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"Twistor" Theory Reignites the Latest Superstring Revolution

In the late 1960s the renowned University of Oxford physicist and mathematician Roger Penrose came up with a radically new way to develop a unified theory of physics. Instead of seeking to explain how particles move and interact within space and time, he proposed that space and time themselves are secondary constructs that emerge out of a deeper level of reality. But his so-called twistor theory never caught on, and conceptual problems stymied its few proponents. Like so many other attempts to unify physics, twistors were left for dead.
In October 2003 Penrose dropped by the Institute for Advanced Study in Princeton, N.J., to visit Edward Witten, the doyen of today's leading approach to unification, string theory. Expecting Witten to chastise him for having criticised string theory as a fad, Penrose was surprised to find that Witten wanted to talk about his forgotten brainchild.

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In a recent study, mathematician George Sparling of the University of Pittsburgh examines a fundamental question pondered since the time of Pythagoras, and still vexing scientists today: what is the nature of space and time? After analysing different perspectives, Sparling offers an alternative idea: space-time may have six dimensions, with the extra two being time-like.

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Title: Spacetime is spinorial; new dimensions are timelike
Authors: George A.J. Sparling

A new theory of fundamental physics is presented; it predicts that the new dimensions that may be observed by the Large Hadron Collider are timelike.

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Twistor theory has been developed by Roger Penrose and his associates since the 1960s. He realised that using the space-time continuum picture to describe physical processes is inadequate not only at the Planck scale of 10-33 cm but also at the much larger scales of elementary particles, or perhaps atoms, where the quantum effects become important. He believes that space-time is created out of quantum processes themselves at the subatomic level. The mathematical tool in field theories is not suitable for the new formulation since the field equations are based on well-behaved functions varying smoothly in space-time. Thus his mathematical tool is geometry instead of differential equations. However, space-time descriptions of the normal kind have been used at the atomic or particle level for long time with extraordinary accuracy. Thus, this new geometrical picture must, at that level, be mathematically equivalent to the normal space-time picture - in the sense that some kind of mathematical transformation must exist between the two pictures.

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Title: Perturbative Gauge Theory As A String Theory In Twistor Space
Author: Edward Witten

Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of cal N=4 super Yang-Mills theory and the D-instanton expansion of a certain string theory, namely the topological B model whose target space is the Calabi-Yau supermanifold CP3|4.

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