Can the two-time interpretation of quantum mechanics solve the measurement problem?

Over many years, Aharonov and co-authors have proposed a new interpretation of quantum mechanics: the two-time interpretation. This interpretation assigns two wavefunctions to a system, one of which propagates forwards in time and the other backwards. In this paper, I argue that this interpretation does not solve the measurement problem. In addition, I argue that it is neither necessary nor sufficient to attribute causal power to the backwards-evolving wavefunction $〈\Phi |$ and thus its existence should be denied, contra the two-time interpretation. Finally, I follow Vaidman in giving an epistemological reading of $〈\Phi |$.     

Against the empirical viability of the Deutsch–Wallace–Everett approach to quantum mechanics

The subjective Everettian approach to quantum mechanics presented by Deutsch and Wallace fails to constitute an empirically viable theory of quantum phenomena. The decision theoretic implementation of the Born rule realized in this approach provides no basis for rejecting Everettian quantum mechanics in the face of empirical data that contradicts the Born rule. The approach of Greaves and Myrvold, which provides a subjective implementation of the Born rule as well but derives it from empirical data rather than decision theoretic arguments, avoids the problem faced by Deutsch and Wallace and is empirically viable. However, there is good reason to cast doubts on its scientific value.     

The origins of Schwinger׳s Euclidean Green׳s functions

This paper places Julian Schwinger׳s development of the Euclidean Green׳s function formalism for quantum field theory in historical context. It traces the techniques employed in the formalism back to Schwinger׳s work on waveguides during World War II, and his subsequent formulation of the Minkowski space Green׳s function formalism for quantum field theory in 1951. Particular attention is dedicated to understanding Schwinger׳s physical motivation for pursuing the Euclidean extension of this formalism in 1958.     

Friedman׳s thesis

This essay examines Friedman׳s recent approach to the analysis of physical theories. Friedman argues against Quine that the identification of certain principles as ‘constitutive’ is essential to a satisfactory methodological analysis of physics. I explicate Friedman׳s characterization of a constitutive principle, and I evaluate his account of the constitutive principles that Newtonian and Einsteinian gravitation presuppose for their formulation. I argue that something close to Friedman׳s thesis is defensible.     

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.     

Émilie Du Châtelet's interpretation of the laws of motion in the light of 18th century mechanics

Émilie Du Châtelet is well known for her French translation of Newton's Philosophiae Naturalis Principia Mathematica. It is the first and only French translation of Newton's magnum opus. The complete work appeared in 1759 under the title Principes mathématiques de la philosophie naturelle, par feue Madame la Marquise Du Chastellet. Before translating Newton's Principia, Du Châtelet worked on her Institutions de physique. In this book she defended the Leibnizian concept of living forces – vis viva. This paper argues that both of these works were part of a critical transformation and consolidation of post-Newtonian mechanics in the early 18th century, beyond Newton and Leibniz. This will be shown by comparing Du Châtelet's translation of Newton's axioms with her own formulations of the laws of motion in light of Thomas Le Seur's and François Jacquier's Geneva edition which holds a special place among the several editions of the Principia that appeared in the early 18th century.     

Conventionalism,structuralism and neo-Kantianism in Poincaré׳s philosophy of science

Poincaré is well known for his conventionalism and structuralism. However, the relationship between these two theses and their place in Poincaré׳s epistemology of science remain puzzling. In this paper I show the scope of Poincaré׳s conventionalism and its position in Poincaré׳s hierarchical approach to scientific theories. I argue that for Poincaré scientific knowledge is relational and made possible by synthetic a priori, empirical and conventional elements, which, however, are not chosen arbitrarily. By examining his geometric conventionalism, his hierarchical account of science and defence of continuity in theory change, I argue that Poincaré defends a complex structuralist position based on synthetic a priori and conventional elements, the mind-dependence of which precludes epistemic access to mind-independent structures.     

‘Shut up and contemplate!’: Lucien Hardy׳s reasonable axioms for quantum theory

Since the beginning of quantum mechanics, attempts were made to derive it from simple natural axioms or assumptions. These reconstructions suffered from various defects, including the questionable naturalness or the overabundance of the axioms, the mathematical difficulty of the derivation, and the inclusion of a wider range of theories than just quantum mechanics. Recently, in 2001, Lucien Hardy propounded “five reasonable axioms” that seem to elude such criticism. The present paper purports to give a simplified version of this new foundation, to discuss Hardy׳s original version and subsequent variants by others authors, and to investigate the nature of the relevant axioms in light of their possible connection with correspondence arguments.     

Einstein׳s Equations for Spin 2 Mass 0 from Noether׳s Converse Hilbertian Assertion

An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether׳s 1918 paper developed Hilbert׳s and Klein׳s reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a ‘curl’ term with identically zero divergence. Noether proved a converse “Hilbertian assertion”: such “improper” conservation laws imply a generally covariant action.Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom (“ghosts”) for stability, along with universal coupling: all energy-momentum including gravity׳s serves as a source for gravity. Those assumptions (all but) imply (for 0 graviton mass) that the energy-momentum is only a term proportional to the field equations and a symmetric “curl,” which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld׳s stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form.The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed.     

Mach׳s principle as action-at-a-distance in GR: The causality question

A part of the revival of interest in Mach׳s principle since the early 1960s has involved work by physicists aimed at calculating various sorts of frame-dragging effects by matter shells surrounding an interior region, and arguing that under certain conditions or in certain limits (ideally, ones that can be viewed as plausibly similar to conditions in our cosmos) the frame dragging becomes “complete” (e.g. Lynden-Bell, Katz, & Bičák, 1995) . Such results can bolster the argument for the satisfaction of Mach׳s principle by certain classes of models of GR. Interestingly, the frame-dragging “effect” of (say) a rotational movement of cosmic matter around a central point is argued by these physicists to be instantaneous—not an effect propagating at the speed of light. Not all physicists regard this as unproblematic. But rather than exploring whether there is something unphysical about such instantaneous “action at a distance”, or a violation of the precepts of Special Relativity, I am interested in exploring whether these physicists׳ calculations should be thought of as showing local inertia (resistance to acceleration) to be an effect, with distant matter distributions being the cause. I will try to apply some leading philosophical accounts of causation to the physical models of frame dragging, to see whether they imply that the frame dragging is superluminal causation. I will then offer reflections on the difficulties of applying causal talk in physical theories.     

Everettian quantum mechanics and physical probability: Against the principle of “State Supervenience”

Everettian quantum mechanics faces the challenge of how to make sense of probability and probabilistic reasoning in a setting where there is typically no unique outcome of measurements. Wallace has built on a proof by Deutsch to argue that a notion of probability can be recovered in the many worlds setting. In particular, Wallace argues that a rational agent has to assign probabilities in accordance with the Born rule. This argument relies on a rationality constraint that Wallace calls state supervenience. I argue that state supervenience is not defensible as a rationality constraint for Everettian agents unless we already invoke probabilistic notions.     

A phenomenological solution to the measurement problem? Husserl and the foundations of quantum mechanics

The London and Bauer monograph occupies a central place in the debate concerning the quantum measurement problem. Gavroglu has previously noted the influence of Husserlian phenomenology on London's scientific work. However, he has not explored the full extent of this influence in the monograph itself. I begin this paper by outlining the important role played by the monograph in the debate. In effect, it acted as a kind of ‘lens’ through which the standard, or Copenhagen, ‘solution’ to the measurement problem came to be perceived and, as such, it was robustly criticized, most notably by Putnam and Shimony. I then spell out the Husserlian understanding of consciousness in order to illuminate the traces of this understanding within the London and Bauer text. This, in turn, yields a new perspective on this ‘solution’ to the measurement problem, one that I believe has not been articulated before and, furthermore, which is immune to the criticisms of Putnam and Shimony.     

“A dedicated missionary”. Charles Galton Darwin and the new quantum mechanics in Britain

In this paper I discuss the work on quantum physics and wave mechanics by Charles Galton Darwin, a Cambridge wrangler of the last generation, as a case study to better understand the early reception of quantum physics in Britain. I argue that his proposal in the early 1920s to abandon the strict conservation of energy, as well as his enthusiastic embracement of wave mechanics at the end of the decade, can be easily understood by tracing his ontological and epistemological commitments to his early training in the Cambridge Mathematical Tripos. I also suggest that Darwin's work cannot be neglected in a study of quantum physics in Britain, since he was one of very few fellows of the Royal Society able to judge and explain quantum physics and quantum mechanics.     

A new interpretation of Shen Kuo’s Ying Biao Yi

This article analyzes the method of orienting a gnomon developed by the eleventh century Chinese scientist Shen Kuo and described in his Ying Biao Yi. I argue that Shen Kuo’s criticism of the traditional orientation method was built on his belief that the earth is flat. The method Shen Kuo presented aims first to find the center of the earth, and only then to orient the gnomon to the cardinal directions. In addition, Shen Kuo developed two new techniques for improving observation with a gnomon: the first method sets the gnomon in a closed chamber with only a small slit for the entrance of the noon sunlight, thereby reducing ambient light and making it easier to see the gnomon’s shadow. Shen’s other innovation is to use a second gnomon together with the first. This can greatly weaken the shadow’s penumbra.     

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.”     

Niels Bohr as philosopher of experiment: Does decoherence theory challenge Bohr׳s doctrine of classical concepts?

Niels Bohr׳s doctrine of the primacy of “classical concepts” is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr׳s doctrine was primarily an epistemological thesis, derived from his understanding of the functional role of experiment. A hitherto largely overlooked disagreement between Bohr and Heisenberg about the movability of the “cut” between measuring apparatus and observed quantum system supports the view that, for Bohr, such a cut did not originate in dynamical (ontological) considerations, but rather in functional (epistemological) considerations. As such, both the motivation and the target of Bohr׳s doctrine of classical concepts are of a fundamentally different nature than what is understood as the dynamical problem of the quantum-to-classical transition. Our analysis suggests that, contrary to claims often found in the literature, Bohr׳s doctrine is not, and cannot be, at odds with proposed solutions to the dynamical problem of the quantum–classical transition that were pursued by several of Bohr׳s followers and culminated in the development of decoherence theory.     

On the relation between the probabilistic characterization of the common cause and Bell׳s notion of local causality

In this paper the relation between the standard probabilistic characterization of the common cause (used for the derivation of the Bell inequalities) and Bell׳s notion of local causality will be investigated in the isotone net framework borrowed from algebraic quantum field theory. The logical role of two components in Bell׳s definition will be scrutinized; namely that the common cause is localized in the intersection of the past of the correlated events; and that it provides a complete specification of the ‘beables’ of this intersection.