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 com- patible 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. 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. Ed Witten, string guru

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 = h f ) 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 four- dimensional 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 Our 4-dimensional space-time 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) Gravity