The relative facts interpretation and Everett's note added in proof

In the published version of Hugh Everett III's doctoral dissertation, he inserted what has become a famous footnote, the “note added in proof”. This footnote is often the strongest evidence given for any of various interpretations of Everett (the many worlds, many minds, many histories and many threads interpretations). In this paper I will propose a new interpretation of the footnote. One that is supported by evidence found in letters written to and by Everett; one that is suggested by a new interpretation of Everett, an interpretation that takes seriously the central position of relative states in Everett's pure wave mechanics: the relative facts interpretation. Of central interest in this paper is how to make sense of Everett's claim in the “note added in proof” that “all elements of a superposition (all “branches”) are “actual,” none any more “real” than the rest.”     

The quantum liar experiment in Cramer's transactional interpretation

Cramer's Transactional Interpretation (TI) is applied to the “quantum liar experiment” (QLE). It is shown how some apparently paradoxical features can be explained naturally, albeit nonlocally (since TI is an explicitly nonlocal interpretation, at least from the vantage point of ordinary spacetime). At the same time, it is proposed that in order to preserve the elegance and economy of the interpretation, it may be necessary to consider offer and confirmation waves as propagating in a “higher space” of possibilities.     

Holism, physical theories and quantum mechanics

Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.     

The metaphysics of D-CTCs: On the underlying assumptions of Deutsch׳s quantum solution to the paradoxes of time travel

I argue that Deutsch׳s model for the behavior of systems traveling around closed timelike curves (CTCs) relies implicitly on a substantive metaphysical assumption. Deutsch is employing a version of quantum theory with a significantly supplemented ontology of parallel existent worlds, which differ in kind from the many worlds of the Everett interpretation. Standard Everett does not support the existence of multiple identical copies of the world, which the D-CTC model requires. This has been obscured because he often refers to the branching structure of Everett as a “multiverse”, and describes quantum interference by reference to parallel interacting definite worlds. But he admits that this is only an approximation to Everett. The D-CTC model, however, relies crucially on the existence of a multiverse of parallel interacting worlds. Since his model is supplemented by structures that go significantly beyond quantum theory, and play an ineliminable role in its predictions and explanations, it does not represent a quantum solution to the paradoxes of time travel.     

The primitive ontology of quantum physics: Guidelines for an assessment of the proposals

The paper seeks to make progress from stating primitive ontology theories of quantum physics—notably Bohmian mechanics, the GRW matter density theory and the GRW flash theory—to assessing these theories. Four criteria are set out: (a) internal coherence; (b) empirical adequacy; (c) relationship to other theories; and (d) explanatory value. The paper argues that the stock objections against these theories do not withstand scrutiny. Its focus then is on their explanatory value: they pursue different strategies to ground the textbook formalism of quantum mechanics, and they develop different explanations of quantum non-locality. In conclusion, it is argued that Bohmian mechanics offers a better prospect for making quantum non-locality intelligible than the GRW matter density theory and the GRW flash theory.     

Why history matters to philosophy of physics

Naturalized metaphysics remains the default presupposition of much contemporary philosophy of physics. As metaphysics is supposed to concern the general structure of reality, so scientific naturalism draws upon our best physical theories to attempt to answer the foundational question “par excellence ” viz., “how could the world possibly be the way this theory says it is?” A particular case study, Hilbert's attempt to analyze and explain a seeming “pre-established harmony” between mind and nature, is offered as a salutary reminder that naturalism's ready inference from physical theory to ontology may be too quick.     

Von Neumann’s impossibility proof: Mathematics in the service of rhetorics

According to what has become a standard history of quantum mechanics, in 1932 von Neumann persuaded the physics community that hidden variables are impossible as a matter of principle, after which leading proponents of the Copenhagen interpretation put the situation to good use by arguing that the completeness of quantum mechanics was undeniable. This state of affairs lasted, so the story continues, until Bell in 1966 exposed von Neumann’s proof as obviously wrong. The realization that von Neumann’s proof was fallacious then rehabilitated hidden variables and made serious foundational research possible again. It is often added in recent accounts that von Neumann’s error had been spotted almost immediately by Grete Hermann, but that her discovery was of no effect due to the dominant Copenhagen Zeitgeist.We shall attempt to tell a story that is more historically accurate and less ideologically charged. Most importantly, von Neumann never claimed to have shown the impossibility of hidden variables tout court, but argued that hidden-variable theories must possess a structure that deviates fundamentally from that of quantum mechanics. Both Hermann and Bell appear to have missed this point; moreover, both raised unjustified technical objections to the proof. Von Neumann’s argument was basically that hidden-variables schemes must violate the “quantum principle” that physical quantities are to be represented by operators in a Hilbert space. As a consequence, hidden-variables schemes, though possible in principle, necessarily exhibit a certain kind of contextuality.As we shall illustrate, early reactions to Bohm’s theory are in agreement with this account. Leading physicists pointed out that Bohm’s theory has the strange feature that pre-existing particle properties do not generally reveal themselves in measurements, in accordance with von Neumann’s result. They did not conclude that the “impossible was done” and that von Neumann had been shown wrong.     

Tuning up mind's pattern to nature's own idea: Eddington's early twenties case for variational derivatives

This paper sets out to show how Eddington's early twenties case for variational derivatives significantly bears witness to a steady and consistent shift in focus from a resolute striving for objectivity towards “selective subjectivism” and structuralism. While framing his so-called “Hamiltonian derivatives” along the lines of previously available variational methods allowing to derive gravitational field equations from an action principle, Eddington assigned them a theoretical function of his own devising in The Mathematical Theory of Relativity (1923). I make clear that two stages should be marked out in Eddington's train of thought if the meaning of such variational derivatives is to be adequately assessed. As far as they were originally intended to embody the mind's collusion with nature by linking atomicity of matter with atomicity of action, variational derivatives were at first assigned a dual role requiring of them not only to express mind's craving for permanence but also to tune up mind's privileged pattern to “Nature's own idea”. Whereas at a later stage, as affine field theory would provide a framework for world-building, such “Hamiltonian differentiation” would grow out of tune through gauge-invariance and, by disregarding how mathematical theory might precisely come into contact with actual world, would be turned into a mere heuristic device for structural knowledge.     

The role of symmetry in the interpretation of physical theories

The symmetries of a physical theory are often associated with two things: conservation laws (via e.g. Noether׳s and Schur׳s theorems) and representational redundancies (“gauge symmetry”). But how can a physical theory׳s symmetries give rise to interesting (in the sense of non-trivial) conservation laws, if symmetries are transformations that correspond to no genuine physical difference? In this paper, I argue for a disambiguation in the notion of symmetry. The central distinction is between what I call “analytic” and “synthetic“ symmetries, so called because of an analogy with analytic and synthetic propositions. “Analytic“ symmetries are the turning of idle wheels in a theory׳s formalism, and correspond to no physical change; “synthetic“ symmetries cover all the rest. I argue that analytic symmetries are distinguished because they act as fixed points or constraints in any interpretation of a theory, and as such are akin to Poincaré׳s conventions or Reichenbach׳s ‘axioms of co-ordination’, or ‘relativized constitutive a priori principles’.     

Norton's material theory of analogy

In his book, The Material Theory of Induction, Norton argues that the quest for a universal formal theory or ‘schema’ for analogical inference should be abandoned. In its place, he offers the “material theory of analogy”: each analogical inference is “powered” by a local fact of analogy rather than by any formal schema. His minimalist model promises a straightforward, fact-based approach to the evaluation and justification of analogical inferences. This paper argues that although the rejection of universal schemas is justified, Norton's positive theory is limited in scope: it works well only for a restricted class of analogical inferences. Both facts and quasi-formal criteria have roles to play in a theory of analogical reasoning.     

Can Bohmian mechanics be made background independent?

The paper presents an inquiry into the question regarding the compatibility of Bohmian mechanics, intended as a non-local theory of moving point-like particles, with background independence. This issue is worth being investigated because, if the Bohmian framework has to be of some help in developing new physics, it has to be compatible with the most well-established traits of modern physics, background independence being one of such traits. The paper highlights the fact that the notion of background independence in the context of spacetime physics is slippery and interpretation-laden. It is then suggested that the best-matching framework developed by Julian Barbour might provide a robust enough meaning of background independence. The structure of Bohmian dynamics is evaluated against this framework, reaching some intermediate results that speak in favor of the fact that Bohmian mechanics can be made background independent.     

The concept of intelligibility in modern physics (1948)

This is an English translation of Paul Feyerabend's earliest extant essay “Der Begriff der Verständlichkeit in der modernen Physik” (1948). In it, Feyerabend defends positivism as a progressive framework for scientific research in certain stages of scientific development. He argues that in physics visualizability (Anschaulichkeit) and intelligibility (Verständlichkeit) are time-conditioned concepts: what is deemed visualizable in the development of physical theories is relative to a specific historical context and changes over time. He concludes that from time to time the abandonment of visualizability is crucial for progress in physics, as it is conducive to major theory change, illustrating the point on the basis of advances in atomic theory.     

The diagrammatic dimension of William Gilbert's De magnete

In De magnete (1600), Gilbert frequently appealed to diagrams. As result of a focus on the experimental methodology of the treatise, its diagrammatic dimension has been overlooked in the scholarship. This paper argues that, in De magnete, at least some diagrams are epistemically relevant; specifically, Gilbert moves from experiments to concepts and theories through diagrams. To show this, I analyze the role that the “Diagram of motions in magnetick orbes” plays in the formulation of Gilbert's rule of alignment of magnetic bodies within the orb of virtue (the space around a magnet where its influence is exerted). If it turns out that diagrams play a genuine role in Gilbert's magnetic investigations, then his investigative strategy goes beyond mere experimentalism.     

A tale of three theories: Feyerabend and Popper on progress and the aim of science

In this paper, three theories of progress and the aim of science are discussed: (i) the theory of progress as increasing explanatory power, advocated by Popper in The logic of scientific discovery (1935/1959); (ii) the theory of progress as approximation to the truth, introduced by Popper in Conjectures and refutations (1963); (iii) the theory of progress as a steady increase of competing alternatives, which Feyerabend put forward in the essay “Reply to criticism. Comments on Smart, Sellars and Putnam” (1965) and defended as late as the last edition of Against method (1993). It is argued that, contrary to what Feyerabend scholars have predominantly assumed, Feyerabend's changing attitude towards falsificationism—which he often advocated at the beginning of his career, and vociferously attacked in the 1970s and 1980s—must be explained by taking into account not only Feyerabend's very peculiar view of the aim of science, but also Popper's changing account of progress.     

Energy Conservation in GTR

The topics of gravitational field energy and energy-momentum conservation in General Relativity theory have been unjustly neglected by philosophers. If the gravitational field in space free of ordinary matter, as represented by the metric g_ab itself, can be said to carry genuine energy and momentum, this is a powerful argument for adopting the substantivalist view of spacetime.This paper explores the standard textbook account of gravitational field energy and argues that (a) so-called stress-energy of the gravitational field is well-defined neither locally nor globally; and (b) there is no general principle of energy-momentum conservation to be found in General Relativity. I discuss the nature and justification of the zero-divergence law for ordinary stress-energy, and its possible connection with the failure of General Relativity to realise Mach's principle.     

Worlds in the Everett interpretation

This is a discussion of how we can understand the world-view given to us by the Everett interpretation of quantum mechanics, and in particular the rôle played by the concept of ‘world’. The view presented is that we are entitled to use ‘many-worlds’ terminology even if the theory does not specify the worlds in the formalism; this is defended by means of an extensive analogy with the concept of an ‘instant’ or moment of time in relativity, with the lack of a preferred foliation of spacetime being compared with the lack of a preferred basis in quantum theory. Implications for identity of worlds over time, and for relativistic quantum mechanics, are discussed.     

Reichenbach on causality in 1923: Scientific inference,coordination, and confirmation

In The Theory of Relativity and A Priori Knowledge (1920b), Reichenbach developed an original account of cognition as coordination of formal structures to empirical ones. One of the most salient features of this account is that it is explicitly not a top-down type of coordination, and in fact it is crucially “directed” by the empirical side. Reichenbach called this feature “the mutuality of coordination” but, in that work, did not elaborate sufficiently on how this is supposed to work. In a paper that he wrote less than two years afterwards (but that he published only in 1932), “The Principle of Causality and the Possibility of its Empirical Confirmation” (1923/1932), he described what seems to be a model for this idea, now within an analysis of causality that results in an account of scientific inference. Recent reassessments of his early proposal do not seem to capture the extent of Reichenbach's original worries. The present paper analyses Reichenbach's early account and suggests a new way to look at his early work. According to it, we perform measurements, individuate parameters, collect and analyse data, by using a “constructive” approach, such as the one with which we formulate and test hypotheses, which paradigmatically requires some simplicity assumptions. Reichenbach's attempt to account for all these aspects in 1923 was obviously limited and naive in many ways, but it shows that, in his view, there were multiple ways in which the idea of “constitution” is embodied in scientific practice.     

Klein-Weyl's program and the ontology of gauge and quantum systems

We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program—that we call the Klein-Weyl program—for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a “structure-endowed entity” equipped with a “group of automorphisms”. First, we analyze what Weyl calls the “problem of relativity” in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are “indices characterizing representations of groups” ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.     

Newton and action at a distance between bodies—A response to Andrew Janiak's “Three concepts of causation in Newton”

This article responds to Professor Andrew Janiak's recent attempt to defend the proposition that Isaac Newton did not believe in action at a distance between bodies (or any other kind of substance) (Janiak, 2013). His argument rests on a distinction between “three concepts of causation in Newton”, which leads him to conclude that although Newton did not believe in action at a distance between bodies, he was able to accept that gravity was a “distant action”. I critically examine Janiak's arguments here, and the historical evidence he brings to bear upon it, and argue that Professor Janiak's latest claims do nothing to undermine the view to which he is opposed, namely, that Newton did believe in the possibility of action at a distance between bodies.     

Zweideutigkeit about “Zweideutigkeit”: Sommerfeld,Pauli, and the methodological origins of quantum mechanics

In early 1925, Wolfgang Pauli (1900–1958) published the paper for which he is now most famous and for which he received the Nobel Prize in 1945. The paper detailed what we now know as his “exclusion principle.” This essay situates the work leading up to Pauli's principle within the traditions of the “Sommerfeld School,” led by Munich University's renowned theorist and teacher, Arnold Sommerfeld (1868–1951). Offering a substantial corrective to previous accounts of the birth of quantum mechanics, which have tended to sideline Sommerfeld's work, it is suggested here that both the method and the content of Pauli's paper drew substantially on the work of the Sommerfeld School in the early 1920s. Part One describes Sommerfeld's turn away from a faith in the power of model-based (modellmässig) methods in his early career towards the use of a more phenomenological emphasis on empirical regularities (Gesetzmässigkeiten) during precisely the period that both Pauli and Werner Heisenberg (1901–1976), among others, were his students. Part two delineates the importance of Sommerfeld's phenomenology to Pauli's methods in the exclusion principle paper, a paper that also eschewed modellmässig approaches in favour of a stress on Gesetzmässigkeiten. In terms of content, a focus on Sommerfeld's work reveals the roots of Pauli's understanding of the fundamental Zweideutigkeit (ambiguity) involving the quantum number of electrons within the atom. The conclusion points to the significance of these results to an improved historical understanding of the origin of aspects of Heisenberg's 1925 paper on the “Quantum-theoretical Reformulation (Umdeutung) of Kinematical and Mechanical Relations.”