2 Quantum Gravity: Where are We? 

This is a non-technical section in which I illustrate the problem of quantum gravity in general, its origin, its importance, and the present state of our knowledge in this regard.

The problem of describing the quantum regime of the gravitational field is still open. There are tentative theories, and competing research directions. For an overview, see [121]. The two largest research programs are string theory and loop quantum gravity. But several other directions are being explored, such as twistor theory [154], noncommutative geometry [68], simplicial quantum gravity [6, 65, 61, 1], Euclidean quantum gravity [104, 107], the Null Surface Formulation [85, 86, 87] and others.

String theory and loop quantum gravity differ not only because they explore distinct physical hypotheses, but also because they are expressions of two separate communities of scientists, scientists who have sharply distinct prejudices, and who view the problem of quantum gravity in surprisingly different manners.

• 2.1 What is the problem? The view of a high energy physicist
• 2.2 What is the problem? The view of a relativist
• 2.3 Strings or loops?

Loop Quantum Gravity Carlo Rovelli http://www.livingreviews.org/lrr-1998-1 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de