Bargmann’s superselection rule, which forbids the existence of superpositions of states with different mass and, therefore, implies the impossibility of describing unstable particles in non-relativistic quantum mechanics, arises as a consequence of demanding Galilean covariance of Schrödinger’s equation. However, the usual Galilean transformations inadequately describe the symmetries of non-relativistic quantum mechanics since they can produce phases in the wavefunction which are relativistic time contraction remnants and therefore, cannot be physically interpreted within the theory. In this paper we (...) review the incompatibility between Bargmann’s rule and Lorentz transformations in the low-velocities limit, we analyze its classical origin and we show that the Extended Galilei group characterizes better the symmetries of the theory. Furthermore, we claim that a proper description of non-relativistic quantum mechanics requires a modification of the notion of spacetime in the corresponding limit, which is noticeable only for quantum particles. (shrink)

The overaraching goal of this paper is to elucidate the nature of superselection rules in a manner that is accessible to philosophers of science and that brings out the connections between superselection and some of the most fundamental interpretational issues in quantum physics. The formalism of von Neumann algebras is used to characterize three different senses of superselection rules (dubbed, weak, strong, and very strong) and to provide useful necessary and sufficient conditions for each sense. It is (...) then shown how the Haag–Kastler algebraic approach to quantum physics holds the promise of a uniform and comprehensive account of the origin of superselection rules. Some of the challenges that must be met before this promise can be kept are discussed. The focus then turns to the role of superselection rules in solutions to the measurement problem and the emergence of classical properties. It is claimed that the role for “hard” superselection rules is limited, but “soft” (a.k.a. environmental) superselection rules or N. P. Landsman’s situational superselection rules may have a major role to play. Finally, an assessment is given of the recently revived attempts to deconstruct superselection rules. (shrink)

This note provides a summary of the meaning of the term `Superselection Rule' in Quantum Mechanics and Quantum-Field Theory. It is a contribution to the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, edited by Friedel Weinert, Klaus Hentschel, Daniel Greenberger, and Brigitte Falkenburg, to be published by Springer Verlag.

A dynamical analysis of standard procedures for subensemble selection is used to show that the state restriction violation proposal in Part I of the paper cannot be realized by employing familiar correlation schemes. However, it is shown that measurement of an observable not commuting with the superselection operator is possible, a violation of the observable restrictions. This is interpreted as supporting the position that each of these restrictions is sufficient but not necessary for the superselection rule. The (...) results do constitute a proposal for superselection rule violation in theories requiring both restrictions, e.g., the axiomatic treatment by Bogolubov, Logunov, and Todorov. It is also concluded that superselection rules place restrictions on procedures for selective state preparations using correlations. More generally, it is conjectured that a mathematically conceivable decomposition of a given density operator does not necessarily represent a possibility for partitioning of the corresponding ensemble into subensembles by any physically realizable means. (shrink)

It is argued that preparation of a quantum state characterized by density operator ρ not commuting with a superselection operatorQ does not by itself constitute an instance of superselection rule violation. It would, however, be an instance of state restriction violation. It is held that superselection rule violation is only possible with simultaneous observable and state restriction violations. It is shown that it is a priori conceivable to subdivide an ensemble whose ρ satisfies[ρ, Q] = (...) 0 into subensembles whose density operators violate the state restrictions. The dynamics of the subdivision process is not considered. (shrink)

The term “frame of reference” is defined for both classical physics and quantum mechanics. The definition is the usual one, simply made explicit. It is used in the study of coherent superposition, and in particular the dependence on the observer (frame of reference) of the coherence of superposition of state vectors. This dependence is then used as the basis of an analysis of a criticism of previous work on the nonexistence of superselection rules. We again reach the conclusion that (...) they do not exist. (shrink)

A superselection rule advanced in the course of a quantum-mechanical treatment of some phenomenon is an assertion to the effect that the superposition principle of quantum mechanics is to be restricted in the application at hand. Superselection accounts of measurement all have in common a decision to represent the indicator states of detectors by eigenspaces of superselection operators named in a superselection rule, on the grounds that the states in question are states of a (...) so-called classical quantity and therefore not subject to quantum interference effects. By this strategy superselectionists of measurement expect to dispense with use of projection postulates in treatments of measurement. I shall argue that superselection accounts of measurement are self-contradictory, and that treatments of infinite systems, if they can avoid the contradiction, are not true superselection accounts. (shrink)

We attempt to clarify the main conceptual issues in approaches to ‘objectification’ or ‘measurement’ in quantum mechanics which are based on superselection rules. Such approaches venture to derive the emergence of classical ‘reality’ relative to a class of observers; those believing that the classical world exists intrinsically and absolutely are advised against reading this paper. The prototype approach (K. Hepp, Helv. Phys. Acta45 (1972), 237–248) where superselection sectors are assumed in the state space of the apparatus is shown (...) to be untenable. Instead, one should couple system and apparatus to an environment, and postulate superselection rules for the latter. These are motivated by the locality of any observer or other (actual or virtual) monitoring system. In this way ‘environmental’ solutions to the measurement problem (H.D. Zeh, Found. Phys.1 (1970), 69–76; W. H. Zurek, Phys. Rev.D26 (1982), 1862–1880 and Progr. Theor. Phys.89 (1993), 281–312) become consistent and acceptable, too. Points of contact with the modal interpretation are briefly discussed. We propose a minimal value attribution to observables in theories with superselection rules, in which only central observables have properties. In particular, the eigenvector-eigenvalue link is dropped. This is mainly motivated by Ockham's razor. (shrink)

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, (...) we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix. (shrink)

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox “absolute” quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling (...) a long-standing debate on the subject. (shrink)

An outstanding problem in so-called modal interpretations of quantum mechanics has been the specification of a dynamics for the properties introduced in such interpretations. We develop a general framework (in the context of the theory of stochastic processes) for specifying a dynamics for interpretations in this class, focusing on the modal interpretation by Vermaas and Dieks. This framework admits many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of them. This approach is applicable (...) to a wider class of theories, in particular, those using (discrete) strict effective—as in decoherence theory—superselection rules. (shrink)

Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection rules is the only non-signaling probabilistic theory in which (i) individual systems are Jordan algebras (equivalently, their cones of unnormalized states are homogeneous and self-dual), (ii) composites are locally tomographic (meaning that states are determined by the joint probabilities they assign to measurement outcomes on the component (...) systems) and (iii) at least one system has the structure of a qubit. Using this result, we also characterize finite dimensional quantum theory among probabilistic theories having the structure of a dagger-monoidal category. (shrink)

Nature seems to be such that we can describe it accurately with quantum theories of bosons and fermions alone, without resort to parastatistics. This has been seen as a deep mystery: paraparticles make perfect physical sense, so why don’t we see them in nature? We consider one potential answer: every paraparticle theory is physically equivalent to some theory of bosons or fermions, making the absence of paraparticles in our theories a matter of convention rather than a mysterious empirical discovery. We (...) argue that this equivalence thesis holds in all physically admissible quantum field theories falling under the domain of the rigorous Doplicher–Haag–Roberts approach to superselection rules. Inadmissible parastatistical theories are ruled out by a locality-inspired principle we call charge recombination. 1 Introduction2 Paraparticles in Quantum Theory3 Theoretical Equivalence3.1 Field systems in algebraic quantum field theory3.2 Equivalence of field systems4 A Brief History of the Equivalence Thesis4.1 The Green decomposition4.2 Klein transformations4.3 The argument of Drühl, Haag, and Roberts4.4 The Doplicher–Roberts reconstruction theorem5 Sharpening the Thesis6 Discussion6.1 Interpretations of Quantum Mechanics6.2 Structuralism and haecceities6.3 Paraquark theories. (shrink)

It is argued that the measurement problem reduces to the problem of modeling quasi-classical systems in a modified quantum mechanics with superselection rules. A measurement theorem is proved, demonstrating, on the basis of a principle for selecting the quantities of a system that are determinate (i.e., have values) in a given state, that after a suitable interaction between a systemS and a quasi-classical systemM, essentially only the quantity measured in the interaction and the indicator quantity ofM are determinate. The (...) theorem justifies interpreting the noncommutative algebra of observables of a quantum mechanical system as an algebra of “beables,” in Bell's sense. (shrink)

Recent work by Wan and McLean has shown that all quantum measurements may be reduced to local position measurements. Using an array of particle detectors as the measuring apparatus we show how a model employing superselection rules and unitary evolution leads to a single detector triggering in each act of measurement. We also present an explicit model of particle detection as a unitary ionization process producing a single ion in the detector, subsequent amplification of which to the visible can (...) be described adequately in classical terms. (shrink)

The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical behaviors are excluded a priori. A more general approach is to ask what other many-particle statistics are consistent with the indistinguishability of identical particles. This strategy offers a way to discuss possible violations of the Pauli Exclusion Principle, and it leads to some (...) interesting issues related to preparation of states and a superselection rule arising from invariance under the permutation group. (shrink)

Traditionally, there has been a clear distinction between classical systems and quantum systems, particularly in the mathematical theories used to describe them. In our recent work on macroscopic quantum systems, this distinction has become blurred, making a unified mathematical formulation desirable, so as to show up both the similarities and the fundamental differences between quantum and classical systems. This paper serves this purpose, with explicit formulations and a number of examples in the form of superconducting circuit systems. We introduce three (...) classes of physical systems with finite degrees of freedom: classical, standard quantum, and mixed quantum, and present a unified Hilbert space treatment of all three types of system. We consider the classical/quantum divide and the relationship between standard quantum and mixed quantum systems, illustrating the latter with a derivation of a superselection rule in superconducting systems. (shrink)

It is shown in this paper that a classical way of speaking about the past can be rejected when quantum systems without superselection rules are considered. To show this, use is made of a formal quantum language. The noncontextuality of quantum measurements is a presupposition of the quantum language. In addition, it is shown that introspective measurements, in contrast to the claims of Albert et al., do not violate the noncontextuality, and hence the result of rejecting the classical way (...) of speaking remains still applicable to introspective measurements. (shrink)

An extension of the Hurwitz transformation to a canonical transformation between phase spaces allows conversion of the five-dimensional Kepler problem into that of a constrained harmonic oscillator problem in eight dimensions. Thus a new regularization of the Kepler problem is established. Then, following Dirac, we quantize the extended phase space, imposing constraint conditions as superselection rules. In that way the interchangeability of the reduction and the quantization procedures is proved.

An integrated view concerning the probabilistic organization of quantum mechanics is obtained by systematic confrontation of the Kolmogorov formulation of the abstract theory of probabilities, with the quantum mechanical representationand its factual counterparts. Because these factual counterparts possess a peculiar spacetime structure stemming from the operations by which the observer produces the studied states (operations of state preparation) and the qualifications of these (operations of measurement), the approach brings forth “probability trees,” complex constructs with treelike spacetime support.Though it is strictly (...) entailed by confrontation with the abstract theory of probabilities as it now stands, the construct of a quantum mechanical probability treetransgresses this theory. It indicates the possibility of an extended abstract theory of probabilities including explicit representations of the cognitive operations involved in the probabilistic descriptions. So quantum mechanics appears to be neither a “normal” probabilistic theory nor an “abnormal” one, but a pioneering particular realization of afuture extended abstract theory of probabilities.The consequences of the integrated perception of the probabilistic organization of quantum mechanics are developed constructively. The current identifications of spectral decompositions, with superpositions of states, are removed. Then: (a) Inside the frontiers of the purely operational-observational orthodox formalism, operators of state preparation and the calculus with these are defined consistently with the definition and the calculus of quantum mechanical operators representing measurable dynamical quantities. This permits to grasp the physical meaning of superselection rules. Furthermore, a complement to the quantum theory of measurements is obtained. These prolongations of the orthodox formalism bring forth a “probabilistic incompleteness” of the quantum theory. (b) Beyond quantum mechanics as it now stands, a model is outlined that removes this probabilistic incompleteness, “the [particle + medium] individual model,”microscopic by certain aspects andcosmic by others.Globally, the approach draws attention upon the possibility and the interest of a general representation of the descriptions of any kind founded upon the explicit specification of the epistemic operations—with their spacetime features—by which the observer, who always is involved, produces the objects to be qualified and the qualifications of these. (shrink)

Powerful ultrastructural tools are providing new insights into neuronal circuits, revealing a wealth of anatomically‐defined synaptic connections. These wiring diagrams are incomplete, however, because functional connectivity is actively shaped by neuromodulators that modify neuronal dynamics, excitability, and synaptic function. Studies of defined neural circuits in crustaceans, C. elegans, Drosophila, and the vertebrate retina have revealed the ability of modulators and sensory context to reconfigure information processing by changing the composition and activity of functional circuits. Each ultrastructural connectivity map encodes multiple (...) circuits, some of which are active and some of which are latent at any given time. (shrink)

From one of the world's most important and enduring minds, Albert Einstein's ideas, thoughts, and philosophies on the world and its people. Copyright © Libri GmbH. All rights reserved.

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

Jesus of Nazareth, like Socrates, left nothing behind written by himself. Yet, the records of his teaching indicate a rich interest in dialogic pedagogy, reflected in his use of the parable, primarily an oral genre, as a dialogic provocation. Working at the interface of pedagogy, theology and philosophy, this article explores the parable of the Good Samaritan from the perspective of dialogic pedagogy. It employs an analytical approach termed diacognition, developed from the notions of dialogue, position and cognition, to analyse (...) the moves within the parable and the teaching situation in which it is located. The article explores how Jesus engages the dialogue of and around the parable to position and reposition his interlocutor, provoking a re-cognition of what it means to love one’s neighbour. It concludes by reflecting on the implications of this analysis for the relation of meaning to knowing and doing. (shrink)

Dialogue is a seminal concept within the work of the Brazilian adult education theorist, Paulo Freire, and the Russian literary critic and philosopher, Mikhail Bakhtin. While there are commonalities in their understanding of dialogue, they differ in their treatment of dialectic. This paper addresses commonalities and dissonances within a Bakhtin-Freire dialogue on the notions of dialogue and dialectic. It then teases out some of the implications for education theory and practice in relation to two South African contexts of learning that (...) facilitate the access to education of disadvantaged groups, one in higher education and the other in early childhood education. (shrink)

The information explosion and digital modes of learning often combine to inform the quest for the best ways of transforming information in digital form for pedagogical purposes. This quest has become more urgent and pervasive with the ‘turn’ to online learning in the context of COVID-19. This can result in linear, asynchronous, transmission-based modes of teaching and learning which commodify, package and deliver knowledge for individual ‘customers’. The primary concerns in such models are often technical and economic – technology as (...) a cost-effective ‘solution’ to educational challenges. In this paper I argue for the importance of dialogic learning space in teaching and learning by means of Information and Communication Technologies, whether in the form of fully online learning, blended learning or face-to-face encounters using ICT affordances. Although the 20th Century theorists Mikhail Bakhtin (1895–1975) and Hans-Georg Gadamer (1900–2002) produced their seminal works before the advent of ICTs, they were both concerned with the quality and authenticity of human engagement with texts and with other persons and contexts. Besides a shared interest in dialogue as an ontological feature of human life and being, they both used spatiotemporal concepts for understanding and interpreting texts. The article draws on Gadamer’s notions of dialogue and horizon, and Bakhtin’s notions of dialogue and chronotope, to conceptualize dialogic possibilities for online education. Its purpose is to provide a framework, grounded in Bakhtin’s and Gadamer’s ideas, for a dialogic approach to online teaching and learning in higher education. (shrink)