Number. To Whom It May Concern: This Lett.: Fill & Download for Free

“When food gets scarce, table manners change.” —R.A.Heinlein (from memory, certainly not perfect, TH)A2A: Various people have various thoughts about any particular topic—and the topic of string theory is no different. (See Christian Santangelo's answer) The area of study itself is not controversial, but whether it belongs to physics is oft contested and disputed.For my own part, I have not myself experienced any animosity. That may well be owing to my statistically limited number of physicists with whom I interact and who bother writing to me unsolicited, “out of the blue.” It may also be because I am not really a string theory “specialist” but a mathematical physicists whose main topics of research (Calabi-Yau, i.e., Ricci-flat manifolds, and supersymmetry) are most closely related to string theory.Most of the controversy about the “physicity” (?) of string theory owes to several implicit equivocations (in no particular order, and with no delusions of being exhaustive):String theory does have physically testable predictions: see my answer to “Does string theory make any predictions that can be tested empirically? Is string theory falsifiable? Does it have to be falsifiable? If it's not falsifiable, can it be considered a scientific theory?”.=> Let me mention one here: Einstein’s equations (and Yang-Mills, and Maxwell’s) are only the 1st order perturbative result in string theory. The 2nd + higher order corrections and the induced corrections to any and all predictions of Einstein’s general relativity and the Standard Model are then all the supposedly elusive testable predictions —and, they are all universal for all string theory models. Of course, those corrections are so hilariously tiny that we may have to wait another century for them to be detected. But, if one was happy to accept gravitational wave chirps (on point of principle) as a testable prediction of Einstein’s general relativity for about a century before they were actually measurable, why not accept the universal corrections to Einstein’s gravity as such a testable prediction? (Yes, I know that other predictions were much faster to be detected; recall however that if it had turned out that gravity did not chirp, Einstein’s general relativity would have been disproven!)String theory is a misnomer. It necessarily (for logical consistency!) involves not only strings but also so-called “ ’branes,” — which are objects which intrinsically extend in several spatial dimensions: 0-branes are point-particles, 1-branes are strings, 2-branes are membranes, etc. This includes “M-theory” and “F-theory.”String theory is not a concrete model (of our Universe and everything in it, as would befit a “Theory of Everything”), but a theoretical (axiomatic) system = a framework of building logically consistent quantum physics models that include gravity. It contains classical mechanics, classical field theory, quantum mechanics, quantum field theory… as suitable limits!Let me rephrase that: all of fundamental physics is built into various “corners” of string theory. String theory may then be seen as a logically consistent unification of all fundamental physics—wherein the various “pieces” are not forcibly squelched together, but dove-tail in a logically consistent and coherent manner.Most physicists will agree that physics is a pragmatic science. Well-nigh no physicist will be content with physics as a haphazard hogde-podge patchwork of capriciously connected models. Most physicists desire a unified, coherent, logically consistent and fully comprehensive understanding of Nature — but focus, perforce, on various particular aspects, levels, perspectives… “When eating an elephant, take a bite at a time.”String theory also involves a respective analysis of how physics models are (to be) built in the first place. In this respect, string theory is also akin to what metamathematics is to mathematics. BTW, “metaphysics” already means something else…Now, for a “foundational” understanding of how all of physics fits together, the achievement of unifying “quantum” and “gravity” in a single, logically consistent theoretical (axiomatic) system is of paramount importance. But, not only is this unified coexistence of “quantum” and “gravity” what string theory can achieve, it is in fact a logical necessity! See #1 in my answer to “Does string theory make any predictions that can be tested empirically? Is string theory falsifiable? Does it have to be falsifiable? If it's not falsifiable, can it be considered a scientific theory?”. To me, this alone is sufficient to “admit” string theory into physics (the science of understanding Nature, φὐσις).Some physicists regard irrelevant or insignificant this foundational prediction of unity (and codependence) of two very real sets of natural phenomena. I shan’t paraphrase David Mermin, whose article “Is the Moon There When Nobody Looks? Reality and the Quantum Theory,” [Physics Today (Apr 1985), 38–47] voices the contention that “physicists who are not bothered by Bell’s theorem and its implications have rocks in their heads.” After all, we cannot all be concerned about the same questions with equal ardor; I’ll agree with Christian Santangelo’s conclusion “to each their own.”Curiousestly, string theory has also been teaching us about other things, such as non-pertubative aspects of QCD (the theory of strong interactions, perhaps not too surprising, as that was where string theory was born), condensed matter physics, as well as other, seemingly unrelated fields in physics. …and also in mathematics, to mention but “mirror symmetry,” see here and here.Especially about those latter mathematical achievements — and to connect with the starting quote — let me repeat that I am a “mathematical physicists.” Which is a person whose research is in the “seven years of riches” easily funded from both physics and mathematics sources; in the “seven lean years,” both agencies send you to the other side.Not surprisingly, one of the unifying themes in attacks on string theory is that it is absorbs too much of the (steadily diminishing) physics funding and resources.Perhaps the introductory chapters of Advanced Concepts in Particle and Field Theory might be of interest?One of the criticisms of string theory, as voiced by John Schlesinger in the comments, is its lack of background independence. OK. Fair ’nuff. Sorta. Which is why in the 3rd bullet above I did not advertise string theory as being background-independent. It nevertheless is a framework wherein quantum stability of the 2D QFT produces (to lowest order, perturbatively, and so by definition depending on the background about which one is perturbing) the equations of motion of Einstein's general relativity and Yang-Mills theory [1].(BTW, from the background independence Wikipedia page says: “Manifest background independence is primarily an aesthetic rather than a physical requirement.” Ahem. So string theory is ugly. Fine. :-PMost of any work done within and related to string theory is not unlike computing a geometric characteristic (say the holonomy group) of a manifold at a particular point, and then tracing how the result depends (or doesn’t) on the choices made in the computation. This is of course not a foundational definition of the object being computed, although it does demonstrate that such an object exists.Attempts to understand string theory non-perturbatively do indicate avenues to unearthing such foundation, but seem to remain unexplored to the best of my knowledge. My personal favorite is geometric quantization of strings, where generalized Ricci-flatness of the loop-space (the configuration space of closed strings) is proposed to be the “equation of motion of closed string theory” [2,3,4]; see Refs. [5,6,7] for the superstring version. Since Ricci-flatness is also the geometric content of Einstein equations when [math]T_{\mu\nu}=0[/math], this condition on the loop-space seems extremely natural, and conceptually reproduces general relativity in the point-limit… Now add open strings, and ’branes…[1] D. Friedan: “Nonlinear Sigma Models in 2+ε Dimensions,” Phys. Rev. Lett. 45 (1980) 1057; expanded in “Nonlinear models in 2+ε dimensions,” Ann. Phys. 163 (1985) 318–419.[2] I.B. Frenkel, H. Garland and G.J. Zuckerman: “Semi-Infinite Cohomology and String Theory.” Proc. Natl. Acad. Sci. USA 83 (1986) 8442.[3] M. J. Bowick and S. G. Rajeev, “String Theory as the Kahler Geometry of Loop Space,” Phys. Rev. Lett. 58 (1987) 535.[4] L. Alvarez-Gaumé, C. Gomez and C. Reina: “Loop Groups, Grassmannians and String Theory.” Phys. Lett. 190B (1987) 55.[5] K. Pilch and N.P. Warner: “Holomorphic Structure of Superstring Vacua.” Class. Quant. Grav. 4 (1987) 1183.[6] P. Oh and P. Ramond: “Curvature of Super-[math]\text{Diff}\,S^1/S^1[/math].” Phys. Lett. 195B (1987) 130.[7] D. Harari, D.K. Hong, P. Ramond and V.G.J. Rogers: “The Superstring, [math]\text{Diff}\,S^1/S^1[/math] and Holomorphic Geometry.” Nucl. Phys. B294 (1987) 556.