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Philosophers have claimed that: (a) the Born-Oppenheimer approximation methods for solving molecular Schr\"odinger equations violate the Heisenberg uncertainty relations; therefore (b) so-called `quantum chemistry' is not fully quantum; and so (c) chemistry does not reduce to physics. This paper analyses the reasoning behind Born-Oppenheimer methods and shows that they are internally consistent and fully quantum mechanical, contrary to (a)-(c). Our analysis addresses important issues of mathematical rigour, physical idealisation, reduction, and classicality in the quantum theory of molecules, and we propose an agenda for the philosophy of quantum chemistry more solidly grounded in scientific practice.

This paper investigates the formation and propagation of wavefunction `branches' through the process of entanglement with the environment. While this process is a consequence of unitary dynamics, and hence significant to many if not all approaches to quantum theory, it plays a central role in many recent articulations of the Everett or `many worlds' interpretation. A highly idealized model of a locally interacting system and environment is described, and investigated in several situations in which branching occurs, including those involving Bell inequality violating correlations; we illustrate how any non-locality is compatible with the locality of the dynamics. Although branching is particularly important for many worlds quantum theory, we take a neutral stance here, simply tracing out the consequences of a unitary dynamics. The overall goals are to provide a simple concrete realization of the quantum physics of branch formation, and especially to emphasise the compatibility of branching with relativity; the paper is intended to illuminate matters both for foundational work, and for the application of quantum theory to non-isolated systems.

We conduct a case study analysis of a proposal for the emergence of time based upon the approximate derivation of three grades of temporal structure within an explicit quantum cosmological model which obeys a Wheeler-DeWitt type equation without an extrinsic time parameter. Our main focus will be issues regarding the consistency of the approximations and derivations in question. Our conclusion is that the model provides a self-consistent account of the emergence of chronordinal, chronometric and chronodirected structure. Residual concerns relate to explanatory rather than consistency considerations.

It has long been thought that observing distinctive traces of quantum gravity in a laboratory setting is effectively impossible, since gravity is so much weaker than all the other familiar forces in particle physics. But the quantum gravity phenomenology community today seeks to do the (effectively) impossible, using a challenging novel class of `tabletop' Gravitationally Induced Entanglement (GIE) experiments, surveyed here. The hypothesized outcomes of the GIE experiments are claimed by some (but disputed by others) to provide a `witness' of the underlying quantum nature of gravity in the non-relativistic limit, using superpositions of Planck-mass bodies. We inspect what sort of achievement it would possibly be to perform GIE experiments, as proposed, ultimately arguing that the positive claim of witness is equivocal. Despite various sweeping arguments to the contrary in the vicinity of quantum information theory or given low-energy quantum gravity, whether or not one can claim to witness the quantum nature of the gravitational field in these experiments decisively depends on which out of two legitimate modelling paradigms one finds oneself in. However, by situating GIE experiments in a tradition of existing experiments aimed at making gravity interestingly quantum in the laboratory, we argue that, independently of witnessing or paradigms, there are powerful reasons to perform the experiments, and that their successful undertaking would indeed be a major advance in physics., Comment: 61 pages

The modeling of black holes is an important desideratum for any quantum theory of gravity. Not only is a classical black hole metric sought, but also agreement with the laws of black hole thermodynamics. In this paper, we describe how these goals are obtained in string theory. We review black hole thermodynamics, and then explicate the general stringy derivation of classical spacetimes, the construction of a simple black hole solution, and the derivation of its entropy. With that in hand, we address some important philosophical and conceptual questions: the confirmatory value of the derivation, the bearing of the model on recent discussions of the so-called 'information paradox', and the implications of the model for the nature of space., Comment: 26 pages, 3 figures

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian W\"uthrich and under contract with Oxford University Press. (More information at https://beyondspacetime.net/.) This chapter introduces the problem of emergence of spacetime in quantum gravity. It introduces the main philosophical challenge to spacetime emergence and sketches our preferred solution to it., Comment: 26 pages, 1 figure

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian W\"uthrich and under contract with Oxford University Press. (More information at www.beyondspacetime.net.) This chapter sketches how spacetime emerges in causal set theory and demonstrates how this question is deeply entangled with genuinely philosophical concerns., Comment: 32 pages, 5 figures

Noncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale - and ultimately the concept of a point - makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes' spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar field Moyal-Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry., Comment: 36 pages, two figures. V2 minor corrections, references added. Synthese (2021)

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian W\"uthrich and under contract with Oxford University Press. (More information at www.beyondspacetime.net.) This chapter investigates the meaning and significance of string theoretic dualities, arguing that they reveal a surprising physical indeterminateness to spacetime., Comment: 32 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1509.06229

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian W\"uthrich and under contract with Oxford University Press. (More information at www.beyondspacetime.net.) This chapter introduces causal set theory and identifies and articulates a 'problem of space' in this theory., Comment: 29 pages, 5 figures

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian W\"uthrich and under contract with Oxford University Press. (More information at www.beyondspacetime.net.) This chapter analyses the nature and derivation of spacetime topology and geometry according to string theory., Comment: 40 pages, 2 figures

This paper examines two cosmological models of quantum gravity (from string theory and loop quantum gravity) to investigate the foundational and conceptual issues arising from quantum treatments of the big bang. While the classical singularity is erased, the quantum evolution that replaces it may not correspond to classical spacetime: it may instead be a non-spatiotemporal region, which somehow transitions to a spatiotemporal state. The different kinds of transition involved are partially characterized, the concept of a physical transition without time is investigated, and the problem of empirical incoherence for regions without spacetime is discussed., Comment: Forthcoming in Philosophy of Science; 13 pages

This paper investigates the significance of T-duality in string theory: the indistinguishability with respect to all observables, of models attributing radically different radii to space -- larger than the observable universe, or far smaller than the Planck length, say. Two interpretational branch points are identified and discussed. First, whether duals are physically equivalent or not: by considering a duality of the familiar simple harmonic oscillator, I argue that they are. Unlike the oscillator, there are no measurements 'outside' string theory that could distinguish the duals. Second, whether duals agree or disagree on the radius of 'target space', the space in which strings evolve according to string theory. I argue for the latter position, because the alternative leaves it unknown what the radius is. Since duals are physically equivalent yet disagree on the radius of target space, it follows that the radius is indeterminate between them. Using an analysis of Brandenberger and Vafa (1989), I explain why -- even so -- space is observed to have a determinate, large radius. The conclusion is that observed, 'phenomenal' space is not target space, since a space cannot have both a determinate and indeterminate radius: instead phenomenal space must be a higher-level phenomenon, not fundamental., Comment: 16 pages, 1 figure; based on a presentation at the The Philosophical Foundations of Dualities in Physics conference, University of Florence, September 2014. To appear in a special issue of Studies in History and Philosophy of Modern Physics

This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question of the paper is whether the existing representation of time is adequate, or whether it can or should be supplemented: especially, do we need a physics incorporating some kind of `dynamical passage' of time? The paper argues that the existing mathematical framework is resistant to such changes, and might have to be rejected by anyone seeking a physics of passage. Then it rebuts two common arguments for incorporating passage into physics, especially the claim that it is an element of experience. Finally the paper investigates whether, as has been claimed, `causal set theory' provides a physics of passage., Comment: 14 pages

Quantum gravity--the marriage of quantum physics with general relativity--is bound to contain deep and important lessons for the nature of physical time. Some of these lessons shall be canvassed here, particularly as they arise from quantum general relativity and string theory and related approaches. Of particular interest is the question of which of the intuitive aspects of time will turn out to be fundamental, and which 'emergent' in some sense., Comment: 18 pages, 1 figure

Numerous approaches to a quantum theory of gravity posit fundamental ontologies that exclude spacetime, either partially or wholly. This situation raises deep questions about how such theories could relate to the empirical realm, since arguably only entities localized in spacetime can ever be observed. Are such entities even possible in a theory without fundamental spacetime? How might they be derived, formally speaking? Moreover, since by assumption the fundamental entities can't be smaller than the derived (since relative size is a spatiotemporal notion) and so can't 'compose' them in any ordinary sense, would a formal derivation actually show the physical reality of localized entities? We address these questions via a survey of a range of theories of quantum gravity, and generally sketch how they may be answered positively., Comment: 18 pages, 1 figure, accepted for publication in Studies in History and Philosophy of Modern Physics

This paper analyses the phenomenon of entanglement exchange in Bohm's pilot wave interpretation of quantum mechanics. The interesting feature of the phenomenon is that systems become entangled without causal interaction; hence it is a useful situation for investigating the unique nature of interaction in Bohmian mechanics. The first two sections introduce, respectively, entanglement exchange in the standard interpretation of quantum mechanics, and the basic principles of Bohmian mechanics. The next section shows that the Bohmian interpretation makes the same experimental predictions about entanglement exchange as the standard one. The final section draws some conclusions about interactions and entanglement in Bohmian mechanics., Comment: 15 pages, 2 figures, submitted for a forthcoming edition of Manuscrito

The principle of the identity of indiscernibles (PII) states that if two systems are qualitatively identical then they are logically identical. French and Redhead (1988) and Butterfield (1993) have shown the sense in which bosons and fermions violate the PII, but did not investigate the issue for particles of other kinds of statistics: i.e., for the (p,q) particles -- or `quarticles' -- of Hartle, Stolt and Taylor (1970). This paper shows that for any type of indistinguishable quarticle the PII is violated but that for distinguishable quarticles there are states in which it is violated by any pair of particles, states in which it is violated only by some pairs of particles and states in which it is violated by no pairs of particles. The updated version corrects a minor statement of mathematical fact, and provides a short proof for a conjecture made in the original., Comment: 11 pages. To appear in K.A. Brading and E. Castellani (eds.), "Symmetries in Physics: Philosophical Reflections", CUP 2003. The updated version (v.2) corrects a minor statement of mathematical fact, and provides a short proof for a conjecture made in the original