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ScienceWeek
HISTORY OF PHYSICS: ON PAUL DIRAC (1902-1984)
The following points are made by Graham Farmelo (Nature 2005 437:323):
1) Of the few authentic visionaries modern science has known, Paul Dirac was the most inscrutable. He was a man of legendary quietness and privacy. His peers were bemused by his strikingly unusual way of looking at the world, while also amazed by the fecundity of his methods. Beginning in 1925, Dirac spent eight years developing quantum mechanics in a series of elegant papers that repeatedly took theoretical physicists by surprise. What, they wondered, lay behind Dirac's unique methods?
2) But colleagues seeking clues about the provenance of Dirac's ideas found none in his papers. He began each one with a deceptively straightforward, equationless introduction, before steam hammering his way through the mathematics, giving no quarter either to the faint hearted or to pedants. Few of his papers contained a diagram and none offered any solace to readers trying to visualize what was represented by the blizzard of abstractions. Dirac would respond to requests to express his quantum reasoning in words or pictures by impassively shaking his head. So it is hardly surprising that Dirac's peers perceived him to be, above all, a brilliant algebraist -- extremely adept at manipulating abstract symbols, but uninterested in visualization.
3) Yet Dirac insisted that he was not primarily an algebraic theoretician. This insistence first emerged almost 40 years after his first quantum papers were published, during an interview with the historian of science Thomas Kuhn (1922-1996) in the spring of 1963. Dirac declared to Kuhn that his approach was fundamentally geometrical and that he was "just no good" at doing "masses of algebraic calculations without picturing what the equation means". Robert Oppenheimer (1904-1967), Dirac's close friend and admirer, was incredulous when he heard this. Oppenheimer had hardly ever seen Dirac draw a diagram but had always been awed by his algebraic skill. No, Oppenheimer assured Kuhn, Dirac was "principally algebraic". Indeed, Oppenheimer went further and commented that Dirac's approach to physics was intuitive, like the mumbling savant Niels Bohr (1885-1962), although the two had completely different ways of communicating. "Bohr regarded mathematics as Dirac regards words, namely as a way to make himself intelligible to other people, which he hardly needs," Oppenheimer said.
4) In a scientific memoir nine years later, Dirac divided mathematicians cleanly into algebraists and geometers (the field of analysis apparently did not count). He had observed that mathematicians with a European training tended to be interested in geometry, following the school of the ancient Greeks, whereas those from an Asian background preferred algebra, which was originally discovered by the Arabs. Dirac remarked that his own preference was "strongly on the side of geometry, and has always remained so". Dirac often said that when he was developing quantum mechanics he used his favorite branch of mathematics --projective geometry -- which concerns the relationships between points and straight lines. But why then did he not mention geometry in his early papers? He expunged his geometrical thinking from his early work, he often said in the 1970s, because it was especially expensive in those days for journals to print diagrams and because he thought most physicists were unfamiliar with projective geometry. Only later, when John von Neumann (1903-1957)invented "state vectors" did the geometric content of quantum mechanics become plain.[1,2]
References (abridged):
1. Galison, P. The Suppressed Drawing: Paul Dirac's Hidden Geometry 145-166 (Univ. California Press, 2000).
2. Darrigol, O. in From c-numbers to q-numbers Ch. 6 (Univ. California Press, 1992).
Nature http://www.nature.com/nature
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HISTORY OF PHYSICS: ON DIRAC, JORDAN, AND QUANTUM THEORY
The following points are made by Kurt Gottfried (Nature 2002 419:117):
1) In the autumn of 1925, Paul Adrien Maurice Dirac (1902-1984), a Cambridge University graduate student of very few words, astonished the world of physics with a remarkable paper on quantum mechanics. His publication heralded the arrival of a mind of exceptional originality and power at the frontier of physics. The discovery by Werner Heisenberg (1901-1976) of quantum mechanics sprang from the fertile soil of Goettingen and Copenhagen, not Cambridge. Nevertheless, Dirac, knowing only Heisenberg's ground-breaking but rather mysterious and fragmentary paper, produced an almost complete formulation of quantum mechanics wholly on his own, mirroring the achievement of the experienced Goettingen collaboration of Max Born (1882-1970), Pascual Jordan (1902-1980) and Heisenberg. Born recalled this as "one of the greatest surprises of my scientific life, for the name of Dirac was completely unknown to me".
2) Dirac, born 100 years ago this year, often displayed an uncanny ability, whenever the need arose, to invent deep mathematical concepts that were new to physicists. Readers of his early paper would ask by what magic had he turned his austere, abstract constructs into quantitative descriptions of physical phenomena. Dirac's genius was quickly recognized -- he was the youngest participant in the elite Solvay Congress of 1927, at which Niels Bohr and Albert Einstein began their long debate about the foundations of quantum mechanics. On first meeting him there, the formidable Wolfgang Pauli (1900-1958) quipped that Dirac believed "there is no God, and Dirac is His prophet".
3) The development of nonrelativistic quantum mechanics -- the microscopic counterpart of newtonian mechanics -- was essentially complete by the end of 1926. But it was not known how to extend the new theory to the electromagnetic field, or to particles moving with velocities approaching the speed of light. Dirac solved both problems, giving birth to quantum electrodynamics. Although Dirac's "quantization" of classical electrodynamics yielded no great surprise, it was the first consistent and correct account of the absorption, emission and scattering of light. Ultimately, all the optical phenomena with which we are so familiar are fully described by Dirac's radiation theory of 1927.
References:
1. Schweber, S. S. QED and the Men Who Made It (Princeton Univ. Press, 1994).
2. Kragh, H. Dirac: A Scientific Biography (Cambridge Univ. Press, 1990).
3. Miller, A. I. Early Quantum Electrodynamics (Cambridge Univ. Press, 1994).
Nature http://www.nature.com/nature
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ON ONE HUNDRED YEARS OF QUANTUM PHYSICS
The following points are made by D. Kleppner and R. Jackiw (Science 2000 289:893):
1) Although quantum mechanics was created to describe an abstract atomic world far removed from daily experience, its impact on our daily lives could hardly be greater. The spectacular advances in chemistry, biology, and medicine -- and in essentially every other science -- could not have occurred without the tools that quantum mechanics made possible. Without quantum mechanics there would be no global economy to speak of, because the electronics revolution that brought us the computer age is a child of quantum mechanics. So is the photonics revolution that brought us the Information Age. The creation of quantum physics has transformed the world, bringing with it all the benefits -- and the risks --of a scientific revolution.
2) The principal players in the creation of quantum theory were young. In 1925, Wolfgang Pauli was 25 years old, Werner Heisenberg and Enrico Fermi were 24 years old, Paul Dirac and Pascual Jordan were 23 years old. Erwin Schroedinger, at age 36, was a late bloomer. Max Born and Niels Bohr were older still, and it is significant that their contributions were largely interpretive. The profoundly radical nature of the intellectual achievement is revealed by Einstein's reaction. Having invented some of the key concepts that led to quantum theory, Einstein rejected it. His paper on Bose-Einstein statistics was his last contribution to quantum physics and his last significant contribution to physics. That a new generation of physicists was needed to create quantum mechanics is hardly surprising. Lord Kelvin described why in a letter to Niels Bohr congratulating Bohr on his 1913 paper proposing the planetary model of the atom. Kelvin said there was much truth in Bohr's paper, but he would never understand it himself. Kelvin recognized that radically new physics would need to come from unfettered minds.
3) The unique situation of quantum theory, this crucial yet elusive theory, is perhaps best summarized by the following observation: Quantum theory is the most precisely tested and most successful theory in the history of science. Nevertheless, not only was quantum mechanics deeply disturbing to its founders, today -- 75 years after the theory was essentially cast in its current form -- some of the luminaries of science remain dissatisfied with its foundations and its interpretations, even as they acknowledge its stunning power.
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