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.     

Vital Instability: Life and Free Will in Physics and Physiology, 1860–1880

During the period 1860–1880, a number of physicists and mathematicians, including Maxwell, Stewart, Cournot and Boussinesq, used theories formulated in terms of physics to argue that the mind, the soul or a vital principle could have an impact on the body. This paper shows that what was primarily at stake for these authors was a concern about the irreducibility of life and the mind to physics, and that their theories can be regarded primarily as reactions to the law of conservation of energy, which was used among others by Helmholtz and Du Bois-Reymond as an argument against the possibility of vital and mental causes in physiology. In light of this development, Maxwell, Stewart, Cournot and Boussinesq showed that it was still possible to argue for the irreducibility of life and the mind to physics, through an appeal to instability or indeterminism in physics: if the body is an unstable or physically indeterministic system, an immaterial principle can act through triggering or directing motions in the body, without violating the laws of physics.     

International Scientific Cooperation During the 1930s. Bruno Rossi and the Development of the Status of Cosmic Rays into a Branch of Physics

During the 1920s and 1930s, Italian physicists established strong relationships with scientists from other European countries and the United States. The career of Bruno Rossi, a leading personality in the study of cosmic rays and an Italian pioneer of this field of research, provides a prominent example of this kind of international cooperation. Physics underwent major changes during these turbulent years, and the traditional internationalism of physics assumed a more institutionalized character. Against this backdrop, Rossi's early work was crucial in transforming the study of cosmic rays into a branch of modern physics. His friendly relationships with eminent scientists — notably Enrico Fermi, Walther Bothe, Werner Heisenberg, Hans Bethe, and Homi Bhabha — were instrumental both for the exchange of knowledge about experimental practices and theoretical discussions, and for attracting the attention of physicists such as Arthur Compton, Louis Leprince-Ringuet, Pierre Auger and Patrick Blackett to the problem of cosmic rays. Relying on material from different archives in Europe and the United States, this case study aims to provide a glimpse of the intersection between national and international dimensions during the 1930s, at a time when the study of cosmic rays was still very much in its infancy, strongly interlaced with nuclear physics, and full of uncertain, contradictory, and puzzling results. Nevertheless, as a source of high-energy particles it became a proving ground for testing the validity of the laws of quantum electrodynamics, and made a fundamental contribution to the origins of particle physics.     

Symmetries and the explanation of conservation laws in the light of the inverse problem in Lagrangian mechanics

Many have thought that symmetries of a Lagrangian explain the standard laws of energy, momentum, and angular momentum conservation in a rather straightforward way. In this paper, I argue that the explanation of conservation laws via symmetries of Lagrangians involves complications that have not been adequately noted in the philosophical literature and some of the physics literature on the subject. In fact, such complications show that the principles that are commonly appealed to to drive explanations of conservation laws are not generally correct without caveats. I hope here to give a clearer picture of the relationship between symmetries and conservation laws in Lagrangian mechanics via an examination of the bearing that results in the inverse problem in the calculus of variations have on this topic.     

Giulio Racah and theoretical physics in Jerusalem

The present article considers Giulio Racah’s contributions to general physical theory and his establishment of theoretical physics as a discipline in Israel. Racah developed mathematical methods that are based on tensor operators and continuous groups. These methods revolutionized spectroscopy. Currently, these are essential research tools in atomic, nuclear and elementary particle physics. He himself applied them to modernizing theoretical atomic spectroscopy. Racah laid the foundations of theoretical physics in Israel. He educated several generations of Israeli physicists, and put Israel on the world map of physics.     

Cosmology,particles, and the unity of science

During the last three decades, there has been a growing realization among physicists and cosmologists that the relation between particle physics and cosmology may constitute yet another successful example of the unity of science. However, there are important conceptual problems in the unification of the two disciplines, e.g. in connection with the cosmological constant and the conjecture of inflation. The present article will outline some of these problems, and argue that the victory for the unity of science in the context of cosmology and particle physics is still far from obvious.     

Properties and causes: An approach to the problem of hypothesis in the scientific methodology of Sir Isaac Newton

This article considers the differential absorption and integration of refugee physicists into various countries during the 1930s, and the social and intellectual factors responsible for this, focusing particularly on the social functions of the British and American university at that period, as well as continuing ideological struggles in the Soviet Union. More generally, the issue of the relative absorption of refugee physicists is used to examine the nature of the physics communities and other institutions of the host societies.     

To envision a new particle or change an existing law? Hypothesis formation and anomaly resolution for the curious case of the β decay spectrum

This paper addresses the question of how scientists determine which type of hypothesis is most suitable for tackling a particular problem by examining the historical case of the anomalous β spectrum in early nuclear physics (1927–1934), a puzzle that occasioned the most diverse hypotheses amongst physicists at the time. It is shown that such determinations are most often implicitly informed by scientists' individual perspectives on the structural relations between the various elements of the theory and the problem at hand. In addition to this main result, it is suggested that Wolfgang Pauli's neutrino idea may well have been an adaptation of Ernst Rutherford's original and older neutron idea, which would provide evidence that the adaptation of older ideas is a more common practice than is often thought.     

The priority of internal symmetries in particle physics

In this paper, I try to decipher the role of internal symmetries in the ontological maze of particle physics. The relationship between internal symmetries and laws of nature is discussed within the framework of “Platonic realism.” The notion of physical “structure” is introduced as representing a deeper ontological layer behind the observable world. I argue that an internal symmetry is a structure encompassing laws of nature. The application of internal symmetry groups to particle physics came about in two revolutionary steps. The first was the introduction of the internal symmetries of hadrons in the early 1960s. These global and approximate symmetries served as means of bypassing the dynamics. I argue that the realist could interpret these symmetries as ontologically prior to the hadrons. The second step was the gauge revolution in the 1970s, where symmetries became local and exact and were integrated with the dynamics. I argue that the symmetries of the second generation are fundamental in the following two respects: (1) According to the so-called “gauge argument,” gauge symmetry dictates the existence of gauge bosons, which determine the nature of the forces. This view, which has been recently criticized by some philosophers, is widely accepted in particle physics at least as a heuristic principle. (2) In view of grand unified theories, the new symmetries can be interpreted as ontologically prior to baryon matter.     

Model choice and crucial tests. On the empirical epistemology of the Higgs discovery

Our paper discusses the epistemic attitudes of particle physicists on the discovery of the Higgs boson at the Large Hadron Collider (LHC). It is based on questionnaires and interviews made shortly before and shortly after the discovery in 2012. We show, to begin with, that the discovery of a Standard Model (SM) Higgs boson was less expected than is sometimes assumed. Once the new particle was shown to have properties consistent with SM expectations – albeit with significant experimental uncertainties –, there was a broad agreement that ‘a’ Higgs boson had been found. Physicists adopted a two-pronged strategy. On the one hand, they treated the particle as a SM Higgs boson and tried to establish its properties with higher precision; on the other hand, they searched for any hints of physics beyond the SM. This motivates our first philosophical thesis: the Higgs discovery, being of fundamental importance and establishing a new kind of particle, represented a crucial experiment if one interprets this notion in an appropriate sense. Duhemian underdetermination is kept at bay by embedding the LHC into the tradition of previous precision experiments and the experimental strategies thus established. Second, our case study suggests that criteria of theory (or model) preference should be understood as epistemic and pragmatic values that have to be weighed in factual research practice. The Higgs discovery led to a shift from pragmatic to epistemic values in physicists’ assessment of the mechanisms of electroweak symmetry breaking. Complex criteria, such as naturalness, combine epistemic and pragmatic values, but are coherently applied by the community.     

‘Let the stars shine in peace!’ Niels Bohr and stellar energy, 1929–1934

Faced with various anomalies related to nuclear physics in particular, in 1929 Niels Bohr suggested that energy might not be conserved in the atomic nucleus and the processes involving it. By this radical proposal he hoped not only to get rid of the anomalies but also saw a possibility to explain a puzzle in astrophysics, namely the energy generated by stars. Bohr repeated his suggestion of stellar energy arising ex nihilo on several occasions but without ever going into detail. In fact, it is not very clear what he meant or how seriously he took the stellar energy hypothesis. This paper relates Bohr's comments to the period's attempts to find a mechanism for stellar energy and also to the role played by astrophysics at the Copenhagen institute. Moreover, it looks at how Bohr's hypothesis was received not only by physicists but also by astronomers. In this regard the disciplinary status of astrophysics and its contemporary relation to the new quantum mechanics is of relevance. It turns out that, with very few exceptions, the hypothesis was met with silence by astronomers and astrophysicists concerned with the problem of stellar energy production. And yet, for a brief period of time it did have an impact on how physicists thought about the interior of the stars.     

The five problems of irreversibility

Thermodynamics has a clear arrow of time, characterized by the irreversible approach to equilibrium. This stands in contrast to the laws of microscopic theories, which are invariant under time-reversal. Foundational discussions of this “problem of irreversibility” often focus on historical considerations, and do therefore not take results of modern physical research on this topic into account. In this article, I will close this gap by studying the implications of dynamical density functional theory (DDFT), a central method of modern nonequilibrium statistical mechanics not previously considered in philosophy of physics, for this debate. For this purpose, the philosophical discussion of irreversibility is structured into five problems, concerned with the source of irreversibility in thermodynamics, the definition of equilibrium and entropy, the justification of coarse-graining, the approach to equilibrium and the arrow of time. For each of these problems, it is shown that DDFT provides novel insights that are of importance for both physicists and philosophers of physics.     

Genesis of Karl Popper's EPR-like experiment and its resonance amongst the physics community in the 1980s

I present the reconstruction of the involvement of Karl Popper in the community of physicists concerned with foundations of quantum mechanics, in the 1980s. At that time Popper gave active contribution to the research in physics, of which the most significant is a new version of the EPR thought experiment, alleged to test different interpretations of quantum mechanics. The genesis of such an experiment is reconstructed in detail, and an unpublished letter by Popper is reproduced in the present paper to show that he formulated his thought experiment already two years before its first publication in 1982. The debate stimulated by the proposed experiment as well as Popper's role in the physics community throughout 1980s is here analysed in detail by means of personal correspondence and publications.     

Mathematical understanding and the physical sciences

The author claims to have developed interactional expertise in gravitational wave physics without engaging with the mathematical or quantitative aspects of the subject. Is this possible? In other words, is it possible to understand the physical world at a high enough level to argue and make judgments about it without the corresponding mathematics? This question is empirically approached in three ways: (i) anecdotes about non-mathematical physicists are presented; (ii) the author undertakes a reflective reading of a passage of physics, first without going through the maths and then after engaging with it and discusses the difference between the experiences; (iii) the aforementioned exercise gives rise to a table of Levels of Understanding of mathematics, and physicists are asked about the level mathematical understanding they applied when they last read a paper. Each phase of empirical research suggests that mathematics is not as central to gaining an understanding of physics as it is often said to be. This does not mean that mathematics is not central to physics, merely that it is not essential for every physicist to be an accomplished mathematician, and that a division of labour model is adequate. This, in turn, suggests that a stream of undergraduate physics education with fewer mathematical hurdles should be developed, making it easier to train wider groups of people in physical science comprehension.     

The making of an intrinsic property: “Symmetry heuristics” in early particle physics

Mathematical invariances, usually referred to as “symmetries”, are today often regarded as providing a privileged heuristic guideline for understanding natural phenomena, especially those of micro-physics. The rise of symmetries in particle physics has often been portrayed by physicists and philosophers as the “application” of mathematical invariances to the ordering of particle phenomena, but no historical studies exist on whether and how mathematical invariances actually played a heuristic role in shaping microphysics. Moreover, speaking of an “application” of invariances conflates the formation of concepts of new intrinsic degrees of freedom of elementary particles with the formulation of models containing invariances with respect to those degrees of freedom. I shall present here a case study from early particle physics (ca. 1930–1954) focussed on the formation of one of the earliest concepts of a new degree of freedom, baryon number, and on the emergence of the invariance today associated to it. The results of the analysis show how concept formation and “application” of mathematical invariances were distinct components of a complex historical constellation in which, beside symmetries, two further elements were essential: the idea of physically conserved quantities and that of selection rules. I shall refer to the collection of different heuristic strategies involving selection rules, invariances and conserved quantities as the “SIC-triangle” and show how different authors made use of them to interpret the wealth of new experimental data. It was only a posteriori that the successes of this hybrid “symmetry heuristics” came to be attributed exclusively to mathematical invariances and group theory, forgetting the role of selection rules and of the notion of physically conserved quantity in the emergence of new degrees of freedom and new invariances. The results of the present investigation clearly indicate that opinions on the role of symmetries in fundamental physics need to be critically reviewed in the spirit of integrated history and philosophy of science.     

Laws and meta-laws of nature: Conservation laws and symmetries

Symmetry principles are commonly said to explain conservation laws—and were so employed even by Lagrange and Hamilton, long before Noether's theorem. But within a Hamiltonian framework, the conservation laws likewise entail the symmetries. Why, then, are symmetries explanatorily prior to conservation laws? I explain how the relation between ordinary (i.e., first-order) laws and the facts they govern (a relation involving counterfactuals) may be reproduced one level higher: as a relation between symmetries and the ordinary laws they govern. In that event, symmetries are meta-laws; they are not mere byproducts of the dynamical and force laws. Symmetries then explain conservation laws whereas conservation laws lack the modal status to explain symmetries. I elaborate the variety of natural necessity that meta-laws would possess. Proposed metaphysical accounts of natural law should aim to accommodate the distinction between meta-laws and mere byproducts of the laws just as they must accommodate the distinction between laws and accidents.     

Experimental : The double standard in the quantum-information approach to the foundations of quantum theory

Among the alternatives of non-relativistic quantum mechanics (NRQM) there are those that give different predictions than quantum mechanics in yet-untested circumstances, while remaining compatible with current empirical findings. In order to test these predictions, one must isolate one's system from environmental induced decoherence, which, on the standard view of NRQM, is the dynamical mechanism that is responsible for the ‘apparent’ collapse in open quantum systems. But while recent advances in condensed-matter physics may lead in the near future to experimental setups that will allow one to test the two hypotheses, namely genuine collapse vs. decoherence, hence make progress toward a solution to the quantum measurement problem, those philosophers and physicists who are advocating an information-theoretic approach to the foundations of quantum mechanics are still unwilling to acknowledge the empirical character of the issue at stake. Here I argue that in doing so they are displaying an unwarranted double standard.     

The role of heuristic appraisal in conflicting assessments of string theory

Over the last three decades, string theory has emerged as one of the leading hopes for a consistent theory of quantum gravity that unifies particle physics with general relativity. Despite the fact that string theory has been a thriving research program for the better part of three decades, it has been subjected to extensive criticism from a number of prominent physicists. The aim of this paper is to obtain a clearer picture of where the conflict lies in competing assessments of string theory, through a close reading of the argumentative strategies employed by protagonists on both sides. Although it has become commonplace to construe this debate as stemming from different attitudes to the absence of testable predictions, we argue that this presents an overly simplified view of the controversy, which ignores the critical role of heuristic appraisal. While string theorists and their defenders see the theoretical achievements of the string theory program as providing strong indication that it is ‘on the right track’, critics have challenged such claims, by calling into question the status of certain ‘solved problems’ and its purported ‘explanatory coherence’. The debates over string theory are therefore particularly instructive from a philosophical point of view, not only because they offer important insights into the nature of heuristic appraisal and theoretical progress, but also because they raise deep questions about what constitutes a solved problem and an explanation in fundamental physics.     

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.