Duality(redirected from dualities)
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The state of having two natures, which is often applied in physics. The classic example is wave-particle duality. The elementary constituents of nature—electrons, quarks, photons, gravitons, and so on—behave in some respects like particles and in others like waves.
Duality is often used in a more precise sense. It indicates that two seemingly different, theoretical descriptions of a physical system are actually mathematically equivalent. Such an occurrence is very useful. Various properties and phenomena are clearer in one or the other of the descriptions, and calculations that are difficult or impossible in one description may be simple in the other. In the case of wave-particle duality, the wave description corresponds to a theory of quantized fields, where the field variables are governed by an uncertainty principle. The particle description corresponds to a Feynman integral over all particle paths in spacetime. The quantized-field and path integral theories sound very different but are mathematically equivalent, making identical predictions. See Feynman integral, Quantum field theory, Quantum mechanics, Uncertainty principle, Wave mechanics
In some systems, there is weak-strong duality, meaning that when the coupling constant g of the original description is large that of the dual description, g′, is small; for example g′ = 1/g. When g is large, so the interactions in the original description are strong and the perturbation theory in this description is highly inaccurate, then perturbation theory in the dual description gives a very accurate description.
Duality in superstring theory
It is believed that a complete theory of all particles and interactions must be based on quantization of one-dimensional objects (loops) rather than points: this is superstring theory. In superstring theory there is again the problem that perturbation theory is the main tool, giving an incomplete description of the physics. The situation has greatly improved with the discovery that weak-strong duality is a general property of string theory. In fact, there are five known string theories, and all are dual to one another. A notable feature in string theory is that in addition to strings and solitons, duality requires certain other objects as well: D-branes, which are local disturbances to which strings become fixed. Remarkably, the same methods have also been used to solve some long-standing problems regarding the quantum mechanics of black holes. See Quantum gravitation;, Superstring theory