Issues

1. Issues • General Relativity is incomplete. Cannot handle singularities yet develops these from smooth initial conditions. The Big Bang; the explosive end of black hole evaporating by Hawking radiation Quantum effects are expected to become important in these extreme circumstances, but traditional quantization fails when applied to gravity This cannot be the whole story

2. String Theory • String theory is (sort of) what you get if you imagine that instead of particles (electrons, quarks, etc) the fundamental building blocks in the world are strings • Strings can vibrate!

3. One string can, by being excited to various vibration states account for many particles • Strings interact by splitting and joining which looks like particle interactions • Can be open or closed Of course, electrons look a lot like particles and not at all like strings That is because strings are small of order 10-33 cm So if we can’t see them, why should we care?

4. What’s the Point? • In a string theory, various particles are not just posited with the properties we find in nature. All observed particles come from the same string! Properties of the particle follow from the vibrational state. • A particularly important one is our friend • Because quantum string theory is well-behaved, strings provide a consistent quantum theory of gravity The particle this describes has mass zero and spin 2 and has not been seen It is, however, thought to exist and is the carrier of gravitational force – the graviton

5. Singularities Tamed • Near singularities the difference between strings and particles becomes meaningful. Strings “wrapping” the singularity are not like any particle states. • Some singular spaces lead to reasonable string dynamics

6. Extra Dimensions • String theories suggest 10 spacetime dimensions. We see 4. • This is a theory of gravity, which means it describes the shape of space. So can imagine the “extra” dimensions are too small to be seen or measured

7. T-Duality • Strings can wind around extra dimensions as well as move there. • Winding modes have energy (mass) of order R • T-dualityexchanges winding and momentum modes, showing that in string theory a radius of R and of 1/R are the same! Relates different types of strings • Size of space indeterminate For more general Calabi-Yau shapes T-duality (mirror symmetry) relates spaces that are topologically different yet lead to identical string theories Topology of space indeterminate

8. D-branes • Strings are not the end of the story. As relativity predicts black holes, string theory predicts black branes • Excitations of brane can be described by open strings ending on the brane • D-branes are dynamical objects and interact with the closed string states • D-branes “wrapping” the singularity “tame” singularities that strings cannot.

9. Brane Worlds • D-branes offer a new way to reconcile the extra dimensions: If all the matter we measure is made of open string excitations of a D-3 brane then we live in 4 dimensions, interact with the “bulk” only through gravitation. • Space as we know it may be only a slice of the universe

10. Conclusions • String theory, while not yet a theory, has given us many new ideas about spacetime • There is reason to believe that when it becomes a theory, spacetime will not be an input but an emergent feature, its properties at every level determined by the dynamics • There is a lot yet to understand!