Einstein's Revenge: The New Geometric Quantum (Edge Essay): Difference between revisions

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 To set the stage, recall that fundamental physics can be divided into two sectors with separate but maddeningly incompatible advantages. The gravitational force has, since Einstein's theory of general relativity, been admired for its four dimensional geometric elegance. The quantum, on the other hand encompasses the remaining phenomena, and is lauded instead for its unparalleled precision, and infinite dimensional analytic depth.
-The story of the geometric quantum begins at some point around 1973-1974, when our consensus picture of fundamental particle theory stopped advancing. This stasis, known as the 'Standard Model', seemed initially like little more than a temporary resting spot on the relentless path towards progress in fundamental physics, and theorists of the era wasted little time proposing new theories in the expectation that they would be quickly confirmed by experimentalists looking for novel phenomena. But that expected entry into the promised land of new physics turned into a 40-year period of half-mad tribal wandering in an arid desert, all but devoid of new phenomena.
+The story of the geometric quantum begins at some point around 1973-1974, when our consensus picture of fundamental particle theory stopped advancing. This stasis, known as the [[Standard Model|'Standard Model']], seemed initially like little more than a temporary resting spot on the relentless path towards progress in fundamental physics, and theorists of the era wasted little time proposing new theories in the expectation that they would be quickly confirmed by experimentalists looking for novel phenomena. But that expected entry into the promised land of new physics turned into a 40-year period of half-mad tribal wandering in an arid desert, all but devoid of new phenomena.
-Yet just as particle theory was failing to advance in the mid 1970s, something amazing was quietly happening over lunch at the State University of New York at Stony Brook. There, Nobel physics laureate CN Yang and geometer (and soon to billionaire) Jim Simons had started an informal seminar to understand what, if anything, modern geometry had to do with quantum field theory. The shocking discovery that emerged from these talks was that both geometers and quantum theorists had independently gotten hold of different collections of insights into a common structure that each group had independently discovered for themselves. A Rosetta stone of sorts called the Wu-Yang dictionary was quickly assembled by the physicists, and Isadore Singer of MIT took these results from Stony Brook to his collaborator Michael Atiyah in Oxford where their research with Nigel Hitchin began a geometric renaissance in physics inspired geometry that continues to this day.
+Yet just as particle theory was failing to advance in the mid 1970s, something amazing was quietly happening over lunch at the State University of New York at Stony Brook. There, Nobel physics laureate [[CN Yang]] and geometer (and soon to billionaire) [[Jim Simons]] had started an informal seminar to understand what, if anything, modern geometry had to do with quantum field theory. The shocking discovery that emerged from these talks was that both geometers and quantum theorists had independently gotten hold of different collections of insights into a common structure that each group had independently discovered for themselves. A Rosetta stone of sorts called the [[Wu-Yang Dictionary|Wu-Yang dictionary]] was quickly assembled by the physicists, and [[Isadore Singer]] of MIT took these results from Stony Brook to his collaborator [[Michael Atiyah]] in Oxford where their research with Nigel Hitchin began a geometric renaissance in physics inspired geometry that continues to this day.
 While the Stony Brook history may be less discussed by some of today's younger mathematicians and physicists, it is not a point of contention between the various members of the community. The more controversial part of this story, however, is that a hoped for golden era of theoretical physics did not emerge in the aftermath to produce a new consensus theory of elementary particles. Instead the interaction highlighted the strange idea that, just possibly, Quantum theory was actually a natural and elegant self-assembling body of pure geometry that had fallen into an abysmal state of pedagogy putting it beyond mathematical recognition. By this reasoning, the mathematical basket case of quantum field theory was able to cling to life and survive numerous near death experiences in its confrontations with mathematical rigor only because it was being underpinned by a natural infinite dimensional geometry, which is to this day still only partially understood.