Emergence in holographic scenarios for gravity
Introduction
During the last twenty years the concept of holography from quantum gravity research has grown into one of the key innovations in theoretical physics. By now it is studied in many diverse subfields and the literature on the subject has become enormous. One of the pioneering papers on holography, the article that announced the celebrated ‘AdS/CFT’ correspondence, has been cited more than ten thousand times.1 Even fields that would seem far removed from quantum gravity are now engaging with holography. For example, central issues in condensed matter physics are addressed using holographic ideas.2 In short, the core idea of holography is that a lower dimensional quantum theory without gravitation (for instance, defined on the two-dimensional surface of a sphere) is capable of describing physical phenomena that include manifestations of gravity in a higher dimensional spacetime (such as the interior of the sphere).3
It is time to pay attention to this important development also from the conceptual side: there are several ideas here that relate not only to theoretical physics but also to more general foundational, conceptual and philosophical issues. Most importantly, holographic ideas clearly touch on philosophical questions of emergence and reduction.4 Also in the physics literature these themes have come up, as reflected in some of the titles of articles on the subject: these announce “Emergent spacetime”, “Emergent gauge fields” or, e.g., promise a discussion of “Aspects of emergent geometry in the AdS/CFT context.”5 One of the publications that we specifically focus on in this article is called “On the origin of gravity and the laws of Newton.”6
We will discuss a number of holographic scenarios and place them in the context of existing ideas about emergence. It is not our aim to focus on a general analysis of the concept of emergence itself. Globally speaking, we sympathize with the characterization of emergence as novel and robust behaviour relative to some appropriate comparison class,7 and we will use the term ‘emergence’ accordingly. What we wish to investigate here is whether, and if so how, recent holographic scenarios can be interpreted as representing such emergence, and whether one theory in a holographic pair can justifiably be called more fundamental than the other. We will discuss three proposals in particular: ׳t Hooft׳s original formulation of the holographic hypothesis, the AdS/CFT duality from string theory, and Erik Verlinde׳s recent ideas. Although these proposals are strongly interrelated, we will argue that only Verlinde׳s account realizes emergence in a straightforward and uncontroversial way: gravity and spacetime here arise as thermodynamic phenomena in a coarse-grained description. As far as we can see, the concept of emergence, of higher dimensional gravity from lower dimensional non-gravitational processes, does not apply to AdS/CFT in its usual interpretation. However, we will argue that the analysis of Verlinde׳s scheme can cast new light on the interpretation of AdS/CFT, and we will accordingly suggest a way to create room for emergence also in that context.
That gravity perhaps originates from some deeper layer of reality and is different from other forces may intuitively be plausible to some extent, even if it is an intuition that has been alien to the string theory program and some of the other quantum gravity programs.8 Gravity distinguishes itself because it is universal: it applies to all forms of matter and energy, and relates to the general framework of space and time itself—this may remind one of the universal character of thermodynamic descriptions. Moreover, gravity is notoriously and essentially more difficult to quantize than other forces. This may suggest a difference of principle from the ordinary physical forces represented in the standard model. As already mentioned, studies of black hole physics have led to the hypothesis that quantum gravity theories within a volume correspond to theories without gravitation on the boundary of this volume. This seems only a small step from the notion that gravity emerges from processes described by a theory without gravity; it is this idea that we will critically analyse here.9
Section snippets
The holographic hypothesis
The central ideas of holography go back to the debates about the black hole information paradox that raged in the early 1990s. Important participants in these discussions were Gerard ׳t Hooft and Stephen Hawking; the latter famously claimed that black holes destroy information, which was opposed by the former.10 In 1993, almost twenty years after the first results on the evaporation of black holes had been announced by Hawking, ׳t Hooft put on the Los Alamos
The AdS/CFT duality and its interpretation
We will first outline the AdS/CFT correspondence (3.1) and then discuss its interpretation, in particular with respect to issues of emergence and fundamentality (3.3). We also introduce the renormalization group (3.2), which is an important ingredient in AdS/CFT and also in Verlinde׳s scenario (to be discussed in Section 4).
Gravity as an entropic force
The third holographic scenario that we want to analyse in some detail is the recent explanation for gravity proposed by Erik Verlinde. We first list its key assumptions, and add details in Section 4.2. We will try to disentangle the logical structure of Verlinde׳s argument and assess some of its conceptual and interpretative consequences in Section 4.3.
Conclusion: emergence and holography
We have reviewed three cases: ׳t Hooft׳s original holographic proposal, AdS/CFT, and Verlinde׳s recent scheme. In ׳t Hooft's (1993) introduction of the holographic hypothesis there is no clear case for emergence, even though ׳t Hooft׳s text in places suggests a more fundamental status for the physics on the boundary. The original introduction of holography was programmatic and rather ambiguous in its interpretational aspects.
The case of AdS/CFT is more clear-cut, because in it the notion of
Acknowledgements
We are grateful to Jeremy Butterfield, Diego Hofman, and two anonymous referees, for their commentary on this article. We also thank Erik Verlinde for feedback on our paper and fruitful discussions; and audiences in Munich, Florence, Chicago and Potsdam for their comments.
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