Samuel C. Fletcher

Similarity, Topology, and Physical Significance in Relativity Theory

Stephen Hawking, among others, has proposed that the topological stability of a property of space-time is a necessary condition for it to be physically significant. What counts as stable, however, depends crucially on the choice of topology. Some physicists have thus suggested that one should find a canonical topology, a single ‘right’ topology for every inquiry. While certain such choices might be initially motivated, some little-discussed examples of Robert Geroch and some propositions of my own show that the main candidates—and each possible choice, to some extent—faces the horns of a no-go result. I suggest that instead of trying to decide what the ‘right’ topology is for all problems, one should let the details of particular types of problems guide the choice of an appropriate topology. 1   Introduction 2   Similarity, Topology, and Physical Significance 3   The Open Topologies 4   Continuity in the Geometric Sense and the Compact-Open Topologies 5   Methodological Contextualism    Appendix 1   Introduction 2   Similarity, Topology, and Physical Significance 3   The Open Topologies 4   Continuity in the Geometric Sense and the Compact-Open Topologies 5   Methodological Contextualism    Appendix

On Noncontextual, Non-Kolmogorovian Hidden Variable Theories

One implication of Bell’s theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms. We generalize a theorem of Feintzeig (Br J Philos Sci 66(4): 905–927, 2015) to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of experimental possibilities.

Indeterminism, Gravitation, and Spacetime Theory

Contemporary discussions of physical determinism that engage with modern spacetime and gravitational theory have typically focused on the question of the global uniqueness of solutions for initial-value problems. In this chapter I investigate the violation of local uniqueness, found in examples like Norton’s dome, which are not typically considered in light of spacetime theory. In particular, I construct initial trajectories for massive particles whose worldlines are not uniquely determined from initial data, both for a charged particle in special relativistic electromagnetism and for a freely falling particle in pure general relativity. I also show that the existence of such examples implies the violation of the Strong Energy Condition, and consider their implications for the interpretation of spacetime theory.

Minimal approximations and Norton’s dome

In this note, I apply Norton’s (Philos Sci 79(2):207–232, 2012) distinction between idealizations and approximations to argue that the epistemic and inferential advantages often taken to accrue to minimal models (Batterman in Br J Philos Sci 53:21–38, 2002) could apply equally to approximations, including “infinite” ones for which there is no consistent model. This shows that the strategy of capturing essential features through minimality extends beyond models, even though the techniques for justifying this extended strategy remain similar. As an application I consider the justification and advantages of the approximation of a inertial reference frame in Norton’s dome scenario (Philos Sci 75(5):786–798, 2008), thereby answering a question raised by Laraudogoitia (Synthese 190(14):2925–2941, 2013).

Evidence amalgamation in the sciences: an introduction

Amalgamating evidence from heterogeneous sources and across levels of inquiry is becoming increasingly important in many pure and applied sciences. This special issue provides a forum for researchers from diverse scientific and philosophical perspectives to discuss evidence amalgamation, its methodologies, its history, its pitfalls, and its potential. We situate the contributions therein within six themes from the broad literature on this subject: the variety-of-evidence thesis, the philosophy of meta-analysis, the role of robustness/sensitivity analysis for evidence amalgamation, its bearing on questions of extrapolation and external validity of experiments, its connection with theory development, and its interface with causal inference, especially regarding causal theories of cancer.

Would Two Dimensions be World Enough for Spacetime

We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions.

Computers in Abstraction/Representation Theory

Recently, Horsman et al. (Proc R Soc Lond A 470:20140182, 2014) have proposed a new framework, Abstraction/Representation (AR) theory, for understanding and evaluating claims about unconventional or non-standard computation. Among its attractive features, the theory in particular implies a novel account of what is means to be a computer. After expounding on this account, I compare it with other accounts of concrete computation, finding that it does not quite fit in the standard categorization: while it is most similar to some semantic accounts, it is not itself a semantic account. Then I evaluate it according to the six desiderata for accounts of concrete computation proposed by Piccinini (Physical computation: a mechanistic account, Oxford University Press, Oxford, 2015). Finding that it does not clearly satisfy some of them, I propose a modification, which I call Agential AR theory, that does, yielding an account that could be a serious competitor to other leading account of concrete computation.

Against the Topologists: Essay Review of New Foundations for Physical Geometry

Tim Maudlin begins New Foundations for Physical Geometry, his first book in a planned pair, with a headlong charge: “The thesis of these books is both simple and audacious. It is so simple that the basic claims can be reduced to two sentences. First: the most fundamental geometrical structure that organizes physical points into a space is the line. Second: what endows spacetime with its geometry is time” (1). Although he hints at applications forthcoming in the second volume to Newtonian and Relativistic spacetime physics, including the problem of black hole evaporation (25), this volume concentrates on an extended development of the mathematics of his Theory of Linear Structures. In fact, Maudlin is interested in contrasting his theory as an alternative to (1) and rival of (112) the field of mathematics called topology, which concerns the features of spaces invariant under continuous deformation. Such deformations preserve properties such as two points being “connected” in the space but not properties like the distance between them (if this is well defined). This is the sense in which Maudlin is attempting to construct a new foundation for “submetrical” geometry: he believes topology has given incorrect analyses and definitions for what he takes to be preexisting geometric concepts such as “continuity,”which the Theory of Linear Structures is attempting to rectify. Accordingly, he insists on using the same words for many concepts and properties defined in his theory as those in topology (e.g., continuity, connectedness, openness, closedness, and convergence) de-

Towards a Graph‐Theoretic Characterization of Popescu‐Rohrlich Box Simulation Strategies

The propensity for certain quantum system to consistently violate Bell inequalities—dubbed quantum nonlocality—has recently been found to be an information theoretic resource in quantum communication that is distinct from entanglement. Accordingly, a useful measurement of “how much” of this resource is present in a given system is needed. One candidate, the PR‐box (sometimes called a nonlocal machine), has been suggested as a possible benchmark, but one of the difficulties in using it has been to determine exactly what kinds of quantum systems are simulable by it. The present work is a first step towards a graph‐theoretic understanding of PR‐boxes that may prove useful in this endeavor.