Juan Maldacena

"It has been a long-standing challege for to construct a theory of quantum gravity. String theory is the leading candidate for a quantum theory of gravity. General Relativity has the seeds of its own destruction in it, since smooth can evolve into singular field configurations ... Classically this is not a problem if the singularities are hidden behind s ... since this means that nothing can come out from the region containing the singularity. However, Hawking showed, under very general assumptions, that quantum mechanics implies that black holes emit particles ... In his approximation this radiation is exactly thermal and contains no information about the state of the black hole. This leads to the , since particles can fall in carrying information but what comes out is featureless thermal radiation ... Hawking argued that this would lead to non-unitary evolution, so that one of the basic principles of quantum mechanics would have to be modified."

"In most situations, the contradictory requirements of quantum mechanics and general relativity are not a problem, because either the quantum effects or the gravitational effects are so small that they can be neglected or dealt with by approximations. When the of spacetime is very large, however, the quantum aspects of gravity become significant. It takes a very large or a great concentration of mass to produce much spacetime curvature. Even the curvature produced near the sun is exceedingly small compared with the amount needed for quantum gravity effects to become apparent. Though these effects are completely negligible now, they were very important in the beginning of the big bang, which is why a quantum theory of gravity is needed to describe how the big bang started. Such a theory is also important for understanding what happens at the center of black holes, because matter there is crushed into a region of extremely high curvature. Because gravity involves spacetime curvature, a quantum gravity theory will also be a theory of quantum spacetime ..."

"These of are very powerful. Let us recall the situation in flat space. If we have a massive in flat space then we can always boost to a . In AdS it is the same: if we consider the oscillating trajectory of a massive particle then we can "boost" to a frame where the particle is at rest. Thus, the moving particle does not know that is moving and, despite appearances, there is no "center" in AdS. The is part of the (as in the ) and there are several choices of Hamiltonian. Once we choose a Hamiltonian ... then we have chosen a "center" and a notion of the , in which a particle sits at this "center.""

"Interestingly, both quantum entanglement and s date back to two articles written by Albert Einstein and his collaborators in 1935. On the surface, the papers seem to deal with very different phenomena, and Einstein probably never suspected that there could be a connection between them. In fact, entanglement was a property of quantum mechanics that greatly bothered the German physicist, who called it How ironic that it now may offer a to extend his relativity theory to the quantum realm."

"... spacetime as a concept leads to some … where the equations fail. This happens in the interiors of the black holes when spacetime somehow collapses ... And, also, most importantly it happened in the beginning of the Big Bang."