Ivancevic_Applied-Diff-Geom

32 Applied Differential Geometry: A Modern Introductionone man.Feynman’s story is very different. All his life he was a profoundly originalscientist, similar to the young Einstein. He refused to take anybody’sword for anything, which meant that he had to reinvent for himself almostthe whole of physics. It took him five years of concentrated work to reinventquantum mechanics. At the end, he got a new version of quantummechanics that he (and only he) could understand. In orthodox physics itwas said: Suppose an electron is in this state at a certain time, then youcalculate its future behavior by solving Schrodinger equation. Instead ofthis, Feynman said simply: “The electron does whatever it likes.” A historyof the electron is any possible path in space and time. The behaviorof the electron is just the result of adding together all histories accordingto some simple rules that Feynman worked out. His path–integral andrelated Feynman diagrams, for long defied rigorous mathematical foundation.However, it is still the most powerful calculation tool in quantum(and statistical) mechanics. Later, Feynman generalized it to encompassphysical fields – which led to his version of quantum electrodynamics (thefirst prototype of a quantum field theory) – and his Nobel Prize. All hiscareer he consistently distrusted official mathematics and invented his ownmaths underpinned with a direct physical intuition.If the story had ended here, we might have said that visual physicalintuition is leading the way of science. However, the story does not end here.The leading authority in contemporary physics is Ed Witten, a physicistwho did not get the Nobel Prize, but rather the Fields Medal – togetherwith his ‘superstring theory of everything’. 45 Witten works at the sameplace where Einstein spent the last 30 years of his life – at the PrincetonInstitute of Advanced Study. He is dreaming Einstein’s dream: a unifiedtheory of everything, using the most powerful maths possible. His prophecy,delivered at a turn of the Century, has been: “In the 21 fist Century,mathematics will be dominated by string theory.”When superstring theory arrived in physics in 1984 as a potential theoryof the universe, it was considered by mainstream physicists as littlebetter than religion in terms of constituting a viable, testable theory. Instring theory, the fundamental particles were string–like, rather than pointparticles; the universe had 10 or 11 dimensions, rather than four; and theTheir joined work on gravity is called the Einstein–Hilbert action.45 Witten joined the ‘old Green–Schwarz bosonic string community’ after he won hisFields Medal for topological quantum field theory (TQFT)