Broken Symmetry: Selected Papers of Y. Nambu (World Scientific Series in 20th Century Physics 13)

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Freeman John Dyson FRS born 15 December is an American theoretical physicist and mathematician known for his work in quantum electrodynamics , solid-state physics , astronomy and nuclear engineering. Dyson originated several concepts that bear his name, such as Dyson's transform , a fundamental technique in additive number theory , [10] which he developed as part of his proof of Mann's theorem ; [11] the Dyson tree , a hypothetical genetically-engineered plant capable of growing in a comet ; the Dyson series , a perturbative series where each term is represented by Feynman diagrams ; the Dyson sphere , a thought experiment that attempts to explain how a space-faring civilization would meet its energy requirements with a hypothetical megastructure that completely encompasses a star and captures a large percentage of its power output; and Dyson's eternal intelligence , a means by which an immortal society of intelligent beings in an open universe could escape the prospect of the heat death of the universe by extending subjective time to infinity while expending only a finite amount of energy.

Dyson believes global warming is caused by increased carbon dioxide through burning fossil fuels , but is skeptical about the simulation models used to predict climate change , arguing that political efforts to reduce causes of climate change distract from other global problems that should take priority. Born on 15 December , at Crowthorne in Berkshire , England , Dyson is the son of the composer George Dyson , who was later knighted.

His mother had a law degree, and after Dyson was born she worked as a social worker. From to Dyson was a scholar at Winchester College , where his father was Director of Music. At age 17 he studied mathematics with G. Hardy at Trinity College, Cambridge where he won a scholarship at age 15 and at age 19 was assigned to war work in the Operational Research Section ORS of the Royal Air Force's Bomber Command , [16] where he developed analytical methods for calculating the ideal density for bomber formations [17] to help the Royal Air Force bomb German targets during the Second World War.

His friend the neurologist and author Oliver Sacks said: "A favourite word of Freeman's about doing science and being creative is the word 'subversive'. He feels it's rather important not only to be not orthodox, but to be subversive, and he's done that all his life. Taylor 's advice and recommendation, Dyson moved to the United States in as a Commonwealth Fellow to earn a physics doctorate with Hans Bethe at Cornell University — The budding English physicist recognized the brilliance of the flamboyant American, and attached himself as quickly as possible.

He then moved to the Institute for Advanced Study —49 , before returning to England —51 , where he was a research fellow at the University of Birmingham. He was the first person after their creator to appreciate the power of Feynman diagrams and his paper written in and published in was the first to make use of them. He said in that paper that Feynman diagrams were not just a computational tool but a physical theory and developed rules for the diagrams that completely solved the renormalization problem.

Dyson's paper and also his lectures presented Feynman's theories of QED in a form that other physicists could understand, facilitating the physics community's acceptance of Feynman's work. Robert Oppenheimer , in particular, was persuaded by Dyson that Feynman's new theory was as valid as Schwinger's and Tomonaga's. Oppenheimer rewarded Dyson with a lifetime appointment at the Institute for Advanced Study, "for proving me wrong", in Oppenheimer's words.

Also in , in related work, Dyson invented the Dyson series. It was this paper that inspired John Ward to derive his celebrated Ward—Takahashi identity. In Dyson joined the faculty at Cornell as a physics professor, though he still had no doctorate, and in he received a permanent post at the Institute for Advanced Study in Princeton, New Jersey , where he has remained. One reason he gave decades later is that his children born in the United States had not been recognized as British subjects.

From to Dyson worked on Project Orion , [29] which proposed the possibility of space-flight using nuclear pulse propulsion. A prototype was demonstrated using conventional explosives , but the Partial Test Ban Treaty , which Dyson was involved in and supported, permitted only underground nuclear weapons testing , so the project was abandoned. In Dyson was a member of the design team under Edward Teller for TRIGA , [30] a small, inherently safe nuclear reactor used throughout the world in hospitals and universities for the production of medical isotopes.

A seminal paper by Dyson came in , when, together with Andrew Lenard and independently of Elliott H. Lieb and Walter Thirring , he proved rigorously that the Pauli exclusion principle plays the main role in the stability of bulk matter. In condensed matter physics , Dyson also analysed the phase transition of the Ising model in 1 dimension and spin waves. Dyson also did work in a variety of topics in mathematics, such as topology, analysis, number theory and random matrices.

He showed his formula to the mathematician Atle Selberg , who said that it looked like something in mathematical physics and that Montgomery should show it to Dyson, which he did.

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Dyson recognized the formula as the pair correlation function of the Gaussian unitary ensemble , which physicists have studied extensively. This suggested that there might be an unexpected connection between the distribution of primes 2, 3, 5, 7, 11, Around Dyson worked with the Institute for Energy Analysis on climate studies.

This group, under Alvin Weinberg 's direction, pioneered multidisciplinary climate studies, including a strong biology group. Dyson retired from the Institute for Advanced Study in As of [update] he was president of the Space Studies Institute , the space research organization founded by Gerard K. O'Neill ; as of he is on its board of trustees. Dyson has won numerous scientific awards, but never a Nobel Prize.

Nobel physics laureate Steven Weinberg has said that the Nobel committee has "fleeced" Dyson, but Dyson himself remarked in , "I think it's almost true without exception if you want to win a Nobel Prize, you should have a long attention span, get hold of some deep and important problem and stay with it for ten years.

1. My first encounters with Yoichiro Nambu

That wasn't my style. In Dyson published with William H. Press a fundamental new result about the prisoner's dilemma in the Proceedings of the National Academy of Sciences of the United States of America. Dyson's eldest daughter, Esther, is a digital technology consultant and investor; she has been called "the most influential woman in all the computer world".

Dyson admits his record as a prophet is mixed, but thinks it is better to be wrong than vague, and that in meeting the world's material needs, technology must be beautiful and cheap. My book The Sun, the Genome, and the Internet describes a vision of green technology enriching villages all over the world and halting the migration from villages to megacities. The three components of the vision are all essential: the sun to provide energy where it is needed, the genome to provide plants that can convert sunlight into chemical fuels cheaply and efficiently, the Internet to end the intellectual and economic isolation of rural populations.

With all three components in place, every village in Africa could enjoy its fair share of the blessings of civilization. Dyson has coined the term "green technologies", based on biology instead of physics or chemistry , to describe new species of microorganisms and plants designed to meet human needs. He argues that such technologies would be based on solar power rather than the fossil fuels whose use he sees as part of what he calls "gray technologies" of industry. He believes that genetically engineered crops, which he describes as green, can help end rural poverty , with a movement based in ethics to end the inequitable distribution of wealth on the planet.

Dyson favors the dual origin theory: that life first formed as cells , then enzymes , and finally, much later, genes. This was first propounded by the Russian Alexander Oparin. Haldane developed the same theory independently. Because of the biochemistry he regards it as too unlikely that genes could have developed fully blown in one process. Current cells contain adenosine triphosphate or ATP and adenosine 5'-monophosphate or AMP, which greatly resemble each other but have completely different functions.

There is no direct evidence for the dual origin theory, because once genes developed, they took over, obliterating all traces of the earlier forms of life. In the first origin, the cells were probably just drops of water held together by surface tension, teeming with enzymes and chemical reactions, and having a primitive kind of growth or replication. When the liquid drop became too big, it split into two drops. Many complex molecules formed in these "little city economies" and the probability that genes would eventually develop in them was much greater than in the prebiotic environment.

Eventually the civilization would enclose the star, intercepting electromagnetic radiation with wavelengths from visible light downward and radiating waste heat outward as infrared radiation. One method of searching for extraterrestrial civilizations would be to look for large objects radiating in the infrared range of the electromagnetic spectrum.

One should expect that, within a few thousand years of its entering the stage of industrial development, any intelligent species should be found occupying an artificial biosphere which surrounds its parent star. Dyson conceived that such structures would be clouds of asteroid -sized space habitats , though science fiction writers have preferred a solid structure: either way, such an artefact is often called a Dyson sphere , although Dyson used the term "shell". Dyson says that he used the term "artificial biosphere" in the article to mean a habitat, not a shape.

Dyson has also proposed the creation of a Dyson tree , a genetically engineered plant capable of growing on a comet. He suggested that comets could be engineered to contain hollow spaces filled with a breathable atmosphere, thus providing self-sustaining habitats for humanity in the outer Solar System. Plants could grow greenhouses These plants could keep warm by the light from a distant Sun and conserve the oxygen that they produce by photosynthesis.

The greenhouse would consist of a thick skin providing thermal insulation, with small transparent windows to admit sunlight. Outside the skin would be an array of simple lenses, focusing sunlight through the windows into the interior Groups of greenhouses could grow together to form extended habitats for other species of plants and animals. I've done some historical research on the costs of the Mayflower's voyage, and on the Mormons' emigration to Utah, and I think it's possible to go into space on a much smaller scale.

Unless it's brought down to that level it's not really interesting to me, because otherwise it would be a luxury that only governments could afford. Dyson has been interested in space travel since he was a child, reading such science fiction classics as Olaf Stapledon 's Star Maker. As a young man, he worked for General Atomics on the nuclear-powered Orion spacecraft.

He hoped Project Orion would put men on Mars by , Saturn by For a quarter-century Dyson has been unhappy about how the government conducts space travel:. The problem is, of course, that they can't afford to fail. The rules of the game are that you don't take a chance, because if you fail, then probably your whole program gets wiped out. He still hopes for cheap space travel, but is resigned to waiting for private entrepreneurs to develop something new and inexpensive.

No law of physics or biology forbids cheap travel and settlement all over the solar system and beyond. But it is impossible to predict how long this will take. Predictions of the dates of future achievements are notoriously fallible. My guess is that the era of cheap unmanned missions will be the next fifty years, and the era of cheap manned missions will start sometime late in the twenty-first century. Any affordable program of manned exploration must be centered in biology, and its time frame tied to the time frame of biotechnology; a hundred years, roughly the time it will take us to learn to grow warm-blooded plants, is probably reasonable.

Dyson also proposed the use of bioengineered space colonies to colonize the Kuiper Belt on the outer edge of our Solar System. He proposed that habitats could be grown from space hardened spores. The colonies could then be warmed by large reflector plant leaves that could focus the dim, distant sunlight back on the growing colony. A direct search for life in Europa's ocean would today be prohibitively expensive. Impacts on Europa give us an easier way to look for evidence of life there. Every time a major impact occurs on Europa, a vast quantity of water is splashed from the ocean into the space around Jupiter.

Some of the water evaporates, and some condenses into snow. Creatures living in the water far enough from the impact have a chance of being splashed intact into space and quickly freeze-dried. Therefore, an easy way to look for evidence of life in Europa's ocean is to look for freeze-dried fish in the ring of space debris orbiting Jupiter. Freeze-dried fish orbiting Jupiter is a fanciful notion, but nature in the biological realm has a tendency to be fanciful.

Nature is usually more imaginative than we are. To have the best chance of success, we should keep our eyes open for all possibilities. Dyson proposed that an immortal group of intelligent beings could escape the prospect of heat death by extending time to infinity while expending only a finite amount of energy. Dyson and Hugh Montgomery discovered an intriguing connection between quantum physics and Montgomery's pair correlation conjecture about the zeros of the Zeta function. The primes 2, 3, 5, 7, 11, 13, 17, 19, Dyson recognized this connection because of a number-theory question Montgomery asked him.

Dyson had published results in number theory in , while a Fellow at Trinity College, Cambridge , and so was able to understand Montgomery's question. If Montgomery had not been visiting the Institute for Advanced Study that week, this connection might not have been discovered. There are in nature one, two, and three dimensional quasicrystals. Mathematicians define a quasicrystal as a set of discrete points whose Fourier transform is also a set of discrete points.

Odlyzko has done extensive computations of the Fourier transform of the nontrivial zeros of the Zeta function, and they seem to form a one-dimensional quasicrystal. This would in fact follow from the Riemann hypothesis. In number theory and combinatorics rank of a partition of a positive integer is a certain integer associated with the partition. Dyson introduced the concept in a paper published in the journal Eureka.

My 50 years of research in particle physics

A different concept, sharing the same name, is used in combinatorics, where the rank is taken to be the size of the Durfee square of the partition. In number theory , the crank of a partition is a certain integer associated with the partition in number theory. Dyson first introduced the term without a definition in a paper in a journal published by the Mathematics Society of Cambridge University.

In , George E. Andrews and Frank Garvan discovered a definition for the crank satisfying the properties Dyson had hypothesized. Astrochicken is the name given to a thought experiment Dyson expounded in his book Disturbing the Universe He contemplated how humanity could build a small, self-replicating automaton that could explore space more efficiently than a manned craft could.

Dyson expanded on von Neumann's automata theories and added a biological component. Dyson has suggested that philosophers can be broadly, if simplistically, divided into splitters and lumpers. These roughly correspond to materialists , who imagine the world divided into atoms, and Platonists , who regard it as made up of ideas.

How does symmetry manifest in quantum physics? What is "symmetry breaking?"

Helios is a design for a spacecraft propulsion system in which small 0. Water would be injected into the chamber, superheated by the explosion and expelled for thrust. Dyson agrees that anthropogenic global warming exists and that one of its main causes is the increase of carbon dioxide in the atmosphere resulting from the burning of fossil fuels. Dyson's views on global warming have been criticized. If he's going to wander into something with major consequences for humanity and other life on the planet, then he should first do his homework—which he obviously has not done on global warming.

In Dyson endorsed the now common usage of "global warming" as synonymous with global anthropogenic climate change, [63] but argued that political efforts to reduce the causes of climate change distract from other global problems that should take priority. Since originally taking interest in climate studies in the s, Dyson has suggested that carbon dioxide levels in the atmosphere could be controlled by planting fast-growing trees.

He calculates that it would take a trillion trees to remove all carbon from the atmosphere. It will take a lot of very hard work before that question is settled. Dyson is a member of the academic advisory council of the Global Warming Policy Foundation , a climate sceptic think tank chaired by Nigel Lawson. All our advice to the commander in chief [went] through the chief of our section, who was a career civil servant.

His guiding principle was to tell the commander in chief things that the commander in chief liked to hear To push the idea of ripping out gun turrets, against the official mythology of the gallant gunner defending his crew mates I agreed emphatically with Henry Stimson. Once we had got ourselves into the business of bombing cities, we might as well do the job competently and get it over with.

I felt better that morning than I had felt for years Those fellows who had built the atomic bombs obviously knew their stuff Later, much later, I would remember [the downside]. I am convinced that to avoid nuclear war it is not sufficient to be afraid of it.

It is necessary to be afraid, but it is equally necessary to understand. And the first step in understanding is to recognize that the problem of nuclear war is basically not technical but human and historical. If we are to avoid destruction we must first of all understand the human and historical context out of which destruction arises. In , in his capacity as a military adviser, Dyson wrote an influential paper on the issue of possible US use of tactical nuclear weapons in the Vietnam War.

When a general said in a meeting, "I think it might be a good idea to throw in a nuke now and then, just to keep the other side guessing Dyson says that the report showed that, even from a narrow military point of view, the US was better off not using nuclear weapons. Dyson stated on the Dick Cavett show that the use of nuclear weaponry was a bad idea for the US at the time because "our targets were large and theirs were small.

Regarding doctrinal or Christological issues, he has said, "I am neither a saint nor a theologian. To me, good works are more important than theology. Science and religion are two windows that people look through, trying to understand the big universe outside, trying to understand why we are here. The two windows give different views, but they look out at the same universe. Both views are one-sided, neither is complete. Both leave out essential features of the real world. And both are worthy of respect. Trouble arises when either science or religion claims universal jurisdiction, when either religious or scientific dogma claims to be infallible.

Religious creationists and scientific materialists are equally dogmatic and insensitive.

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By their arrogance they bring both science and religion into disrepute. The media exaggerate their numbers and importance. The media rarely mention the fact that the great majority of religious people belong to moderate denominations that treat science with respect, or the fact that the great majority of scientists treat religion with respect so long as religion does not claim jurisdiction over scientific questions. Dyson partially disagrees with the famous remark by his fellow physicist Steven Weinberg that "With or without religion, good people can behave well and bad people can do evil; but for good people to do evil—that takes religion.

Weinberg's statement is true as far as it goes, but it is not the whole truth. The molecules inside a magnet are themselves little magnetic dipoles. If we switch on a small magnetic field, then the rotational symmetry is broken explicitly and all of the dipoles align themselves in the direction of the magnetic field. That is simple. The interesting phenomenon is that the dipoles continue to be aligned in the same direction, even after the external magnetic field is switched off.

Here the rotational symmetry is broken spontaneously. Nevertheless, the fact that the underlying laws respect rotational symmetry has a consequence: if we gently disturb one of the dipoles from its perfectly aligned position, it gently nudges its neighbours and they nudge their neighbours, and the result is a wave that propagates through the magnet. Such a wave has very low energy and is called a spin wave. This is a special case of a general phenomenon where a spontaneously broken symmetry has an associated low-energy mode, or in quantum theory an associated massless particle.

Nambu took the concept of spontaneous symmetry breaking to a new level. Superconductors are materials that conduct electric current without any resistance. Superconductors also repel external magnetic fields — an effect called the Meissner effect. However, a massive photon appears to be inconsistent with gauge invariance — a basic property of electromagnetism.

It was Nambu in , and independently Philip Anderson a little earlier in , who understood what was going on.

They realised that in the absence of electromagnetic interactions the superconducting state broke the symmetry spontaneously. This symmetry is unlike the rotation symmetry that is spontaneously broken in magnets or crystals. It is a symmetry associated with the fact that electric charge is conserved. Also, if we imagine switching off the electromagnetic interaction, this symmetry breaking would also result in very low-energy waves, like spin waves in a magnet — a massless particle.

Now comes a great discovery: if we switch on the electromagnetic interaction, which is there, we can undo the apparent symmetry breaking by a gauge transformation, which is local in space and time , without any energy cost. Hence, there is no massless particle, and in fact the photon becomes massive together with a massive neutral particle, which explains the Meissner effect.

Soon after finishing his work on superconductivity, Nambu returned to particle physics. The first thing he noticed was that the Bogoliubov equations describing excitations near the Fermi surface in a superconductor are very similar to the Dirac equation that describes nucleons.

The energy gap in a superconductor translates to the mass of nucleons. The charge symmetry that is spontaneously broken in a superconductor electromagnetism switched off also has an analogue — chiral symmetry. If the energy gap in a superconductor is a result of spontaneous symmetry breaking of charge symmetry, could it be that the mass of a nucleon is the result of spontaneous symmetry breaking of chiral symmetry? Unlike the charge symmetry in a superconductor, chiral symmetry is a global symmetry that can be truly spontaneously broken, leading to a massless particle — which Nambu identified with the pion.

This is exactly what Nambu proposed in a short paper in , soon followed by two papers with Jona-Lasinio. This was a revolutionary step. In all previous examples, spontaneous symmetry breaking happened in situations where there were constituents the molecular dipoles in a magnet, for example and the underlying laws did not permit them to arrange themselves maintaining the symmetry. Nambu, however, proposed that there are situations where spontaneous symmetry breaking can happen in the vacuum of the world.

How can a symmetry be broken — even spontaneously — when there is nothing around? The vacuum, to us, was and always had been a vacuum — it had, since Einstein got rid of the aether, been the epitome of emptiness…I, at least, had my mind encumbered with the idea that if there was a condensate, there was something there…This is why it took a Nambu to break the first symmetry. Nambu was proposing that the masses of elementary particles have an origin — something we can calculate.

The revolutionary nature of this idea cannot be overstated. Soon after the papers of Nambu and Jona-Lasinio, Goldstone came up with a simpler renormalisable model of superconductivity, which also illustrates the phenomenon of spontaneous symmetry breaking by construction and provided a general proof that such symmetry breaking always leads to a massless particle. It became the key to formulating the Standard Model of particle physics by Weinberg and Salam, building on the earlier work of Glashow, and resulting in our current understanding of electromagnetic and weak forces.

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The analogue of the special massive state in a superconductor is the Higgs particle, discovered at CERN in We now know, for certain, that chiral symmetry is spontaneously broken in strong interactions. However, the final realisation of this idea had to wait until another work by Nambu. The idea that all hadrons particles that experience strong forces are made of quarks was proposed by Gell-Mann, and independently Zweig, in However, the idea soon ran into serious trouble.

According to the spin-statistics theorem, they should be fermions obeying the exclusion principle. However, it appeared that if quarks are indeed the constituents of all hadrons, they cannot at the same time be fermions. In his first proposal, quarks have two such colours. Two quarks may appear identical and therefore cannot be on top of each other if their colour is ignored.

This is because he made another remarkable one: colour is like another kind of electric charge. A quark not only produced an ordinary electric field, but a new kind of generalised electric field. This new kind of electric field causes a new kind of force between quarks, and the energy is minimum when the quarks form a colour singlet.

This force, Nambu claimed, is the basic strong force that holds the quarks together inside a nucleon. This proposal turned out to be essentially correct, and is now known as quantum chromodynamics QCD.