The appearance here of threads such as(adsbygoogle = window.adsbygoogle || []).push({}); Causes of loss of interest in the String programandIs string theory really science?are for me a symptom of the frustration of modern physicists struggling to formulate in a predictive way the concept of elementary objects that are geometrically linear, rather than old-style points.

A century ago, when Einstein was engaged in his struggle to formulate his new concept: gravity as a distortion of simple Euclidian spacetime, his frustration became relieved by learning about tensors, a recent geometrical invention of the mathematicians Tullio Levi-Civita and Gregorio Ricci-Curbastro. Modern physics owes a great deal to these 19th Century Italians. Here I’d like to suggest that we might yet come to owe even more to like folk.

Einstein singled out one kind of distortion of Euclidian geometry; that described in the 19th century by Bernhard Riemann. I’m guessing here that this step opened the door, as it were, to other kinds geometrical distortions being used to help describe yet more fundamental stuff, as string theory seems to be struggling to do.

It’s not clear to me whether today’s string theorists are aware of another Italian

mathematician’s work and its extensive later 20th century ramifications, which have to do with the physics of crystals. Like Luigi Bianchi,Vito Volterrawas a student of the 19th Century differential geometer and topologist Enrico Betti. Volterra described stringy topological defects in continuous elastic media –calleddistorsioni; later dislocations and disclinations. In the 20th Century these stringy line defects were applied to explain much of practical importance in real crystalline materials. There’s a huge literature about this; see for example F.R.N. Nabarro, Theory of Crystal Dislocations, OUP, 1967.

From my level of (great) ignorance I’d be interested to know whether Volterra’s work has had, or could have, any utility in string theory. Einstein is surely a good act to follow!

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# Line defects and String Theory

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