Ten years of general relativity, some reflections

Carlo Rovelli, Centre de Physique Theorique, Marseille carlo@rovelli.org

Ten years of Matters of Gravity (thanks a lot, Jorge!), ten years of research in general relativity. It has been a period of triumph for GR: We have seen evidence for gravitational emission from binary pulsars, with theory and observations matching with a level of accuracy previously found only in quantum field theory. We have been enchanted by the gravitational lensing images. Black holes have moved from exotic theoretical hypothesis to realistic objects in the sky. Last month, I got lost in a trip, and could trace my way back thanks to a small electronic device that wouldn't work without taking GR's corrections into account. Particle physicists, that not long ago kind of looked down at GR, nowadays use Einstein's space-times in every other paper. Observational cosmology has exploded, relativistic astrophysics is solidly established; the problem of quantizing the theory is now recognized as perhaps the main problem in theoretical physics, and the papers devoted to it keep growing. Large resources are being invested internationally in the search for gravitational waves and computational GR ... The list of successes could continue. How long a road from the sleepy and a bit esoteric GR community, when black holes were badly understood exotic theoretical hypotheses, the only experimental support came from the three ``classic tests" and the rest of physics looked at us with suspicion, if it payed any attention at all. It has been a breathtaking decade.

Many problems remain open, and so much remains to be done. And there are also some dangers ahead. We are all holding our breath waiting for the gravitational waves. We are solidly beyond our colleagues involved in this adventure and we are optimistic, but also a bit concerned: the community has taken some risks with this search, and if it took too long, it wont be good for all of us. Great efforts are been put in computational GR. Again, let's hope for the better, but we should keep in mind the experience with computational lattice QCD, where great skills and money were expended, and great hopes raised, with far less results than hoped for. Excitement is high in my own field, loop quantum gravity, where the feeling is that perhaps we are having true glimpses into the quantum structure of spacetime. But let us not forget how many tentative quantum theories of gravity have claimed victory and then were proven unsatisfactory.

The worst danger, I think, is that theoretical physics, and sometimes even experimental physics, is nowadays often so far removed from the actual final experimental outcome (the only final arbiter), that the temptation is dangerously high to keep selling for good whatever we have. I am afraid that some portion of physics have moved down this dangerous path. But success, I think, can only be granted by scrupulous intellectual honesty. The high respect and the credibility that science enjoys rely on the intellectual honesty of the scientists. Several people now begin to suspect that something has got wrong on this in the last decade. At a recent conference I had a conversation with a brilliant young researcher. In the conversation, two theories were mentioned: GR and some particular supersymmetric theory in high dimension. Casually, I said that at least we knew that one of the two was experimentally supported. My young friend asked which one. I thought he was joking, but he was not. In his mind there was absolutely no understanding of the distinction between a theory whose novel peculiar predictions have found a huge wealth of empirical support, and a complex theoretical hypothesis that for the moment has no empirical support whatever.

The distinction between what we have learned about the world on the one hand, and our attempts to understand more on the other hand, is the rock over which science bases its strength. I am afraid that this distinction is becoming a bit obfuscated in some areas of theoretical physics, and hypotheses are too often sold for facts. This may increase funding, positions and political power in the short run, but it is a recipe for disaster in the long run. I think that the theoretical physics community should seriously react against this attitude, which is endangering its own position in the world. I have heard many scientists repeating this privately in the corridors of the conferences. Perhaps they should say it more vocally and more publicly.

As a result of the successes of GR (and also of the overwhelming and unexpected empirical success of the particle physics standard model), the relation between the GR community and the rest of physics has much changed in this decade. Ten years ago, the divide between the GR community and the rest of theoretical physics was sharp. Outside our small community, spacetime was unquestionably flat and non dynamical. Today, some basic ideas of GR pervade large parts of theoretical research. GR is being finally universally accepted as a component of our present understanding of the world.

But, as we know well, GR is much more than a theory of gravity, namely much more than the specific theory for a specific physical interaction. It is a rethinking of the notions of space and time, which involves the entirety of our understanding of the world. In my opinion, the deepness and the richness of the shift in perspective produced by GR is far from being fully understood and fully absorbed. GR does not claim only that spacetime is curved and satisfies certain equations. Rather the most far reaching physical consequence of the theory, which follows from the invariance properties of its equations, is the discovery that no physical meaning can be attached to the coordinates, and physical localization can therefore only be defined relationally. Dynamical objects are physically localized only with respect to each others. This is a huge conceptual jump out of Newtonianism, which brings our understanding of spacetime back to Cartesian (and Aristotelian) relational notions of space. The Newtonian localization with respect to space (that allows Newton to define acceleration as absolute) is reinterpreted in GR as localization with respect to a particular dynamical object: the gravitational field.

In my opinion, Einstein's discovery that the gravitational field and the spacetime metric are the same entity, is not well expressed by saying that there is no gravitational field, just a curved spacetime. Rather, it is better expressed by saying that there is no spacetime, just the gravitational field. The gravitational field is, dynamically, a field like the others. But the fields do not live over a spacetime, they leave, so to say, over each other.

I think that this profound change of perspective on the world, has not yet been completely absorbed. The hardest part to digest is not the relational nature of space; it is the relational nature of time. To this, many instinctively resist. Giving up the idea of an external flowing time along which things happen is hard, as it was hard giving up the idea of the center of the universe, or the idea of absolute rest. I am convinced that this change of perspective reflects a deeper understanding of the physical structure of the world and will stay with us for a while in the physics of the future.

But while the Einstein equations are being widely used in fundamental physics, this conceptual revolution is still little understood. World famous theoreticians still search the fundamental theory over a background Minkowski spacetime (perhaps in high dimensions). In my opinion, they have not understood what we have learned about the world with GR.

Large sectors of basic physics still expect to be thought again from scratch at the light of this conceptual revolution. Classical Hamiltonian mechanics has proven flexible enough to consistently extend to general covariant physics (where there is no canonical time and no Hamiltonian). But thermodynamics and statistical mechanics still wait to find a formulation sufficiently general to take the GR revolution into account. And of course, so does quantum theory. In the XXth century, quantum theory and general relativity have changed in depth our understanding of the world; we are still far from a consistent picture of the physical world that can take the two conceptual novelties into account. The great scientific revolution opened by the XXth century is not over: the cards are one the table and expect to be put in the right order. Could there be a more exciting period for researching in fundamental physics?

Jorge Pullin