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The topic is the history of the concepts of equivalence relation, Cauchy sequence, and metric space. The thesis is that disused definitions of these notions could profitably be revived.
The history of the canonical basis and crystal basis of a quantized enveloping algebra and its representations is presented
The histories of core-collapse supernova theory and of neutrino physics have paralleled one another for more than seventy years. Almost every development in neutrino physics necessitated modifications in supernova models. What has emerged is a complex and rich dynamical scenario for stellar death that is being progressively better tested by increasingly sophisiticated computer simulations. Though there is still much to learn about the agency and details of supernova explosions, whatever final theory emerges will have the neutrino at its core. I summarize in this brief contribution some of the salient developments in neutrino physics as they related to supernova theory, while avoiding any attempt to review the hundreds of pivotal papers that have pushed supernova theory forward. My goal has been merely to highlight the debt of supernova astrophysics to neutrino physics.
String theorists are certain that they are practicing physicists. Yet, some of their recent critics deny this. This paper argues that this conflict is really about who holds authority in making rational judgment in theoretical physics. At bottom, the conflict centers on the question: who is a proper physicist? To illustrate and understand the differing opinions about proper practice and identity, we discuss different appreciations of epistemic virtues and explanation among string theorists and their critics, and how these have been sourced in accounts of Einstein's biography. Just as Einstein is claimed by both sides, historiography offers examples of both successful and unsuccessful non-empirical science. History of science also teaches that times of conflict are often times of innovation, in which novel scholarly identities may come into being. At the same time, since the contributions of Thomas Kuhn historians have developed a critical attitude towards formal attempts and methodological recipes for epistemic demarcation and justification of scientific practice. These are now, however, being considered in the debate on non-empirical physics.
On a centennial timescale, solar activity was quantified based on records of instrumental sunspot observations. This article briefly discusses several aspects of the recent archival investigations of historical sunspot records in the 17th to 18th centuries. This article also reviews the recent updates for the active day fraction and positions of the reported sunspot groups of the Maunder Minimum to show their significance within the observational history. These archival investigations serve as base datasets for reconstructing solar activity.
Traditional interpretations of quantum theory in terms of wave function collapse are particularly unappealing when considering the universe as a whole, where there is no clean separation between classical observer and quantum system and where the description is inherently relativistic. As an alternative, the consistent histories approach provides an attractive "no collapse" interpretation of quantum physics. Consistent histories can also be linked to path-integral formulations that may be readily generalized to the relativistic case. A previous paper described how, in such a relativistic spacetime path formalism, the quantum history of the universe could be considered to be an eignestate of the measurements made within it. However, two important topics were not addressed in detail there: a model of measurement processes in the context of quantum histories in spacetime and a justification for why the probabilities for each possible cosmological eigenstate should follow Born's rule. The present paper addresses these topics by showing how Zurek's concepts of einselection and envariance can be applied in the context of relativistic spacetime and quantum histories. The result is a model
We show that representations of the group of spacetime diffeomorphism and the Dirac algebra both arise in a phase-space histories version of canonical general relativity. This is the general-relativistic analogue of the novel time structure introduced previously in history theory: namely, the existence in non-relativistic physics of two types of time translation; and the existence in relativistic field theory of two distinct Poincare groups.
We show that the relativistic analogue of the two types of time translation in a non-relativistic history theory is the existence of two distinct Poincaré groups. The `internal' Poincaré group is analogous to the one that arises in the standard canonical quantisation scheme; the `external' Poincaré group is similar to the group that arises in a Lagrangian description of the standard theory. In particular, it performs explicit changes of the spacetime foliation that is implicitly assumed in standard canonical field theory.
We show that the Bub-Clifton uniqueness theorem for 'no collapse' interpretations of quantum mechanics (Studies in the History and Philosophy of Modern Physics 27, 181-219 (1996)) can be proved without the 'weak separability' assumption.
A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values for projection operators (such as values less than zero) always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application of Luders' Rule. It is argued that an assumption of reverse causality (a form of time symmetry) implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterised as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions.