [photon] delivers its entire energy to a single electron; we shall assume that is what happens.”

Each photon, if it does anything measurable, is captured by one electron and transfers all its energy to that electron. Once an electron captures a photon and carries away as its own kinetic energy the photon’s original energy, the electron attempts to work its way out of the metal and contribute to the measured photo-electric current. As an electron edges its way through the crowd of atoms in the metal, it loses energy, so it emerges from the metal surface carrying the captured energy minus whatever energy has been lost in the metal. If the energy that the metal erodes from an electron is labelled P, if the captured photon’s original energy, also the energy initially transferred to the electron, is represented with Planck’s *hv* (*v* is now the frequency of the illuminating ultraviolet light), and if energy is conserved in the photoelectric process, the energy *E* of an electron emerging from the target can be written

*E = hv – P*

Einstein’s picture of electrons being bumped out of metal targets in single photon-electron encounters easily explains the anomaly found by Lenard. Each interaction leads to the same photon-to-electron energy transfer, regardless of light intensity. Therefore electrons joining the photoelectric current from some definite part of the metallic target have the same energy whether just one or countless photons strike the metal per second. Although admirably simple, this explanation must have seemed almost as far-fetched to Einstein’s sceptical audience as the rest of his arguments. The rule that one photon is captured by one electron “not only prohibits the killing of two birds by one stone,” as the British theorist James Jeans remarked, “but also the killing of one bird by two stones.”

More than anything else Einstein achieved in physics, his photon theory was treated with distrust and scepticism. Not until 1926 was the now standard term “photon” introduced by Gilbert Lewis. What was obvious to Einstein by simply exercising his imagination and intuition was still being seriously questioned twenty years later. It took something approaching a mountain of evidence to make a permanent place for photons in the world of quantum theory.

While Einstein was beginning his bold explorations of the quantum realm, Planck was becoming the chief critic of his own theory. Planck seems to have had no regrets–perhaps he was pleased–that the work of building quantum theory had passed to Einstein and a new generation. Late in his life he wrote, with no sense of the personal irony, “a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because….. a new generation grows up that is familiar with it.”

**The Exclusion Principle (p. 259)**

Pauli was first drawn to the frustrations and mysteries of quantum theory as a student listening to Sommerfeld’s lectures. He soon became conversant with Sommerfield’s elaborate extension of Bohr’s theory and developed a complex application of that theory to the structure of the hydrogen molecule. At the same time, he was critical of the Bohr-Sommerfeld theory, remarking to his fellow student Werner Heisenberg that the whole thing was “atomysticism.” To Pauli, with his extraordinarily sensitive ear for the harmonies of formal argument–a sort of mathematical perfect pitch–the quantum theory of the time seemed “muddled.” “Everyone is still groping about in a thick mist,” Pauli complained to Heisenberg, “and it will probably be quite a few years before it lifts. Sommerfeld hopes that experiments will help us find some new laws. He believes in numerical links, almost a kind of number mysticism.”

Ever since Bohr’s first work, it had been known that certain states representing atomic behaviour had discrete energies that could be calculated from integers called “quantum numbers,” and that when an atom changes its energy it does so in “quantum jumps” between these “stationary states.” For about ten years following Bohr’s 1913 papers, much of the work on quantum theory focused on the theme of quantum numbers. One of the questions that always had to be answered in the making of atomic models based on quantum numbers was how many quantum numbers were needed for each electronic state to account for the observed physical and chemical behaviour of atoms. First there was one quantum number (Bohr’s model), then two, then three, and finally, according to Pauli, four.

Pauli found that he could work wonders with a fourfold array of quantum numbers assigned to each state available to an atom’s electrons. The key to the model was a set of rules that dictated each electron’s choice of quantum numbers. Two rules introduced by Bohr were applicable: the same set of quantum number assignments is available to all electrons in all atoms, and electrons occupy available states lying lowest in energy first. To these Pauli added a broad principle, later called the “exclusion principle” and the “Pauli Principle,” which did as much to clarify atomic and molecular theory as the more sophisticated theories that followed. Pauli asserted, with a degree of simplicity uncommon in quantum physics, that the set of four quantum numbers describing a state inhabited by an atomic electron must be unique for that electron: no two electrons in a given atom can occupy a state characterised by exactly the same set of values for the four quantum numbers.

Later theory established that the Pauli principle applies to any system of electrons. Wherever electrons gather–in atoms, molecules, or solids – they must organise themselves under the Pauli Principle. No two electrons in proximity can be sufficiently alike physically to occupy states carrying exactly the same set of quantum numbers. This often means that electrons simply avoid each other; in atoms they collect in concentric shells.

**Spin**

That four-and not three-quantum numbers were necessary to make the electron story complete was for a time a deep theoretical puzzle. It had become clear in the earlier theory that the quantum number count for an electronic state is a reflection of the number of dimensions in which an electron moves. An atomic electron in orbital motion around a nucleus moves in three dimensions, and therefore requires three quantum numbers, but only three, for its description. What physical significance could be attached to a fourth quantum number? If analogies to classical physics could be trusted, there was one obvious speculative answer. Electrons, like planets, might have spin motion around an internal axis, in addition to orbital motion.

This idea had occurred to several theorists, including Arthur Compton, Heisenberg, Bohr, and Pauli, but it had problems. For one thing, the ordinary spin of planets and baseballs is rotational motion in three dimensions. If that was the way electrons spun, no fourth quantum number should have been needed. Perhaps, then, spinning electrons were not like spinning baseballs; in some mysterious way, could electron spin be motion outside the familiar three spatial dimensions underlying classical physics? Although he was sceptical about the spin concept, Pauli believed that his fourth quantum number did relate to something “which cannot be described from the classical point of view.”

This is where matters stood in late 1925, when, as B.L. van der Waerden puts it, “the spell was broken.” What the esteemed theorists feared to do was done quickly and easily by two Dutch graduate students, George Uhlenbeck and Samuel Goudsmit, at the University of Leiden. With Pauli as their inspiration, they arrived at the essentials of the electron spin concept. Uhlenbeck explains their initial reasoning:

*Goudsmit and myself hit upon this idea by studying a paper by Pauli, in which the famous exclusion principle was formulated and in which for the first time, four quantum numbers were ascribed to the electron. This was done rather formally; no concrete pictures were connected with it. To us, this was a mystery. We were so conversant with the proposition that every quantum number corresponds to a degree of freedom, and on the other hand with the idea of a point electron (with no three-dimensional structure like that of planets and baseballs), which obviously had (only) three degrees of freedom, that we could not place the fourth quantum number.*

The two young graduate students saw immediately the advantages of identifying the fourth quantum number with a special kind of spin motion available to electrons in a realm beyond the usual three spatial dimensions. More slowly they saw the disadvantages. They consulted with their mentor, Paul Ehrenfest, professor of theoretical physics at Leiden. They also got help from the founder of the Leiden school, Hendrik Lorentz ( Ehrenfest was his successor), who was interested but not encouraging. After preparing a summary of their findings for Ehrenfest, they thought better of it and told Ehrenfest they had decided not to publish. But Ehrenfest was wiser than they were in the ways scientific careers are made. He said he had already sent the paper to a journal. While better known theoreticians worried about the peculiar details of a spin concept, Uhlenbeck and Goudsmit had a fine opportunity: “Both of you are young enough to afford a stupidity,” Ehrenfest told them.

One of the many who lost out in the competition to write a successful electron spin theory was Pauli’s assistant, Ralph Kronig. Several months before the Uhlenbeck-Gouldsmit paper reached a journal via Ehrenfet, Kronig arrived at similar conclusions and discussed them with Pauli. But Kronig was not so lucky as his Dutch counterparts. Pauli, the relentless critic, talked him out of publishing. Peierls remarks that in later years, “Pauli did not like to be reminded of this story.” Electron spin is certainly one of the seminal ideas of twentieth-century physics and chemistry. Yet Uhlenbeck and Goudsmit did not receive a Nobel Prize for their theory. Kronig’s claims possibly explain the omission.

Not only electrons but all of the other elementary particles (for example, protons, neutrons, and positrons) have spin motion, and most of them are allowed just two spin states. The theory dictates that the quantum numbers specifying the spin states are + ½ and – ½. (Most quantum numbers have integer values. Spin quantum numbers, with half-integer values, are exceptional.) The two spin states are pictured roughly with the spin axis oriented “up” for one state and “down” for the other.

In view of what has been said about quantum numbers counting the dimensions in which electrons move, the reader may wonder about the hydrogen atom electron, certainly moving in three dimensions and also endowed with spin motion, yet in Bohr’s theory accurately described by the *single* quantum number *n*. Like all other electrons in other atoms, the hydrogen electron is represented by four quantum numbers. But hydrogen is a special case. In hydrogen, and in no other atoms, the energies of electron states depend to a good approximation only on the single quantum number* n*, and not on the other three. Bohr was lucky: he could build his model of the hydrogen atom as if it were one dimensional.

Pauli’s grasp of physical problems was supreme among his contemporaries, probably not surpassed even by Einstein. Born recalled that “ever since the time he had been my assistant in Gottingen, I had been aware that he was a genius, comparable with Einstein himself. Indeed from the point of view of pure science, he was possibly greater than Einstein.”

**Spin and Isospin (p. 409)**

The particles of matter are known by their mass, electrical charge, mode of motion, and assorted other properties such as parity. The motion of a particle can take it from one place to another, as seen in the paths traced in the bubble chamber, and also give it a kind of spin. The term “spin” is a crude name for a property that actually exists only in the quantum realm. Feynman suggests that we should emphasize the abstract nature of particle spin by calling it “quantspin” rather than just spin. It is *nothing* like the spin of a golf ball or baseball. For one thing, electrons, neutrinos, and quarks have spin motion even though the theory does not allow them to have measurable size: they are points.

Another peculiarity is that these particles, like all of the elementary particles of matter, have just two spin modes or states. One says in the parlance of quantum mechanics that electrons, neutrinos, and quarks have spin ½ and that their two spin states have the quantum numbers – ½ and + ½. It is sufficient for our purposes to interpret these two spin modes as simply clockwise and counter clockwise.

All particles with spin ½ are called “fermions,” for their statistical behaviour, first mentioned by Fermi and a little later by Dirac. The statistical rule, which was also clarified by Pauli, is that two fermions cannot be found in the same quantum state. This profoundly important rule dictates the electronic shell structures of atoms and the electronic bonding between atoms in molecules. It guided Gell-Mann and others to some of the fundamental features of quark theory. Particles that are not elementary can also have two spin states, or more. For example, a particle with spin 3/2 has four spin states whose quantum numbers are – 3/2, – 1/2, + ½, and +3/2. Notice that the recipe here is that only quantum numbers separated by one unit are allowed. This particle, and any other with half-integer spin (eg. 7/2, 9/2 etc.), is also classified as a fermion.

Photons are elementary particles, and they too have spin. Their behaviour indicates a spin of 1, and allows three spin states with quantum numbers -1, 0, and +1. In direct contrast to fermions, any number of them can inhabit the same quantum state, a pattern that was discovered by Satyendranath Bose and elaborated by Einstein. Photons and all other particles with integer spin (1, 2, 3. etc), elementary or otherwise, are called “bosons.”

Early in the history of particle physics (1932), Heisenberg took the concept of spin one step further in abstraction. He assumed that, as a model for nuclear structure, the constituent particles in nuclei are neutrons and protons, and that they are affected primarily by strong nuclear forces and much more weakly by electrical forces (among the positively charged protons). Noting this relative indifference to electrical charge, that the neutron and proton have nearly the same mass, and that the neutron can convert into the proton and vice versa, he constructed a theory based on the concept that the neutron and the proton are simply different states of a single entity called the “nucleon.” The two states of the nucleon reminded Heisenberg of the two spin states of fermions with spin ½, and he introduced the “isospin” concept: the nucleon has an *isospin* of ½ (analogous to the* spin* ½ of an electron), and has two *isospin* states with quantum numbers – ½ and + ½, which are observed as the neutron and the proton (analogous to the electron’s two *spin* states with the same quantum numbers). Heisenberg’s motivation was strictly mathematical: he did not imagine any kind of real spin motion. But abstract as it is, the isospin concept, extended and combined with Gell-Mann’s strangeness rules, displays just what theorists want to know: the underlying symmetries of the nucleon and its hadron relatives……………………….. .