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Transcript

Relativity + Quantum + Gravity • These three concepts are the basis of physics. • They contain the three fundamental constants c,ħ,G , which form a complete system of units. • Are these concepts compatible with each other? - Relativity and gravity (= general relativity) are designed to be compatible. - Relativity and quantum physics are made compatible by quantum field theory. - Quantum physics and gravity are incompatible when trying it with quantum field theory. The weakness of gravity String theory A quantum theory of gravity: Various attempts to combine gravity and quantum physics failed . Gravity is very different from the other three forces. It is much weaker, and its boson has spin 2. Ed Witten, string guru Infinities pose a mathematical problem: Point-like particles create mathematical problems when two particles meet. The forces become infinite. This problem is avoided in string theory by stretching a point out into a tiny loop, a string. Feynman diagrams in string theory point Time (c t) string Space (x) • World lines become tubes in string theory. • They connect smoothly. • That avoids dealing with infinitely small points. What happens at the smallest conceivable length ? Quantum physics meets gravity at the Planck length. The uncertainty relation makes space itself uncertain. String theorists view space as a collection of vibrating strings. Brian Greene: “The elegant Universe” Strings on Nova Strings can vibrate in many ways A single string can explain a whole zoo of particles : Different vibration frequencies f Different energy quanta (Planck’s E = hf ) Different particle masses (Einstein’s E = m c2) Results of string theory • A string can produce a boson with spin 2. That’s what one needs for the graviton, the boson that mediates gravity (analogous to the photon in electromagnetism). • So string theory produces a quantum theory of gravity. • This is our best attempt to make gravity compatible with quantum physics without getting into trouble with infinities. Extra dimensions • String theory requires 10-dimensional space-time for mathematical reasons. • How do we get from 10 dimensions down to our fourdimensional space-time ? • Two proposals: A) Make the extra dimensions tiny by folding them tightly down to the Planck length. B) Make the extra dimensions large and restrict our space-time to a 4-dimensonal surface (membrane) of a higher-dimensional bulk region. Small extra dimensions A huge number of different folding options. Which one ? Large extra dimensions Gravity is so weak, because it lives on a different membrane (= brane) and gets diluted by connecting with us across the 5-dimensional bulk. (Physics Today, July 2007, p. 80)