Emergence in holographic scenarios for gravity

‘Holographic’ relations between theories have become an important theme in quantum gravity research. These relations entail that a theory without gravity is equivalent to a gravitational theory with an extra spatial dimension. The idea of holography was first proposed in 1993 by Gerard ׳t Hooft on the basis of his studies of evaporating black holes. Soon afterwards the holographic ‘AdS/CFT’ duality was introduced, which since has been intensively studied in the string theory community and beyond. Recently, Erik Verlinde has proposed that even Newton׳s law of gravitation can be related holographically to the ‘thermodynamics of information’ on screens. We discuss these scenarios, with special attention to the status of the holographic relation in them and to the question of whether they make gravity and spacetime emergent. We conclude that only Verlinde׳s scheme straightforwardly instantiates emergence. However, assuming a non-standard interpretation of AdS/CFT may create room for the emergence of spacetime and gravity there as well.     

Taking times out: Tense logic as a theory of time

Ulrich Meyer’s book The Nature of Time uses tense logic to argue for a ‘modal’ view of time, which replaces substantial times (as in Newton’s Absolute Time) with ‘ersatz times’ constructed using conceptually basic tense operators. He also argues against Bertrand Russell’s relationist theory, in which times are classes of events, and against the idea that relativity compels the integration of time and space (called by Meyer the Inseparability Argument). I find fault with each of these negative arguments, as well as with Meyer’s purported reconstruction of empty spacetime from tense operators and substantial spatial points. I suggest that Meyer’s positive project is best conceived as an elimination of time in the mode of Julian Barbour's The End of Time.     

On the equivalence of Goodman’s and Hempel’s paradoxes

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for the conclusion that these paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other.     

What's nu? A re-examination of Maxwell's ‘ratio-of-units’ argument,from the mechanical theory of the electromagnetic field to ‘On the elementary relations between electrical measurements’

This re-examination of the earliest version of Maxwell's most important argument for the electromagnetic theory of light—the equality between the speed of wave propagation in the electromagnetic ether and the ratio of electrostatic to electromagnetic measures of electrical quantity—establishes unforeseen connections between Maxwell's theoretical electrical metrology and his mechanical theory of the electromagnetic field. Electrical metrology was not neutral with respect to field-theoretic versus action-at-a-distance conceptions of electro-magnetic interaction. Mutual accommodation between these conceptions was reached by Maxwell on the British Association for the Advancement of Science (BAAS) Committee on Electrical Standards by exploiting the measurement of the medium parameters—electric inductive capacity and magnetic permeability—on an arbitrary scale. While he always worked within this constraint in developing the ‘ratio-of-units’ argument mathematically, I maintain that Maxwell came to conceive of the ratio ‘as a velocity’ by treating the medium parameters as physical quantities that could be measured absolutely, which was only possible via the correspondences between electrical and mechanical quantities established in the mechanical theory. I thereby correct two closely-related misconceptions of the ratio-of-units argument—the counterintuitive but widespread notion that the ratio is naturally a speed, and the supposition that Maxwell either inferred or proved this from its dimensional formula.     

Space and Time in Particle and Field Physics

Textbooks present classical particle and field physics as theories of physical systems situated in Newtonian absolute space. This absolute space has an influence on the evolution of physical processes, and can therefore be seen as a physical system itself; it is substantival. It turns out to be possible, however, to interpret the classical theories in another way. According to this rival interpretation, spatiotemporal position is a property of physical systems, and there is no substantival spacetime. The traditional objection that such a relationist view could not cope with the existence of inertial effects and other manifestations of the causal efficacy of spacetime can be answered successfully. According to the new point of view, the spacetime manifold of classical physics is a purely representational device. It represents possible locations of physical objects or events; but these locations are physical properties inherent in the physical objects or events themselves and having no existence independently of them. In relativistic quantum field theory the physical meaning of the spacetime manifold becomes even less tangible. Not only does the manifold lose its status as a substantival container, but also its function as a representation of spacetime properties possessed by physical systems becomes problematic. ‘Space and time’ become ordering parameters in the web of properties of physical systems. They seem to regain their traditional meaning only in the non-relativistic limit in which the classical particle concept becomes approximately applicable.     

On miracles and spacetime

What have recently been dubbed two ‘miracles’ of general relativity—(1) that all non-gravitational interactions are locally governed by Poincaré invariant dynamical laws; and (2) that, in the regime of experimental practice in which curvature effects may be ignored, the local Poincaré symmetries of the dynamical laws governing matter fields coincide with the local Poincaré symmetries of the dynamical metric field—remain unaccounted for in that theory. In this paper, I demonstrate that these two ‘miracles’ admit of a natural explanation in one particular successor theory to general relativity—namely, perturbative string theory. I argue that this point has important implications when considering both the ‘chronogeometricity’ (that is, the object in question being surveyed by rods and clocks built from matter fields) and spatiotemporal status of the dynamical metric field in both general relativity and perturbative string theory.     

Background independence: Lessons for further decades of dispute

Background independence begins life as an informal property that a physical theory might have, often glossed as ‘doesn't posit a fixed spacetime background’. Interest in trying to offer a precise account of background independence has been sparked by the pronouncements of several theorists working on quantum gravity that background independence embodies in some sense an essential discovery of the General Theory of Relativity, and a feature we should strive to carry forward to future physical theories. This paper has two goals. The first is to investigate what a world must be like in order to be truly described by a background independent theory given extant accounts of background independence. The second is to argue that there are no non-empirical reasons to be more confident in theories that satisfy extant accounts of background independence than in theories that don't. The paper concludes by drawing a general moral about a way in which focussing primarily on mathematical formulations of our physical theories can adversely affect debates in the metaphysics of physics.     

Comparing dualities and gauge symmetries

We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the ‘flavour’ that two dual theories are ‘closer in content’ than you might think. For both points, we adopt a simple conception of a duality as an ‘isomorphism’ between theories: more precisely, as appropriate bijections between the two theories’ sets of states and sets of quantities.The first point (Section 3) is that this conception of duality meshes with two dual theories being ‘gauge related’ in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be ‘gauge’.The second point (4 Gauge/gravity duality, 5 Some complications for gauge invariance, 6 Galileo׳s ship, (Local)) is much more specific. We give a result about gauge/gravity duality that shows its relation to gauge symmetries (in the physical sense of symmetry transformations that are spacetime-dependent) to be subtler than you might expect. For gauge theories, you might expect that the duality bijections relate only gauge-invariant quantities and states, in the sense that gauge symmetries in one theory will be unrelated to any symmetries in the other theory. This may be so in general; and indeed, it is suggested by discussions of Polchinski and Horowitz. But we show that in gauge/gravity duality, each of a certain class of gauge symmetries in the gravity/bulk theory, viz. diffeomorphisms, is related by the duality to a position-dependent symmetry of the gauge/boundary theory.     

Holography and emergence

In this paper, I discuss one form of the idea that spacetime and gravity might ‘emerge’ from quantum theory, i.e. via a holographic duality, and in particular via AdS/CFT duality. I begin by giving a survey of the general notion of duality, as well as its connection to emergence. I then review the AdS/CFT duality and proceed to discuss emergence in this context. We will see that it is difficult to find compelling arguments for the emergence of full quantum gravity from gauge theory via AdS/CFT, i.e. for the boundary theory's being metaphysically more fundamental than the bulk theory.     

Popper’s response to Dingle on special relativity and the problem of the observer

Dingle contended that Einstein’s special theory of relativity was physically impossible for the simple reason that it required clocks to be simultaneously faster and slower than each other. McCrea refuted Dingle using an operationalist argument. An operational response did not satisfy Popper, who wrote an unpublished essay to counter Dingle’s claim. Popper developed an analysis that avoided operationalism by using a system of coinciding clocks, contending that this system showed that special relativity withstood Dingle’s criticism that it was not a symmetrical and consistent physical theory. However, Popper mistakenly included an asymmetric calculation in his analysis. Once this is corrected, the amended result supports Dingle’s position. Popper went on to argue that to avoid determinism, special relativity had to be reconciled with absolute time; this too supports Dingle. Popper’s failure to refute Dingle calls into question his claim that ‘the observer’ is superfluous to special relativity.     

The Whewell-Mill debate on predictions,from Mill's point of view

John Stuart Mill, in his debate with William Whewell on the nature and logic of induction, is regarded as being the first to dismiss the supposed value of successful predictions as merely psychological. I shall argue that this view of the Whewell-Mill debate on predictions misconstrues Mill’s position and argument. From Mill’s point of view, the controversial point was not the question whether predictions ‘count more’ than ex-post explanations but the alleged assertion by Whewell that the successful predictions of the wave theory of light prove the existence of the ether. Mill argued that, on the one hand, the predictions of the wave theory of light do not and cannot provide evidence for the existence of the ether; as evidence for the laws of the theory, on the other hand, the predictions are superfluous, the laws being already well-confirmed. Mill actually endorsed a requirement of independent support closely resembling Whewell’s requirements for hypotheses; the controversy on the value of predictions is a product of the 20th century.     

<Emphasis Type="Italic">Newton's Argument for Proposition 1 of the</Emphasis> Principia

The first proposition of the Principia records two fundamental properties of an orbital motion: the Fixed Plane Property (that the orbit lies in a fixed plane) and the Area Property (that the radius sweeps out equal areas in equal times). Taking at the start the traditional view, that by an orbital motion Newton means a centripetal motion – this is a motion ``continually deflected from the tangent toward a fixed center' – we describe two serious flaws in the Principia's argument for Proposition 1, an argument based on a polygonal impulse approximation. First, the persuasiveness of the argument depends crucially on the validity of the Impulse Assumption: that every centripetal motion can be represented as a limit of polygonal impulse motions. Yet Newton tacitly takes the Impulse Assumption for granted. The resulting gap in the argument for Proposition 1 is serious, for only a nontrivial analysis, involving the careful estimation of accumulating local errors, verifies the Impulse Assumption. Second, Newton's polygonal approximation scheme has an inherent and ultimately fatal disability: it does not establish nor can it be adapted to establish the Fixed Plane Property. Taking then a different view of what Newton means by an orbital motion – namely that an orbital motion is by definition a limit of polygonal impulse motions – we show in this case that polygonal approximation can be used to establish both the fixed plane and area properties without too much trouble, but that Newton's own argument still has flaws. Moreover, a crucial question, haunted by error accumulation and planarity problems, now arises: How plentiful are these differently defined orbital motions? Returning to the traditional view, that Newton's orbital motions are by definition centripetal motions, we go on to give three proofs of the Area Property which Newton ``could have given' – two using polygonal approximation and a third using curvature – as well as a proof of the Fixed Plane Property which he ``almost could have given.' (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

Spacetime without Reference Frames: An Application to the Velocity Addition Paradox

Much conceptualisation in contemporary physics is bogged down by unnecessary assumptions concerning a specific choice of coordinates which often leads to misunderstandings and paradoxes. Considering an absolute (coordinate-free) formulation of special relativistic spacetime, we show clearly that the velocity addition paradox emerged because the use of coordinates obscures that the space of relativistic observers is ‘more relative’ than the space of non-relativistic observers.     

Minkowski spacetime and Lorentz invariance: The cart and the horse or two sides of a single coin?

Michel Janssen and Harvey Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties—that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive interpretation of special relativity—are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invariance, a misconception that in turn sheds more shadows than light on our understanding of the explanatory nature and power of Einstein׳s theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and unidirectional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers.     

Duncan F. Gregory,William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction

This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on ‘algebraical geometry’ and ‘geometrical algebra’ in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the ‘abstract algebra’ and ‘abstract geometry’ of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to ‘algebraical geometry’ and ‘geometrical algebra’ of the second generation of ‘scientific’ symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s–1840s.     

The Principle of Equivalence

We start from John Norton's analysis (1985) of the reach of Einstein's version of the principle of equivalence which is not a local principle but an extension of the relativity principle to reference frames in constant acceleration on the background of Minkowski spacetime. We examine how such a point of view implies a profound, and not generally recognised, reconsideration of the concepts of inertial system and field in physics. We then reevaluate the role that the infinitesimal principle, if adequately formulated, can legitimately be claimed to play in general relativity. We show that what we call the ‘punctual equivalence principle’ has significant physical content and that it permits the derivation of the geodesic law.     

Experimental economics' inconsistent ban on deception

According to what I call the ‘argument from public bads’, if a researcher deceived subjects in the past, there is a chance that subjects will discount the information that a subsequent researcher provides, thus compromising the validity of the subsequent researcher's experiment. While this argument is taken to justify an existing informal ban on explicit deception in experimental economics, it can also apply to implicit deception, yet implicit deception is not banned and is sometimes used in experimental economics. Thus, experimental economists are being inconsistent when they appeal to the argument from public bads to justify banning explicit deception but not implicit deception.     

Suppressing spacetime emergence

One of the primary tasks in building a quantum theory of gravity is discovering how to save spatiotemporal phenomena using a theory which, putatively, does not include spacetime. Some have taken this task a step further and argue for the actual emergence of spacetime from a non-spatiotemporal ontology in the low-energy regime. In this paper, it is argued that the account of spacetime emergence presented in Huggett and Wüthrich (2013) and then assumed in Baron (2019), Crowther (2016), Wüthrich (2017), and Wüthrich and Lam (2018) fails to accomplish the task to which it is set. There is a prima facie contradiction between the scale-independent ontology of spacetime in GR and the scale-dependent account of emergence proposed by this literature. One can avoid this contradiction but only at the cost of changing the target of emergence and by endorsing a perspectival theory of ontology – a view I call “ontic-perspectivism”. Though this paper explicitly addresses spacetime emergence, many of the following arguments are applicable to other accounts where objects of ontology, or their properties, are claimed to emerge in the low-energy regime.