Category Archives: physicisrs

Yet another little portrait of Hermann Weyl: as painted by John Archibald Wheeler

Reference: 

The Continuum, Hermann Weyl, translated by Stephen Pollard and Thomas Bole.

This is what famous physicist, John Archibald Wheeler writes as the foreword:

Hermann Weyl was-is-for many of us, and for me, a friend, a teacher, and a hero. A North German who became an enthusiastic American, he was a mathematical master figure to mathematicians, and to physicists a pioneer in quantum theory and relativity and discoverer of gauge theory. He lives for us today, and will live in time to come, in his great findings, his papers and books, and his human influence.

I last knew Weyl after I last knew him. Day after day in Zurich in late 1955 he had been answering letters of congratulations and good wishes received on his seventieth birthday, walking to the mailbox, posting them, and returning home. December eighth, thus making his way homeward, he collapsed on the sidewalk and murmuring, “Ellen, died. News of his unexpected death reached Princeton by the morning New York Times. Some days later our postman brought my wife and me Weyl’s warm note of thanks. I like to think he sent it in that last mailing.

I first knew Weyl before I first knew him. Picture a youth of nineteen seated in a Vermont hillside pasture, at his family’s summer place, with grazing cows around, studying Weyl’s great book, Theory of Groups and Quantum Mechanics, sentence by sentence, in the original German edition, day after day, week after week. That was one student’s introduction to quantum theory. And what an introduction it was! His style is that of a smiling figure on horseback, cutting a clean way through, on a beautiful path, with a swift bright sword.

Some years ago I was asked, like others, I am sure, to present to the Library of the American Philosophical Society the four books that had most influenced me. Theory of Groups and Quantum Mechanics was not last on my list. That book has, each time I read it, some great new message.

If I had to come up with a single word to characterize Hermann Weyl, the man, as I saw and knew him then and in the years to come, it would be that old fashioned word, so rarely heard in out day, “nobility.” I use it here not only in the dictionary sense of “showing qualities of high moral character, as courage, generosity, honour,” but also in the sense of showing exceptional vision. Weyl’s eloquence in pointing out the peaks of the past in the world of learning and his aptitude in discerning new peaks in newly developing fields of thought surely were part and parcel of his lifelong passion for everything that is high in nature and man.

Erect, bright-eyed, smiling Hermann Weyl I first saw in the flesh when 1937 brought me to Princeton. There I attended his lectures on the Elie Cartan calculus of differential forms and their application to electromagnetism — eloquent, simple, full of insights. Little did I dream that in thirty-five years I would be writing, in collaboration with Charles Misner and Kip Thorne, a book on gravitation, in which two chapters would be devoted to exactly that topic. At another time Weyl arranged to give a course at Princeton University on the history of mathematics. He explained to me one day that it was for him an absolute necessity to review, by lecturing, his subject of concern in all its length and breadth. Only so, he remarked, could he see the great lacunae, the places where deeper understanding is needed, where work should focus.

The man who ranged so far in his thought had mathematics as the firm backbone of his intellectual life. Distinguished as a physicist, as a philosopher, as a thinker, he was above all a great mathematician, serving as professor of mathematics from 1913 to 1930 at Zurich, from 1930 to 1933 at Gottingen, and at the Princeton Institute for Advanced Study from October 1933 to his retirement. What thinkers and currents of thought guided Weyl into his lifework: mathematics, philosophy, physics?

“As a schoolboy,” he recalls, “I came to know Kant’s doctrine of the ideal character of space and time, which at once moved me powerfully.” He was still torturing himself, he tells us, with Kant’s Schematismus der reinen Verstandesbegriffe when he arrived as a university student at Gottingen. That was one year before special relativity burst on the world. What a time to arrive, just after David Hilbert, world leader of mathematics, had published his Grundlagen der Geometrie, breaking with Kant’s predisposition for Euclidean geometry and taking up, in the great tradition of Karl Friedrich Gauss and Bernhard Riemann, the construction and properties of non-Euclidean geometries, and — having just published an important book on number theory Zahlericht — was giving absorbing lectures on that field of research. Philosophy! Mathematics! Physics! Each was sounding its stirring trumpet blast to an impressionable young man. Mathematics, being represented in Gottingen by its number one man, won the number one place in Weyl’s heart.

Weyl tells us the impression made upon him by Hilbert’s irresistible optimism, “his spiritual passion, his unshakable faith in the supreme value of science, and his firm confidence in the power of reason to find simple and clear answers to simple and clear questions.” No one who in his twenties had the privilege to listen to Weyl’s lectures can fail to turn around and apply to Weyl himself those very words. Neither can anyone who reads Weyl, and admires his style, fail to be reminded of Weyl’s own writing by what he says of the lucidity of Hilbert: “It is as if you are on a swift walk through a sunny open landscape; you look freely around, demarcation lines and connecting roads are pointed out to you before you must brace yourself to climb the hill; then the path goes straight up, no ambling around, no detours.”

Electrified by Leibnitz and Kant, and under the magnetic influence of Hilbert, Weyl leaped wholeheartedly, as he later put it, into “the deep river of mathematics.” That leap marked the starting point of his lifelong contributions to ever widening spheres of thought.

For the advancing army of physics, battling for many a decade with heat and sound, fields and particles, gravitation and spacetime geometry, the cavalry of mathematics, galloping out ahead, provided what it thought to be the rationale for the real number system. Encounter with the quantum has taught us, however, that we acquire our knowledge in bits; that the continuum is forever beyond our reach. Yet for daily work the concept of the continuum has been and will continue to be as indispensable for physics as it is for mathematics. In either field of endeavour, in any given enterprise, we can adopt the continuum and give up absolute logical rigour, or adopt rigour and give up the continuum, but we can’t pursue both approaches at the same time in the same application.

Adopt rigour or adopt the contiuum ? These ways of speaking should not be counted as contradictory, but as complementary. This complementarity between the continuum and logical rigour we accept and operate with today in the realm of mathematics. The hard-won power thus to assess correctly the continuum of the natural numbers grew out of titanic struggles in the realm of mathematical logic in which Hermann Weyl took a leading part. His guidance, his insights and his wisdom shine out afresh to the English-speaking world with the publication of the present volume. The level of synthesis achieved by now in mathematics is still far beyond our reach today in physics. Happily the courageous outpost-cavalry of mathematical logic prepares the way, not only for the main cavalry that is mathematics, but also for the army that is physics, and nowhere more critically so than in its assault on the problem of existence.

Hermann Weyl has not died. His great works speak prophecy to us in this century and will continue to speak wisdom in the coming century. If we seek a single word to stand for the life and work of Hermann Weyl, what better word can we find than passion? Passion to understand the secret of existence was his, passion for that clear, luminous beauty of conception which we associate with the Greeks, passionate attachment to the community of learning, and passionate belief in the unity of knowledge.

— John Archibald Wheeler, University of Texas, Austin.

Richard Feyman: colourful life.

https://www.hindustantimes.com/more-lifestyle/feyn-balance-meet-one-of-the-world-s-most-influential-colourful-physicists/story-a6T3fQUHspE47zxYHGoHWO.html

Thanks to Hindustan Times and Rachel Lopez.

 

Remembering Richard Feynman on his 100th birth centenary

https://www.hindustantimes.com/more-lifestyle/infectious-enthusiastic-relevant-a-physicist-s-take-on-richard-feynman/story-jD3jualkHCX5WuXcCp0ndL.html

Thanks to Hindustan Times and Prof. Arnab Bhattacharya, TIFR, Mumbai.

Stephen Hawking in his own words: excerpts: My Brief History

I. Another early memory was getting my first train set. Toys were not manufactured during the war, at least not for the home market. But, I had a passionate interest in model trains. My father tried making me a wooden train, but that didn’t satisfy me, as I wanted something that moved on its own. So, he got a secondhand clockwork train, repaired it with a soldering iron, and gave it to me for Christmas when I was nearly three. That train didn’t work very well. But my father went to America just after the war, and when he came back on the Queen Mary he bought my mother some nylons, which were not obtainable in Britain at that time. He bought my sister Mary a doll that closed its eyes when you laid it down. And he brought me an American train, complete with a cowcatcher and a figure-eight track. I can still remember my excitement as I opened the box.

Clockwork trains, which you had to wind up, were all very well, but I really wanted were electric trains. I used to spend hours watching a model railway club layout in Crouch End, near Highgate. I dreamed about electric trains. Finally, when both my parents were away somewhere, I took the opportunity to draw out of the Post Office bank all of the very modest amount of money that people had given me on special vacations, such as my christening. I used the money to buy an electric train set, but frustratingly enough, it didn’t work very well either. I should have taken the set back and demanded that the shop or the manufacturer replace it, but in those days the attitude was that it was a privilege to buy something and it was just your bad luck, if it turned out to be faulty. So, I paid for the electric motor of the engine to be serviced, but it never worked very well, even then.

Later on, in my teens, I built model aeroplanes and boats. I was never very good with my hands, but I did this with my school friend John McClenahan, who was much better and whose father had a workshop in their house. My aim was always to build working models that I could control. I didn’t care what they looked like. I think it was the same drive that led me to invent a series of very complicated games with another school friend, Roger Ferneyhough. There was a manufacturing game, complete with factories in which units of different colours were made, roads and railways on which they were carried, and a stock market. There was a war game, played on a board of 4000 squares, and even a feudal game, in which each player was a whole dynasty, with a family tree. I think these games, as well as the trains, boats, and aeroplanes, came from an urge to know how systems worked and how to control them. Since I began my PhD, this need has been met by research into cosmology. If you understand how the universe operates, you control it, in a way.

II. When I was thirteen, my father wanted me to try for Westminister School, one of Britain’s main public schools (what in the United States are called private schools). At that time, there was a sharp division in education along class lines, and my father felt that the social graces such a school would give me would be an advantage in life. My father believed that his own lack of poise and connections had led to him being passed over in his career in favour of people of less ability. He had a bit of a chip on his shoulder because he felt that other people who were not as good but who had the right background and connections had got ahead of him. He used to warn me against such people.

Because my parents were not well-off, I would have to win a scholarship in order to attend Westminister. I was ill at the time of the scholarship examination, however, and did not take it. Instead, I remained at St. Albans School, where I got an education that was as good as, if not better than, the one I would have had at Westminister. I have never found that my lack of social graces has been a hindrance. But I think physics is a bit different from medicine. In physics it doesn’t matter what school you went to or whom you are related. It matters what you do.

I was never more than about halfway up the class (it was a very bright class.) My classwork was untidy, and my handwriting was the despair of my teachers. But, my classmates gave me the nickname Einstein, so presumably they saw signs of something better. When I was twelve, one of my friends bet another friend a bag of sweets that I would never amount to anything. I don’t know if this bet was ever settled, and if so, which way it was decided.

I had six or seven close friends, most of whom I’m still in touch with. We used to have long discussions and arguments about everything from radio-controlled models to religion and from parapsychology to physics. One of the things we talked about was the origin of the universe and whether it had required a God to create it and set it going. I had heard that light from distant galaxies was shifted towards the red end of the spectrum and that this was supposed to indicate that the universe was expanding. (A shift towards the blue would have meant it was contracting.) But, I was sure there must be some other reason for the red shift. An essentially unchanging and everlasting universe seemed so much more natural. Maybe light just got tired, and more red, on its way to us, I speculated. It was only after about two years of PhD research that I realized that I had been wrong.

I was always very interested in how things operated, and I used to take them apart to see how they worked, but I was not so good at putting them back together again. My practical abilities never matched up to my theoretical inquiries. My father encouraged my interest in science, and he even coached me in mathematics until I got to a stage beyond his knowledge. With this background and my father’s job, I took it as natural that I would go into scientific research.

When I came to the last two years of school, I wanted to specialize in mathematics and physics. There was an inspiring maths teacher, Mr. Tanta, and the school had also just built a new maths room, which the maths set had as their classroom. But my father was very much against it because he thought there wouldn’t be any jobs for mathematicians except as teachers. He would really have liked me to do medicine, but I showed no interest in biology, which seemed to me to be too descriptive and not sufficiently fundamental. It also had a rather low status at school. The brightest boys did mathematics and physics; the less bright did biology.

My father knew I wouldn’t do biology, but he made me do chemistry and only a small amount of mathematics. He felt this would keep my scientific options open. I am now professor of mathematics, but I have not had any formal instruction in mathematics since I left St. Albans School at the age of seventeen. I have had to pick up what I know as I went along. I used to supervise undergraduates at Cambridge and kept one week ahead of them in the course.

Physics was always the most boring subject at school because it was so easy and obvious. Chemistry was much more fun because unexpected things, such as explosions kept happening. But physics and astronomy offered the hope of understanding where we came from and why we are here. I wanted to fathom the depths of the universe. Maybe I have succeeded to a small extent, but there’s still plenty I want to know.

III. My early work showed that classical general relativity broke down at singularities in the Big Bang and black holes. My later work has shown how quantum theory can predict what happens at the beginning and end of time. It has been a glorious time to be alive and doing research in theoretical physics. I’m happy if I have added something to our understanding of the universe.

A humble tribute to Professor Hawking …to understand him from a layman’s viewpoint…by Nalin Pithwa.

Reference: My Brief History by Stephen Hawking, Bantam Press.

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