The aim of this chapter is to introduce the general ideas on which this book is based and to present the picture of quantum spacetime that emerges from loop quantum gravity, in a heuristic and intuitive manner. The style of the chapter is therefore conversational, with little regard for precision and completeness. In the course of the book the ideas and notions introduced here will be made precise, and the claims will be justified and formally derived.
The problem of quantum gravity
Quantum mechanics (QM) and general relativity (GR) have greatly widened our understanding of the physical world. A large part of the physics of the last century has been a triumphant march of exploration of new worlds opened up by these two theories. QM led to atomic physics, nuclear physics, particle physics, condensed matter physics, semiconductors, lasers, computers, quantum optics … GR led to relativistic astrophysics, cosmology, GPS technology … and is today leading us, hopefully, towards gravitational wave astronomy.
But QM and GR have destroyed the coherent picture of the world provided by prerelativistic classical physics: each was formulated in terms of assumptions contradicted by the other theory. QM was formulated using an external time variable (the t of the Schrödinger equation) or a fixed, nondynamical background spacetime (the spacetime on which quantum field theory is defined). But this external time variable and this fixed background spacetime are incompatible with GR. In turn, GR was formulated in terms of riemannian geometry, assuming that the metric is a smooth and deterministic dynamical field.