We present the arguments suggesting that time is emergent in quantum gravity and discuss extensively, but without any technical detail, the many aspects that can be involved in such emergence. We refer to both the physical issues that need to be tackled, by quantum gravity formalisms, to realize concretely this emergent picture of time, and the conceptual challenges that have to be addressed in parallel to achieve a proper understanding of it.of phenomena and depending on the control paramaters. Due to the symmetric nature of the relation, speaking of emergence in this case can be seen as an abuse of language. However, on the one hand, this use of the term is found regularly in the physics literature (and very often in the philosophical one too); on the other hand, our definition of emergence, given above following Butterfield et al did not include any asymmetry condition, thus we have no reason at this stage to exclude tis case from consideration. We point out that no reduction is involved by this third kind of emergence, per se, even if in all examples we can think of there is an underlying reduction relation, not between the two sides of this "emergence relation of the third kind", but between each of them and a third set of phenomena, common to both.Looking at the concrete physical situations in which these three kinds of emergence are identified, they are often labeled as synchronic emergence, for the first two kinds, and diachronic emergence, for the third. This is because the third is often associated to physical processes taking place in time, while the first two do not refer to temporal change at all. As we will discuss, this terminology is problematic, first of all because at the theoretical level, also the third kind of emergence can be defined in a way that makes no reference to temporal evolution, but also, and most importantly for our present purposes, any implicit or explicit reference to time would obviously mess up the application of these concepts to the case of time itself and for the understanding of its own emergent nature.All these kinds of emergence should be considered in the case of spacetime in quantum gravity, and time in particular, as we do in the following. Our discussion should be seen in the context of a growing body of work on spacetime emergence in quantum gravity in the philosophy literature [22,23,24,25,26,27,28], in addition of course to the quantum gravity literature.
Making things concrete: an example of emergent behaviourThe above discussion is certainly overly sketchy and abstract. Therefore, let us give a concrete illustration of the various notions of emergence, using an example that is as uncontroversial as it can get, at least from the point of view of the usual physics parlance 3 . Consider the physical system identified as water molecules 4 . They are well described in the mathematical language of non-relativistic quantum mechanics, with a Schroedinger evolution equation for their quantum states, an Hamiltonian encoding the relevant forces between them and, in case, ...