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. (shrink)

Although the laws of thermodynamics are well established for black hole horizons, much less has been said in the literature to support the extension of these laws to more general settings such as an asymptotic de Sitter horizon or a Rindler horizon (the event horizon of an asymptotic uniformly accelerated observer). In the present paper we review the results that have been previously established and argue that the laws of black hole thermodynamics, as well as their underlying statistical mechanical content, (...) extend quite generally to what we call here “causal horizons.” The root of this generalization is the local notion of horizon entropy density. (shrink)

The procedures of canonical quantization of the gravitational field apparently lead to entities for which any interpretation in terms of spatio-temporal localization or spatio-temporal extension seems difficult. This fact is the main ground for the suggestion that can often be found in the physics literature on canonical quantum gravity according to which spacetime may not be fundamental in some sense. This paper aims to investigate this radical suggestion from an ontologically serious point of view in the cases of two standard (...) forms of canonical quantum gravity, quantum geometrodynamics and loop quantum gravity. We start by discussing the physical features of the quantum wave functional of quantum geometrodynamics and of the spin networks of loop quantum gravity that motivate the view according to which spacetime is not fundamental. We then point out that, by contrast, for any known ontologically serious understanding of quantum entanglement, the commitment to spacetime seems indispensable. Against this background, we then critically discuss the idea that spacetime may emerge from more fundamental entities. As a consequence, we finally suggest that the emergence of classical spacetime in canonical quantum gravity faces a dilemma: either spacetime ontologically emerges from more fundamental non-spatio-temporal entities or it already belongs to the fundamental quantum gravitational level and the emergence of the classical picture is merely a matter of levels of description. On the first horn of the dilemma, it is unclear how to make sense of concrete physical entities that are not in spacetime and of the notion of ontological emergence that is involved. The second horn runs into the difficulties raised by the physics of canonical quantum gravity. (shrink)

This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation in physics, especially limiting relations between physical theories. I shall take emergence as behaviour that is novel and robust relative to some comparison class. I shall take reduction as deduction using appropriate auxiliary definitions. And I shall take supervenience as a weakening of reduction, viz. to allow infinitely long definitions. The overall claim (...) of this paper will be that emergence is logically independent both of reduction and of supervenience. In particular, one can have emergence with reduction, as well as without it; and emergence without supervenience, as well as with it. Of the subsidiary claims, the four main ones are: : I defend the traditional Nagelian conception of reduction ; : I deny that the multiple realizability argument causes trouble for reductions, or ``reductionism'' ; : I stress the collapse of supervenience into deduction via Beth's theorem ; : I adapt some examples already in the literature to show supervenience without emergence and vice versa. (shrink)

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics). (shrink)

This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world.

Condensed matter approaches to quantum gravity suggest that spacetime emerges in the low-energy sector of a fundamental condensate. This essay investigates what could be meant by this claim. In particular, I offer an account of low-energy emergence that is appropriate to effective field theories in general, and consider the extent to which it underwrites claims about the emergence of spacetime in effective field theories of condensed matter systems of the type that are relevant to quantum gravity.