weylmann.com - Hermann Weyl

Time 2020-12-23 07:03:12

Web Name: weylmann.com - Hermann Weyl

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Truth with the Beautiful, but when Ihad to choose one or the other, I usually chose the Beautiful. Hermann WeylKlaus Hugo Weyl (1885-1955).German mathematical physicist. In 1918, proposed an early form of gaugesymmetry in an attempt to unify electrodynamics and gravitation.Subsequently applied a similar approach to quantum physics anddiscovered what is today considered one of the most profound andbeautiful concepts in modern physics -- the principleof gaugeinvariance. Shortlyafter Einstein announced his theory of general relativity (gravitation)in November 1915, Weylbegan an intensive study of the theory's mathematics and was soonpublishing related scientific papers dealing with its physicalapplications. In 1918 Weyl published his book Raum-Zeit-Materie(Space-Time-Matter), which provided the first fully comprehensiveanalysis ofthe geometric aspects of the theory and itsrelationship with spacetime physics. One of the topics covered in thebook was Weyl's idea that gravity and electromagnetism might both bederivable from a generalization of Riemannian geometry, themathematical basis from which Einstein had developed his relativitytheory. Weyl's idea was based on a new mathematical symmetry that hecalled gauge invariance. I came acrossWeyl's book in 1975, but it didn't impress me very much because Ididn't know general relativity. However, in the summer of that year I stumbled acrossMisner-Thorne-Wheeler'smassive Gravitationduring a one-week work assignment in the microscopic rural town of LonePine, California (which then had a populationof perhaps 500 people). Miraculously, the town's tiny public librarysomehowhad this book, which is now regarded as a classic graduate text ongeneral relativity. I checked out thebook and brought it back to the hotel room to read in the off-hours.book took immediate and total possession of me, and motivated me tolearn everything I could about general relativity. (Ispokeco-author Kip Thorne about this in 1994, and he was quite amusedtolearn where one of his books had ended up.) But Gravitationis not an easy read,and I had to look for more introductory texts. I soon came across Adler/Bazin/Schiffer's Introductionto General Relativity,which besides being easier had a chapter on unified field theory,includingWeyl's 1918 theory of the combined gravitational-electromagnetic field.For whatever reason,the theory's mathematical beauty absolutelyfascinated me. I had known about local and global phase invariancefrom my studies of quantum mechanics,but I was not aware that Weyl's theory was the origin of this powerfulsymmetry principle in quantum physics. Ihave since read all of Weyl's books andmany of his papers. Although today I believe that my interest is nowbased more on an appreciation of modern gauge theory (easily the mostprofound and beautiful concept of physics), I credit Weyl for havinginitiated the idea in 1918 and for his subsequent (1929) seminalapplication of the idea to the then still-developing quantum theory. In his 2002biographical memoirs, the great contemporary mathematician Sir MichaelF. Atiyah praised Weyl as the discoverer of the gauge concept and asthe driving force behind the current emphasis of gaugetheories on modern theoretical physics: The past 25 yearshave seen the rise of gauge theories--Kaluza-Klein models of highdimensions, string theories, and now M-theory, as physicists grapplewith the challenge of combining all the basic forces of nature into oneall embracing theory. This requires sophisticated mathematics involvingLie groups, manifolds, differential operators, all of which are part ofWeyl's inheritance. There is no doubt that he would have been anenthusiastic supporter and admirer of this fusion of mathematics andphysics.No othermathematician could claim to have initiated more of the theories thatare now being explored. His vision has stood the test of time. Weylwas an exceptionally gifted mathematician and physicist, but he wasalso a highly cultured man in the classical German tradition. Hestudied and wrote extensively on philosophy and was a serious studentof German poetry and literature. His mathematical writing style couldbe exceedingly obtuse, but his other writings reveal a genuinely warmperson who truly understood the human condition. Weyl was also veryhuman himself; he could be overlythoughtful and cautious, often to the point of being unable to takeaction or make even basic decisions, and sometimes with the result thathe became physically incapacitated. He was a devoted and loving husbandand father, yet he could also be persuaded to stray, in accordance withthe surprisingly liberal attitudes of post-World War I Weimarsociety. Thiswebsite is my feeble attempt to document (and in many cases expand on)Weyl's ideas and thoughts ongauge symmetry in a manner that will be accessible to anyone with abasic understanding of calculus. Not a lot has been written about theoriginal theory's underlying mathematics, and I wanted to provide afairly detailed and complete mathematical description for those whowant to learn about Weyl's ideas and to appreciate the beauty of hisgauge theory (I'm even of the opinion that much of Weyl's work can beunderstood and appreciated at the high school/beginning universitylevel). As this site progresses, I will also include discussionsof other topics in mathematical physics (as well as some relatedscientific philosophy) which exhibit a similar mathematical beauty andelegance. Note: I no longer postto this site. See AfterMathfor what I'm doing now.

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