Carlo Rovelli

Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

If there is a ‘platonic world’ \ of mathematical facts, what does \ contain precisely? I observe that if \ is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it is not independent of us. Both alternatives challenge mathematical platonism. I suggest that the universality of our mathematics may be a prejudice and illustrate contingent aspects of classical geometry, arithmetic and linear algebra, making the case that what we call “mathematics” is always contingent.

Without addressing the measurement problem (i. e., what causes the wave function to “collapse,” or to ”branch,” or a history to become realized, or a property to actualize), I discuss the problem of the timing of the quantum measurement: Assuming that in an appropriate sense a measurement happens, when precisely does it happen? This question can be posed within most interpretations of quantum mechanics. By introducing the operator M, which measures whether or not the quantum measurement has happened, I suggest that, contrary to what is often claimed, quantum mechanics does provide a precise answer to this question, although a somewhat surprising one

We observe entropy decrease towards the past. Does this imply that in the past the world was in a non-generic microstate? I point out an alternative. The subsystem to which we belong interacts with the universe via a relatively small number of quantities, which define a coarse graining. Entropy happens to depends on coarse-graining. Therefore the entropy we ascribe to the universe depends on the peculiar coupling between us and the rest of the universe. Low past entropy may be due to the fact that this coupling is non-generic. I argue that for any generic microstate of a sufficiently rich system there are always special subsystems defining a coarse graining for which the entropy of the rest is low in one time direction. These are the subsystems allowing creatures that “live in time” —such as those in the biosphere— to exist. I reply to some objections raised to an earlier presentation of this idea, in particular by Bob Wald, David Albert and Jim Hartle.

All human civilizations have thought that the world was made of sky above and the Earth below. All except one. For the Greeks, the Earth was a rock floating in space, and under the earth there was no ground, no turtles, nor the gigantic columns of which the Bible speaks. How did the Greeks understand that the Earth is suspended in nothingness? Who understood this and how? It is this unique "scientific revolution" of Anaximander of which the author speaks, which Karl Popper called "one of the most daring ideas, revolutionary and portentous in the entire history of human thought" The concern is with the conflict that was opened, still burning, with the nature of scientific thought, its critical and rebellious character, the force with which it subverts the order of things and our image of the world of scientific knowledge, and the highly effective "error" at the same time --as we teach physics in the twentieth century. Speaking of Anaximander, the author invites us to reflect on what his ideas mean to the scientific revolution opened by Einstein.

Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role at all. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must “forget time”, and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time

The term ‘locality’ is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum non-locality. The present article shows that the failure of ‘locality’ in the sense of Bell, once interpreted in the relational framework, reduces to the existence of a common cause in an indeterministic context. In particular, there is no need to appeal to a mysterious space-like influence to understand it.