Interpretation neutrality in the classical domain of quantum theory

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie–Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified picture that treats reduction as a matter of simply taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest׳s Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest׳s Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity.     

Ehrenfest’s adiabatic theory and the old quantum theory, 1916–1918

I discuss in detail the contents of the adiabatic hypothesis, formulated by Ehrenfest in 1916. I focus especially on the paper he published in 1916 and 1917 in three different journals. I briefly review its precedents and thoroughly analyze its reception until 1918, including Burgers’s developments and Bohr’s assimilation of them into his own theory. I show that until 1918 the adiabatic hypothesis did not play an important role in the development of quantum theory. An erratum to this article can be found at     

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.     

Einstein’s quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics

In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924–1925. Although it failed to attract the attention of Einstein’s contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein’s quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein’s confusion with his initial success in extending Bose’s results and in realizing the consequences of what later came to be called Bose–Einstein statistics. We discuss Einstein’s motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein’s belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as well as of dimensional analysis. These techniques were well known to Einstein from earlier work on Wien’s displacement law, Planck’s radiation theory and the specific heat of solids. We also investigate the possible role of Ehrenfest in the gestation of the theory.     

Multiplicity in Everett׳s interpretation of quantum mechanics

Everett׳s interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves unitarily. It then claims that whenever an observable is measured, all possible results of the measurement exist. This notion of multiplicity has been understood in different ways by proponents of Everett׳s theory. In fact the spectrum of opinions on various ontological questions raised by Everett׳s approach is rather large, as we attempt to document in this critical review. We conclude that much remains to be done to clarify and specify Everett׳s approach.     

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.     

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.     

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.     

From aether impulse to QED: Sommerfeld and the Bremsstrahlen theory

The radiation that is due to the braking of charged particles has been in the focus of theoretical physics since the discovery of X-rays by the end of the 19th century. The impact of cathode rays in the anti-cathode of an X-ray tube that resulted in the production of X-rays led to the view that X-rays are aether impulses spreading from the site of the impact. In 1909, Arnold Sommerfeld calculated from Maxwell׳s equations the angular distribution of electromagnetic radiation due to the braking of electrons. He thereby coined the notion of “Bremsstrahlen.” In 1923, Hendrik A. Kramers provided a quantum theoretical explanation of this process by means of Bohr׳s correspondence principle. With the advent of quantum mechanics the theory of bremsstrahlung became a target of opportunity for theorists like Yoshikatsu Sugiura, Robert Oppenheimer, and–again–Sommerfeld, who presented in 1931 a comprehensive treatise on this subject. Throughout the 1930s, Sommerfeld׳s disciples in Munich and elsewhere extended and improved the bremsstrahlen theory. Hans Bethe and Walter Heitler, in particular, in 1934 presented a theory that was later regarded as “the most important achievement of QED in the 1930s” (Freeman Dyson). From a historical perspective the bremsstrahlen problem may be regarded as a probe for the evolution of theories in response to revolutionary changes in the underlying principles.     

QED and the man who didn׳t make it: Sidney Dancoff and the infrared divergence

Sidney Dancoff׳s paper “On Radiative Corrections for Electron Scattering” is generally viewed in the secondary literature as a failed attempt to develop renormalized quantum electrodynamics (QED) a decade early, an attempt that failed because of a mistake that Dancoff made. I will discuss Dancoff׳s mistake and try to reconstruct why it occurred, by relating it to the usual practices of the quantum field theory of his time. I will also argue against the view that Dancoff was on the verge of developing renormalized QED and will highlight the conceptual divides that separate Dancoff׳s work from the QED of the late 1940s. I will finally discuss how the established view of Dancoff׳s paper came to be and how the reading of this specific anecdote relates to more general assessments of the conceptual advances of the late 1940s (covariant techniques, renormalization), in particular to their assessment as being conservative rather than revolutionary.     

Measurement,coordination, and the relativized a priori

The problem of measurement is a central issue in the epistemology and methodology of the physical sciences. In recent literature on scientific representation, large emphasis has been put on the “constitutive role” played by measurement procedures as forms of representation. Despite its importance, this issue hardly finds any mention in writings on constitutive principles, viz. in Michael Friedman׳s account of relativized a priori principles. This issue, instead, was at the heart of Reichenbach׳s analysis of coordinating principles that has inspired Friedman׳s interpretation. This paper suggests that these procedures should have a part in an account of constitutive principles of science, and that they could be interpreted following the intuition originally present (but ultimately not fully developed) in Reichenbach׳s early work.     

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.     

The constitutive a priori and the distinction between mathematical and physical possibility

This paper is concerned with Friedman׳s recent revival of the notion of the relativized a priori. It is particularly concerned with addressing the question as to how Friedman׳s understanding of the constitutive function of the a priori has changed since his defence of the idea in his Dynamics of Reason. Friedman׳s understanding of the a priori remains influenced by Reichenbach׳s initial defence of the idea; I argue that this notion of the a priori does not naturally lend itself to describing the historical development of space-time physics. Friedman׳s analysis of the role of the rotating frame thought experiment in the development of general relativity – which he suggests made the mathematical possibility of four-dimensional space-time a genuine physical possibility – has a central role in his argument. I analyse this thought experiment and argue that it is better understood by following Cassirer and placing emphasis on regulative principles. Furthermore, I argue that Cassirer׳s Kantian framework enables us to capture Friedman׳s key insights into the nature of the constitutive a priori.     

Space–time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry,conventionality, and underdetermination

What if gravity satisfied the Klein–Gordon equation? Both particle physics from the 1920–30s and the 1890s Neumann–Seeliger modification of Newtonian gravity with exponential decay suggest considering a “graviton mass term” for gravity, which is algebraic in the potential. Unlike Nordström׳s “massless” theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman–Cunningham conformal group. It therefore exhibits the whole of Minkowski space–time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein׳s principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the ‘true’ geometry, one might wonder, in line with Poincaré׳s modal conventionality argument? Infinitely many theories exhibit this bimetric ‘geometry,’ all with the total stress–energy׳s trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers–Pirani–Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities—indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein׳s equations along the lines of Einstein׳s newly re-appreciated “physical strategy” and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz found in 1939). The Putnam–Grünbaum debate on conventionality is revisited with an emphasis on the broad modal scope of conventionalist views. Massive scalar gravity thus contributes to a historically plausible rational reconstruction of much of 20th–21st century space–time philosophy in the light of particle physics. An appendix reconsiders the Malament–Weatherall–Manchak conformal restriction of conventionality and constructs the ‘universal force’ influencing the causal structure.Subsequent works will discuss how massive gravity could have provided a template for a more Kant-friendly space–time theory that would have blocked Moritz Schlick׳s supposed refutation of synthetic a priori knowledge, and how Einstein׳s false analogy between the Neumann–Seeliger–Einstein modification of Newtonian gravity and the cosmological constant Λ generated lasting confusion that obscured massive gravity as a conceptual possibility.     

Becker–Blaschke problem of space

In a letter to Weyl, Becker proposed a new way to solve the problem of space in the relativistic context. This is the result of Becker׳s encounter with the two traditions of thinking about space: Husserlian transcendental phenomenology and Blaschke׳s equiaffine differential geometry. I reconstruct the mathematical content of the Becker–Blaschke solution to the problem of space and highlight the philosophical ideas that guide this construction. This permits me to underline some common properties of Riemannian and Minkowskian manifolds in terms of an unusual notion of isotropy. Finally, I will use this construction as a support to analyze several philosophical differences between Weyl׳s and Becker׳s proposals.     

Introduction to the special issue Hermann Weyl and the philosophy of the ‘New Physics’

This Special Issue Hermann Weyl and the Philosophy of the ‘New Physics’ has two main objectives: first, to shed fresh light on the relevance of Weyl's work for modern physics and, second, to evaluate the importance of Weyl's work and ideas for contemporary philosophy of physics. Regarding the first objective, this Special Issue emphasizes aspects of Weyl's work (e.g. his work on spinors in n dimensions) whose importance has recently been emerging in research fields across both mathematical and experimental physics, as well as in the history and philosophy of physics. Regarding the second objective, this Special Issue addresses the relevance of Weyl's ideas regarding important open problems in the philosophy of physics, such as the problem of characterizing scientific objectivity and the problem of providing a satisfactory interpretation of fundamental symmetries in gauge theories and quantum mechanics. In this Introduction, we sketch the state of the art in Weyl studies and we summarize the content of the contributions to the present volume.     

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’.     

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.     

Quantum probability and many worlds

We discuss the meaning of probabilities in the many worlds interpretation of quantum mechanics. We start by presenting very briefly the many worlds theory, how the problem of probability arises, and some unsuccessful attempts to solve it in the past. Then we criticize a recent attempt by Deutsch to derive the quantum mechanical probabilities from the non-probabilistic parts of quantum mechanics and classical decision theory. We further argue that the Born probability does not make sense even as an additional probability rule in the many worlds theory. Our conclusion is that the many worlds theory fails to account for the probabilistic statements of standard (collapse) quantum mechanics.