The relation between Kruskal and Schwarzschild coordinates is analogous to that between hyperboloid and de Sitter coordinates; the Kruskal diagram is analogous to the hyperboloid diagram; and the crossing over of horizons in Kruskal space is analogous to the well-known crossing over of the particle horizon and the event horizon in cosmology.

Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the "reality" of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e., inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what (...) a particle is, and how a "particle" will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the *very same* region of spacetime. We shall defend the idea that these representations provide *complementary descriptions* of the same state of the field against the claim that they embody completely *incommensurable theories* of the field. (shrink)

The physical, mathematical, and philosophical foundations of the quantum theory of free Bose fields in fixed general relativistic spacetimes are examined. It is argued that the theory is logically and mathematically consistent whereas semiclassical prescriptions for incorporating the back-reaction of the quantum field on the geometry lead to inconsistencies. Still, the relations and heuristic value of the semiclassical approach to canonical and covariant schemes of quantum gravity-plus-matter are assessed. Both conventional and rigorous formulations of the theory and of its principal (...) predictions, cosmological particle creation and horizon radiation, are expounded and compared. Special attention is devoted to spacetime properties needed for the existence or uniqueness of the relevant theoretical elements , renormalization of the stress tensor). The emergence of unitarily inequivalent representations in a single dynamical context is used as motivation for the introduction of the abstract $\rm C\sp{\*}$-algebraic axiomatic formalism. The operationalist and conventionalist claims of the original abstract algebraic program are criticized in favor of its tempered outgrowth, local quantum physics. The interpretation of the theory as a wave mechanics of classical field configurations, deriving from the Schrodinger representations of the abstract algebra, is discussed and is found superior, at least on the level of analogy, to particle or harmonic oscillator interpretations. Further, it is argued that the various detector results and the Fulling nonuniqueness problem do not undermine the particle concept in the ways commonly claimed. In particular, arguments are offered against the attribution of particle status to the Rindler quanta, against the physical realizability of the Rindler vacuum, and against the more general notion of observer-dependence as to the definition of 'particle' or 'vacuum'. However, the question of the ontological status of particles is raised in terms of the consistency of quantum field theory with non-reductive realism about particles, the latter being conceived as entities exhibiting attributes of discreteness and localizability. Two arguments against non-reductive realism about particles, one from axiomatic algebraic local quantum theory in Minkowski spacetime and one from quantum field theory in curved spacetime, are developed. (shrink)

It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots of all physical phenomena. The connection between this theory and Verlinde’s entropic gravity theory is also investigated.

I examine some problems standing in the way of a successful `field interpretation' of quantum field theory. The most popular extant proposal depends on the Hilbert space of `wavefunctionals.' But since wavefunctional space is unitarily equivalent to many-particle Fock space, two of the most powerful arguments against particle interpretations also undermine this form of field interpretation. IntroductionField Interpretations and Field OperatorsThe Wavefunctional InterpretationFields and Inequivalent Representations 4.1. The Rindler representation 4.2. Spontaneous symmetry breaking 4.3. Coherent representations The Fate of (...) Fields in Interacting QFTConclusions. (shrink)

We discuss the intertwined topics of Fulling non‐uniqueness and the Unruh effect. The Fulling quantization, which is in some sense the natural one for an observer uniformly accelerated through Minkowski spacetime to adopt, is often heralded as a quantization of the Klein‐Gordon field which is both physically relevant and unitarily inequivalent to the standard Minkowski quantization. We argue that the Fulling and Minkowski quantizations do not constitute a satisfactory example of physically relevant, unitarily inequivalent quantizations, and indicate what it would (...) take to settle the open question of whether a satisfactory example exists. A popular gloss on the Unruh effect has it that an observer uniformly accelerated through the Minkowski vacuum experiences a thermal flux of Rindler quanta. Taking the Unruh effect, so glossed, to establish that the notion of particle must be relativized to a reference frame, some would use it to demote the particle concept from fundamental status. We explain why technical results do not support the popular gloss and why the attempted demotion of the particle concept is both unsuccessful and unnecessary. Fulling non‐uniqueness and the Unruh effect merit attention despite these negative verdicts because they provide excellent vehicles for illustrating key concepts of quantum field theory and for probing foundational issues of considerable philosophical interest. (shrink)

We discuss the intertwined topics of Fulling non-uniqueness and the Unruh effect. The Fulling quantization, which is in some sense the natural one for an observer uniformly accelerated through Minkowski spacetime to adopt, is often heralded as a quantization of the Klein-Gordon field which is both physically relevant and unitarily inequivalent to the standard Minkowski quantization. We argue that the Fulling and Minkowski quantizations do not constitute a satisfactory example of physically relevant, unitarily inequivalent quantizations, and indicate what it would (...) take to settle the open question of whether a satisfactory example exists. A popular gloss on the Unruh effect has it that an observer uniformly accelerated through the Minkowski vacuum experiences a thermal flux of Rindler quanta. Taking the Unruh effect, so glossed, to establish that the notion of particle must be relativized to a reference frame, some would use it to demote the particle concept from fundamental status. We explain why technical results do not support the popular gloss and why the attempted demotion of the particle concept is both unsuccessful and unnecessary. Fulling non-uniqueness and the Unruh effect merit attention despite these negative verdicts because they provide excellent vehicles for illustrating key concepts of quantum field theory and for probing foundational issues of considerable philosophical interest. (shrink)

Rob Clifton was one of the most brilliant and productive researchers in the foundations and philosophy of quantum theory, who died tragically at the age of 38. Jeremy Butterfield and Hans Halvorson collect fourteen of his finest papers here, drawn from the latter part of his career (1995-2002), all of which combine exciting philosophical discussion with rigorous mathematical results. Many of these papers break wholly new ground, either conceptually or technically. Others resolve a vague controversy intoa precise technical problem, which (...) is then solved; still others solve an open problem that had been in the air for soem time. All of them show scientific and philosophical creativity of a high order, genuinely among the very best work in the field. The papers are grouped into four Parts. First come four papers about the modal interpretation of quantum mechanics. Part II comprises three papers on the foundations of algebraic quantum field theory, with an emphasis on entanglement and nonlocality. The two papers in Part III concern the concept of a particle in relativistic quantum theories. One paper analyses localization; the other analyses the Unruh effect (Rindler quanta) using the algebraic approach to quantum theory. Finally, Part IV contains striking new results about such central issues as complementarity, Bohr's reply to the EPR argument, and no hidden variables theorems; and ends with a philosophical survey of the field of quantum information. The volume includes a full bibliography of Clifton's publications. Quantum Entanglements offers inspiration and substantial reward to graduates and professionals in the foundations of physics, with a background in philosophy, physics, or mathematics. (shrink)

We propose a new quantum ontology, in which properties are the fundamental building blocks. In this property ontology physical systems are defined as bundles of type-properties. Not all elements of such bundles are associated with definite case-properties, and this accommodates the Kochen and Specker theorem and contextuality. Moreover, we do not attribute an identity to the type-properties, which gives rise to a novel form of the bundle theory. There are no “particles” in the sense of classical individuals in this (...) ontology, although the behavior of such individuals is mimicked in some circumstances. This picture leads in a natural way to the symmetrization postulates for systems of many “identical particles”. (shrink)

Dispositional monists believe that all properties are essentially causal. Recently, an overdetermination argument has been proposed by Trenton Merricks to support nihilism about ordinary objects. I argue that this argument can be extended to target both nihilism about ordinary objects and nihilism about physical particles when dispositional monism is assumed. It implies that a philosopher who both endorses dispositional monism and takes seriously the overdetermination argument should not believe in the existence of physical particles. I end up by (...) discussing possible objections. I suggest, then, that if we live in a world that is inhabited by causal properties but not by chairs and tables, then we also live in a world without electrons and quarks, a world of dispositional properties, that is, a world of causal fields. (shrink)

In his paper ``What is Structural Realism?'' James Ladyman drew a distinction between epistemological structural realism and metaphysical (or ontic) structural realism. He also drew a suggestive analogy between the perennial debate between substantivalist and relationalist interpretations of spacetime on the one hand, and the debate about whether quantum mechanics treats identical particles as individuals or as `non-individuals' on the other. In both cases, Ladyman's suggestion is that an ontic structural realist interpretation of the physics might be just what (...) is needed to overcome the stalemate. The main thesis of this paper is that, whatever the interpretative difficulties of generally covariant spacetime physics are, they do not support or suggest structural realism. In particular, I hope to show that there is in fact no analogy that supports a similar interpretation of the metaphysics of spacetime points and of quantum particles. (shrink)

I argue against the currently prevalent view that algebraic quantum field theory (AQFT) is the correct framework for philosophy of quantum field theory and that “conventional” quantum field theory (CQFT), of the sort used in mainstream particle physics, is not suitable for foundational study. In doing so, I defend that position that AQFT and CQFT should be understood as rival programs to resolve the mathematical and physical pathologies of renormalization theory, and that CQFT has succeeded in this task and AQFT (...) has failed. I also defend CQFT from recent criticisms made by Doreen Fraser. (shrink)

This volume brings together eleven essays by the distinguished philosopher of science, Peter Achinstein. The unifying theme is the nature of the philosophical problems surrounding the postulation of unobservable entities such as light waves, molecules, and electrons. How, if at all, is it possible to confirm scientific hypotheses about "unobservables"? Achinstein examines this question as it arose in actual scientific practice in three nineteenth-century episodes: the debate between particle and wave theorists of light, Maxwell's kinetic theory of gases, and J.J. (...) Thomson's discovery of the electron. The book contains three parts, each devoted to one of these topics, beginning with an essay presenting the historical background of the episode and an introduction to the philosophical issues. There is an illuminating evaluation of various scientific methodologies, including hypothetico-deductivism, inductivism, and the method of independent warrant which combines features of the first two. Achinstein assesses the philosophical validity of both nineteenth-century and modern answers to questions about unobservables, and presents and defends his own solutions. (shrink)

In the original formulation of quantum mechanics the existence of a precise border between a microscopic world, governed by quantum mechanics, and a macroscopic world, described by classical mechanics was assumed. Modern theoretical and experimental physics has moved that border several times, carefully investigating its definition and making available to observation larger and larger quantum systems. The present book examines a paradigmatic case of the transition from quantum to classical behavior: A quantum particle is revealed in a tracking chamber as (...) a trajectory obeying the laws of classical mechanics. The authors provide here a purely quantum-mechanical description of this behavior, thus helping to illuminate the nature of the border between the quantum and the classical. (shrink)

I consider the idea of a structure of fundamental physical particles being causal. Causation is traditionally thought of as involving relations between entities—objects or events—that cause and are affected. On structuralist interpretations, however, it is unclear whether or how precisely fundamental particles can be causally efficacious. On some interpretations, only relations exist; on others, particles are ontologically dependent on their relations in ways that problematize the traditional picture. I argue that thinking about causal efficacy in this context (...) generates an inevitable pattern of reasoning. To assess the cogency of a given structuralist proposal one must take a stand with respect to a significant metaphysical challenge. Two options then emerge: skepticism about the form of structuralism at issue; or a dissolution of the challenge by means of a contentious ontological primitive. I contend that the choice between these options cannot be forced on scientific or philosophical grounds alone. (shrink)

Properties sometimes attributed to the “particle” aspect of a neutron, e.g., mass and magnetic moment, cannot straightforwardly be regarded in the Bohm interpretation of quantum mechanics as localized at the hypothetical position of the particle. This is shown by examining a series of effects in neutron interferometry. A related thought-experiment also provides a variation of a recent demonstration that which-way detectors can appear to behave anomolously in the Bohm theory.

A new version of quantum theory is proposed, according to which probabilistic events occur whenever new statioinary or bound states are created as a result of inelastic collisions. The new theory recovers the experimental success of orthodox quantum theory, but differs form the orthodox theory for as yet unperformed experiments.

The paper explains response particles like yes and no as anaphoric elements that pick up propositional discourse referents that are introduced by preceding sentences. It is argued that negated antecedent clauses introduce two propositional discourse referents, which results in ambiguities of answers that are partly resolved by pragmatic optimization. The paper also discusses response particles like okay, right, uh-huh, uh-uh, and German ja, nein and doch.

Recently, Clifton and Halvorson have tried to salvage a particle phenomenology in the absence of particle ontology within algebraic relativistic quantum field theory. Their idea is that the detection of a particle is the measurement of a local observable which simulates the measurement of an almost local observable that annihilates the vacuum. In this note, we argue that the measurements local particle detections are supposed to simulate probe radically holistic aspects of relativistic quantum fields. We prove that in an axiomatic (...) (Haag-Araki) quantum field theory on Minkowski spacetime, formulated in a Hilbert space $\mathcal{H}$ , there is no positive observable C, with norm less than or equal to 1, satisfying the conditions: (1) the expectation value of C in the vacuum state Ω is zero, (2) there is at least one vector state Ψ in $\mathcal{H}$ in which the expectation value of C is different from zero, and (3) there exists at least one spacetime region $\mathcal{O}$ such that the non-selective measurement of C leaves the expectation values of all observables in the local algebra of that region unaltered regardless of the state the system is in. The result reveals a tension between intuitions regarding localization and intuitions regarding causality: to save “particle phenomena” in the absence of particle ontology, one has to feign “particle” detectors with “good” properties as to locality but “bad” behavior as to causality. (shrink)

In a quantum mechanical two-slit experiment one can observe a single photon simultaneously as particle (measuring the path) and as wave (measuring the interference pattern) if the path and the interference pattern are measured in the sense of unsharp observables. These theoretical predictions are confirmed experimentally by a photon split-beam experiment using a modified Mach—Zehnder interferometer.

It is customary to identify three broad classes of grading particles: additive particles like also, exclusive particles like only, and scalar particles like even (cf. König (1991); in the examples, grave accent stands for the main, falling accent).

I present a new perspective on the meaning of indistinguishability of classical particles. This leads to a solution to the problem in statistical mechanics of justifying the inclusion of a factor N! in a probability distribution over the phase space of N indistinguishable classical particles.

Six years ago, the Singer lab published a landmark paper which described how individual mRNA particles cross the nuclear pore complex in mammalian tissue culture cells. This involved the simultaneous imaging of mRNAs, each labeled by a large number of tethered fluorescent proteins and fluorescently tagged nuclear pore components. Now two groups have applied this technique to the budding yeast Saccharomyces cerevisiae. Their results indicate that in the course of nuclear export, mRNAs likely engage complexes that are present on (...) either side of the pore and that these interactions are modulated by proteins present in the messenger ribonucleoprotein (mRNP) complex. These findings lend support to the notion that just before and/or after the completion of nuclear export, mRNPs undergo one or more maturation steps that prepare the packaged mRNAs for translation. These results represent new and exciting insights into the mechanism of mRNA nuclear export. (shrink)

A draft version of Chapter 11 of the edited volume 'Interpreting Bodies. Classical and Quantum Objects in Modern Physics',. The Chapter is devoted to illustrating the group-theoretic approach to the issue of physical objects. In particular, the Chapter discusses the group-theoretic constitution of classical and quantum particles in the nonrelativistic case.

We extend the work of French and Redhead [1988] further examining the relation of quantum statistics to the assumption that quantum entities have the sort of identity generally assumed for physical objects, more specifically an identity which makes them susceptible to being thought of as conceptually individuatable and labelable even though they cannot be experimentally distinguished. We also further examine the relation of such hypothesized identity of quantum entities to the Principle of the Identity of Indiscernibles. We conclude that although (...) such an assumption of identity is consistent with the facts of quantum statistics, methodological considerations show that we should take quantum entities to be entirely unindividuatable, in the way suggested by a Fock space description. (shrink)

Particle physics intertwines theory and experiments, and this text demonstrates and develops the interplay between the two, following the author's detailed and original approach. This complete and comprehensive treatise, written for a two-semester Master's or graduate course, covers all aspects of modern particle physics. Richly illustrated with more than 450 figures, this text guides students through all the intricacies of quantum mechanics and quantum field theory in an intuitive manner that few books achieve. Featuring rigorous step-by-step derivations and more than (...) 100 end-of-chapter problems for additional practice, it ensures that students will not only understand the material but also be able to apply their knowledge. Containing up-to-date experimental material, including the discovery of the Higgs boson at CERN and of neutrino oscillations, this monumental volume also serves as a one-stop reference for particle physics researchers of all levels and specialties. (shrink)

Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory require us to abandon (...) classical logic and whether quantum logic can resolve the paradoxes produced by quantum mechanics. He argues that quantum logic does not dispose of the problems faced by classical logic, that no reasonable interpretation of quantum mechanics in terms of 'hidden variables' can be found, and that after all these years quantum mechanics remains a mystery to us. Particles and Paradoxes provides a much-needed and valuable introduction to the philosophy of quantum mechanics and, at the same time, an example of just what it is to do the philosophy of physics. (shrink)

The extremely successful _Standard Model of Particle Physics_ allows one to define the so-called _Elementary Particles_. From another point of view, how can we think of them? What kind of a status can be attributed to Elementary Particles and their associated quantised fields? Beyond the unprecedented efficiency and reach of quantum field theories, the current paper attempts at understanding the nature of what these theories describe, the enigmatic reality of the quantum world.

In this paper a model in particle dynamics of a well-known supertask is constructed. As a consequence, a new and simple result about the failure of determinism of classical particle dynamics can be proved which is related to the non-existence of boundary conditions at spatial infinity. This result is much more accessible to the non-technical reader than similar ones in the scientific literature.

The consensus view among philosophers of physics is that relativistic quantum field theory does not describe particles. That is, according to QFT, particles are not fundamental entities. How is this negative conclusion compatible with the positive role that the particle notion plays in particle physics? The first part of this chapter lays out multiple lines of negative argument that all conclude that QFT cannot be given a particle interpretation. These arguments probe the properties of the `particles' in (...) standard formulations of QFT and the limited applicability of `particle' representations. The second part of the chapter surveys proposals for non-fundamental roles that the particle concept plays in particle physics. The conclusion suggests directions for future philosophical research. (shrink)

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. (shrink)

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic quantum field theories to generate dynamics for the underlying fields. However, it does not produce trajectories for the particles associated with these fields. Bell has shown that an extension of Bohm’s approach can be used to provide dynamics for the fermionic occupation numbers in a relativistic quantum field theory. In the present (...) paper, Bell’s formulation is adopted and elaborated on, with a full account of all technical detail required to apply his approach to a bosonic quantum field theory on a lattice. This allows an explicit computation of trajectories for massive and massless particles in this theory. Also particle creation and annihilation, and their impact on particle propagation, is illustrated using this model. (shrink)

This paper discusses two possible formal approaches to the semantic/pragmatic characterisation of a subclass of the modal particles. It may well be that the approaches can be applied to other particles or that they can be applied to certain intonational patterns (e.g. contrastive stress), to morphemes (past tense, agreement) or to words (pronouns), constructions (some uses of definite descriptions, clefts), but I will not try to to show that here. The first approach is based on the optimality theoretic (...) reconstruction of Blutner & J¨ ager (2000) of the theory of presupposition that has become fairly standard, the Heim (1983) and van der Sandt (1992) view of presuppositions as anaphora (see Zeevat (1992) for an introduction and comparison). The first half of the paper critically reviews my earlier views on the treatment of particles in this setting, the second part introduces a novel view, again based on optimality theory, which takes as a starting point the marking constraints that are a necessary ingredient of my earlier treatment. (shrink)

There are significant problems involved in determining the ontology of quantum field theory. An ontology involving particles seems to be ruled out due to the problem of defining localized position operators, issues involving interactions in QFT, and, perhaps, the appearance of unitarily inequivalent representations. While this might imply that fields are the most natural ontology for QFT, the wavefunctional interpretation of QFT has significant drawbacks. A modified field ontology is examined where determinables are assigned to open bounded regions of (...) spacetime instead of spacetime points. (shrink)

Demonstrating that in George Berkeley's last major work, Siris, Berkeley had converted to a belief in the usefulness of the concept and existence of minute particles, Moked here posits that Berkeley developed a highly original brand of corpuscularian physics.

This thesis analyses the ontological nature of quantum particles. In it I argue that quantum particles, despite their indistinguishability, are objects in much the same way as classical particles. This similarity provides an important point of continuity between classical and quantum physics. I consider two notions of indistinguishability, that of indiscernibility and permutation symmetry. I argue that neither sort of indistinguishability undermines the identity of quantum particles. I further argue that, when we understand in distinguishability in (...) terms of permutation symmetry, classical particles are just as indistinguishable as quantum particles; for classical physics also possesses permutation symmetry. (shrink)

We extend the work of French and Redhead [1988] further examining the relation of quantum statistics to the assumption that quantum entities have the sort of identity generally assumed for physical objects, more specifically an identity which makes them susceptible to being thought of as conceptually individuatable and labelable even though they cannot be experimentally distinguished. We also further examine the relation of such hypothesized identity of quantum entities to the Principle of the Identity of Indiscernibles. We conclude that although (...) such an assumption of identity is consistent with the facts of quantum statistics, methodological considerations show that we should take quantum entities to be entirely unindividuatable, in the way suggested by a Fock space description. (shrink)

We critically review the recent debate between Doreen Fraser and David Wallace on the interpretation of quantum field theory, with the aim of identifying where the core of the disagreement lies. We show that, despite appearances, their conflict does not concern the existence of particles or the occurrence of unitarily inequivalent representations. Instead, the dispute ultimately turns on the very definition of what a quantum field theory is. We further illustrate the fundamental differences between the two approaches by comparing (...) them both to the Bohmian program in quantum field theory. (shrink)

Peter Achinstein (1990, 1991) analyses the scientific debate that took place in the eighteenth and nineteenth centuries concerning the nature of light. He offers a probabilistic account of the methods employed by both particle theorists and wave theorists, and rejects any analysis of this debate in terms of coherence. He characterizes coherence through reference to William Whewell's writings concerning how "consilience of inductions" establishes an acceptable theory (Whewell, 1847) . Achinstein rejects this analysis because of its vagueness and lack of (...) reference to empirical data, concluding that coherence is insufficient to account for the belief change that took place during the wave-particle debate. (shrink)

In this work we discuss issues of ontological commitment towards one of the most important examples of contemporary fundamental science: the standard model of particle physics. We present a new form of selective structural realism, which uses as its basis the distinction between what have been called framework and interaction theories. This allows us to advance the ongoing debate about the ontological status of (quasi-)particles and quantum fields, by emphasising the distinction between quantum field theory serving as a framework, (...) and the standard model itself, which we argue is an interaction theory embedded within this framework. Following a discussion of what ontological commitments corresponds to each of these two classes, we argue that some of the previous proposals in the literature might have been misguided by the blending of quantum field theory and the standard model into an undifferentiated unity, and defend a moderate form of object realism with respect to particle-like entities. (shrink)

This article compares treatments of the Stern–Gerlach experiment across different physical theories, building up to a novel analysis of electron spin measurement in the context of classical Dirac field theory. Modeling the electron as a classical rigid body or point particle, we can explain why the entire electron is always found at just one location on the detector but we cannot explain why there are only two locations where the electron is ever found. Using non-relativistic or relativistic quantum mechanics, we (...) can explain both uniqueness and discreteness. Moving to more fundamental physics, both features can be explained within a quantum theory of the Dirac field. In a classical theory of the Dirac field, the rotating charge of the electron can split into two pieces that each hit the detector at a different location. In this classical context, we can explain a feature of electron spin that is often described as distinctively quantum but we cannot explain another feature that could be explained within any of the other theories. (shrink)

The arguments by Pandres that the double valued spherical harmonics provide a basis for the irreducible spinor representation of the three dimensional rotation group are further developed and justified. The usual arguments against the inadmissibility of such functions, concerning hermiticity, orthogonality, behaviour under rotations, etc., are all shown to be related to the unsuitable choice of functions representing the states with opposite projections of angular momentum. By a correct choice of functions and definition of inner product those difficulties do not (...) occur. And yet the orbital angular momentum in the ordinary configuration space can have integer eigenvalues only, for the reason which have roots in the nature of quantum mechanics in such space. The situation is different in the velocity space of the rigid particle, whose action contains a term with the extrinsic curvature. (shrink)