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)

In this work, a neo-classical relativistic mechanics theory is presented where the spin of an electron is an inherent part of its world space-time path as a point particle. The fourth-order equation of motion corresponds to the same covariant Lagrangian function in proper time as in special relativity except for an additional spin energy term. The theory provides a hidden-variable model of the electron where the dynamic variables give a complete description of its motion, giving a classical mechanics (...) explanation of the electron’s spin, its dipole moments, and Schrödinger’s zitterbewegung, These features are also described mathematically by quantum mechanics theory, of course, but without any physical picture of an underlying reality. The total motion of the electron can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called here the spin center. The global motion is sub-luminal and described by Newton’s Second Law in proper time, the time for a clock fixed at the spin center, while the total motion occurs at the speed of light c, consistent with the eigenvalues of Dirac’s velocity operators having magnitude c. The local spin motion is an inherent perpetual motion, which for a free electron is periodic at the ultra-high zitterbewegung frequency and its path is circular in a spin-center reference frame. In an electro-magnetic field, this spin motion generates magnetic and electric dipole energies through the Lorentz force on the electron’s point charge. The electric dipole energy corresponds to the spin-orbit coupling term involving the electric field that appears in the corrected Pauli non-relativistic Hamiltonian, which has long been used to explain the doublet structure of the spectral lines of the excited hydrogen atom. Pauli’s spin-orbit term is usually derived, however, from his magnetic dipole energy term, including also the effect of Thomas precession, which halves this energy. The magnetic dipole energy from Pauli’s and Dirac’s theory is twice that in the neo-classical theory, a discrepancy that has not been resolved. By defining a spin tensor as the angular momentum of the electron’s total motion about its spin center, the fundamental equations of motion can be re-written in an identical form to those of the Barut–Zanghi electron theory. This allows the equations of motion to be expressed in an equivalent form involving operators applied to a state function of proper time satisfying a neo-classical Dirac–Schrödinger spinor equation. This state function produces the dynamic variables from the same operators as in Dirac’s theory for the electron but without any probability implications. It leads to a neo-classical wave function that satisfies Dirac’s relativistic wave equation for the free electron by applying the Lorentz transformation to express proper time in the state function in terms of an observer’s space-time coordinates, showing that there is a close connection between the neo-classical theory and quantum mechanics theory for the electron’s dynamics. (shrink)

Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincaré group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we also derive a classical-particle (...) version of the Higgs mechanism. (shrink)

The worldline of a free electron is revealed by applying Dirac’s velocity operator to its Dirac wave function whose space-time arguments are expressed in a proper time by a Lorentz transformation. This motion can be decomposed into two parts: the electron’s global motion of its inertia (or spin) center and an inherent local periodic motion about this point that produces the electron’s spin and has the zitterbewegung frequency found by Schrödinger in his operator analysis of Dirac’s wave equation. (...) This zitter motion corresponds to the so-called polarization and magnetization currents in Gordon’s decomposition of Dirac’s current. In an inertial “rest”-frame fixed at the inertia center, Dirac’s wave function for a free electron with its spin in a specified direction implies that the zitter motion is a perpetual circular motion about the inertia center in a plane orthogonal to this spin direction with a radius one half of the Compton radius and moving at the speed of light. The electron continuously accelerates about the spin center without any external force because the inertia is effective at the spin center, rather than at its charge center where the electron interacts with the electro-magnetic field. This analysis confirms the nature of zitterbewegung directly from Dirac’s wave equation, agreeing with the conclusions of Barut and Zanghi, Beck, Hestenes, Rivas and Salesi from their classical Dirac particle models of the electron. Furthermore, these five classical models are equivalent and express the same free electron dynamics as Dirac’s equation.. (shrink)

In the so-called “Spin-Echo Experiments” the behaviour of a spin’s system seems to violate the second law of thermodynamics. For this reason the “Spin-Echo Experiments” are considered of particular interest for the Foundations of Physics. Interventionists have provided a classical explanation (Blatt 1959; Ridderbos & Redhead 1998) and a quantum-based explanation (Hemmo & Shenker 2005) of these experiments. Here both interventionist explanations are assessed by means of the Manipulability Theory of Causal Explanation (Woodward 2003). It is argued (...) that interventionism would gain explanatory depth by providing functional relations and predicting relaxation times. En los llamados “experimentos espín-eco” el comportamiento del sistema de espines parece violar la segunda ley de la termodinámica. Por esta razón, los “experimentos espín-eco” son considerados de gran interés en Fundamentos de la Física. Los intervencionistas han ofrecido explicaciones clásicas (Blatt 1959; Ridderbos & Redhead 1998) y explicaciones basadas en mecánica cuántica (Hemmo & Shenker 2005) de dichos experimentos. Aquí ambas explicaciones intervencionistas son analizadas mediante la Teoría Manipulabilista de las Explicaciones Causales (Woodward 2003). Se argumenta que el intervencionismo ganaría profundidad explicativa si proporcionara relaciones funcionales y realizara predicciones de los tiempos de relajación. (shrink)

A formulation by Einstein of the Einstein-Podolsky-Rosen incompleteness argument found in his scientific manuscripts is presented and briefly commented on. It is the only known version in which Einstein discussed the argument for spin observables. The manuscript dates, in all probability, from late 1954 or early 1955 and hence also represents Einstein's latest version of the incompleteness argument and one of his last statements on quantum theory in general. A puzzling formulation raises the question of Einstein's interpretation of space (...) quantization and the non-classical spin degree of freedom. (shrink)

Relativistic quantum mechanics has been formulated as a theory of the evolution ofevents in spacetime; the wave functions are square-integrable functions on the four-dimensional spacetime, parametrized by a universal invariant world time τ. The representation of states with spin is induced with a little group that is the subgroup of O(3, 1) leaving invariant a timelike vector nμ; a positive definite invariant scalar product, for which matrix elements of tensor operators are covariant, emerges from this construction. In a previous (...) study a second-order equation was introduced similar to the second-order Dirac equation, based on a quadratic function of two operators which are the self-adjoint parts, in this new scalar product, of γμpμ. It is shown in this paper that one of these operators, in fact the one from which the gyromagnetic moment is obtained, can be used to construct a first-order equation. The corresponding quantum theory is somewhat analogous to Dirac's spinor form; the Hamilton equations appear to describe dynamical degrees of freedom in a spacelike hyperplane orthogonal to nμ (in Dirac's theory the motion appears to be lightlike). It is shown that the integration over nμ required by unitarity results in timelike motion (as in the expectation value of Dirac's α). Explicit forms are obtained for the wave functions and currents for free motion. The general form of the theory is written for the (five-dimensional) pre-Maxwell fields required by gauge invariance. (shrink)

The quantum evolution equation of Loop Quantum Cosmology (LQC)—the quantum Hamiltonian constraint—is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models with an integrable differential-difference nonlinear Schrödinger type equation, which in turn is known to be associated with integrable, discrete Heisenberg spin chain models in condensed matter physics. We illustrate the similarity between both systems with a simple constraint in the linear regime.

It is generally believed that the de Broglie-Bohm model does not admit a particle interpretation for massive relativistic spin-0 particles, on the basis that particle trajectories cannot be defined. We show this situation is due to the fact that in the standard representation of the Klein-Gordon equation the wavefunction systematically contains superpositions of particle and anti-particle contributions. We argue that by working in a Foldy-Wouthuysen type representation uncoupling the particle from the anti-particle evolutions, a positive conserved density for a (...) particle and associated density current can be defined. For the free Klein-Gordon equation the velocity field obtained from this current density appears to be well-behaved and sub-luminal in typical instances. As an illustration, Bohmian trajectories for a spin-0 boson distribution are computed numerically for free propagation in situations in which the standard velocity field would take arbitrarily high positive and negative values. (shrink)

Quantum correlations for pairs of particles with higher spin in the singlet state • Designing raffles to simulate these quantum correlations • Classical polyhedra with more and more vertices and facets and getting closer and closer to the elliptope.

A great effort has been devoted to formulating a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in connecting classical and quantum theories rests in finding a parameter that plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneering works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of (...) Barut and Zanghi. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level, we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail. (shrink)

The Hamiltonian for n relativistic electrons without interaction but in a Coulomb potential is well known. If in this Hamiltonian we take r ′ u =r′, P ′ u =P′ with u=1,2,..., n, we obtain a one-body problem in a Coulomb field, but the appearance of n of the α u , u=1,..., n, each of which corresponds to spin $\tfrac{1}{2}$ , indicates that we may have spins up to (n/2). We analyze this last problem first by denoting the (...) 4×4 matrices α, β as direct products of 2×2 matrices which correspond to the ordinary spin, and a new concept, also related to the SU(2) group, which we call sign spin. In this new notation our problem depends on the sixteen generators of a U(4) group reduced along the chain Û(2)⊗Ŭ(2) sub-groups associated with the ordinary and sign spins. We now make a change of variables in our Hamiltonian so a term ε related to the frequency ω of an oscillator, which will be our variational parameter, appears in it, and later construct the full states of the problem with a harmonic oscillator of frequency 1 and ordinary and sign spin parts. Finally we obtain the matrix representation of our Hamiltonian with respect to the states mentioned and discuss the energy spectra of the problem where the partition {h} representing the irrep of U(4) and j the total angular momentum, take the values {h}=[1], j= $\tfrac{1}{2}$ ; {h}=[11], j=0; {h}=[2], j=0. (shrink)

© 2016, CERN for the benefit of the ATLAS collaboration.This paper presents a dedicated search for exotic decays of the Higgs boson to a pair of new spin-zero particles, H→ aa, where the particle a decays to b-quarks and has a mass in the range of 20–60 GeV. The search is performed in events where the Higgs boson is produced in association with a W boson, giving rise to a signature of a lepton, missing transverse momentum, and multiple jets (...) from b-quark decays. The analysis is based on the full dataset of pp collisions at s=13TeV recorded in 2015 by the ATLAS detector at the CERN Large Hadron Collider, corresponding to an integrated luminosity of 3.2 fb-1. No significant excess of events above the Standard Model prediction is observed, and a 95% confidence-level upper limit is derived for the product of the production cross section for pp→ WH times the branching ratio for the decay H→ aa→ 4 b. The upper limit ranges from 6.2 pb for an a-boson mass ma=20GeV to 1.5 pb for ma=60GeV. (shrink)

Level statistics and nodal point distribution in a rectangular semiconductor quantum dot are studied for different degrees of spin-orbit coupling. The chaotic features occurring from the spin-orbit coupling have no classical counterpart. Using experimental values for GaSb/InAs/GaSb semiconductor quantum wells we find that level repulsion can lead to the semi-Poisson distribution for nearest level separations. Nodal lines and nodal points are also investigated. Comparison is made with nodal point distributions for fully chaotic states.

The study of the motion of the magnetic top—a classical spherical top which carries magnetic moment proportional to its angular momentum, is motivated and inspired by the quantum mechanical relation between spin angular momentum and spin magnetic moment. Inversely, the magnetic top, taken to be the classical model of quantum spin, implies the description of spin states by probability amplitudes of the top orientation angles, instead of by Pauli spinors. This opens new possibilities for the interpretation (...) of many interesting spin experiments which serve as tests of basic principles of quantum mechanics and of the postulates of the quantum theory of measurement. (shrink)

In this work we review the derivation of Dirac and Weinberg equations based on a “principle of indistinguishability” for the (j,0) and (0,j) irreducible representations (irreps) of the homogeneous Lorentz group (HLG). We generalize this principle and explore its consequences for other irreps containing j≥1. We rederive Ahluwalia–Kirchbach equation using this principle and conclude that it yields $\mathcal{O}(p^{2j} )$ equations of motion for any representation containing spin j and lower spins. We also use the obtained generators of the HLG (...) for a given representation to explore the possibility of the existence of first order equations for that representation. We show that, except for j= $ - \frac{1}{2}$ , there exists no Dirac-like equation for the (j,0)⊕(0,j) representation nor for the ( $ - \frac{1}{2}$ , $ - \frac{1}{2}$ ) representation. We rederive Kemmer–Duffin–Petieau (KDP) equation for the (1,0)⊕( $ - \frac{1}{2}$ , $ - \frac{1}{2}$ )⊕(0,1) representation by this method and show that the (1, $ - \frac{1}{2}$ )⊕( $ - \frac{1}{2}$ ,1) representation satisfies a Dirac-like equation which describes a multiplet of $j = \frac{3}{2}{\text{ and }}j = \frac{1}{2}$ with masses m and m/2, respectively. (shrink)

We develop here the general treatment of the Bethe—Salpeter equation for the bound state of two spin-l particles interacting through an electromagnetic interaction. The treatment here, which can be generalized to strong interactions, combines the two-component approach utilized previously by the author in conjunction with spontaneous symmetry breaking. This is done by using a Lagrangian having SU(2)×U(1) symmetry (without fermions) and then choosing the ′t Hooft gauge. In this way, a renormalizable theory for the interaction of two spin-l (...) particles via an electromagnetic interaction is ensured. (shrink)

Quasi-probability distribution functions fj WW, fj MM for quantum spin-j systems are derived based on the Wigner-Weyl, Margenau-Hill approaches. A probability distribution fj sph which is nonzero only on the surface of the sphere of radius √j(j+1) is obtained by expressing the characteristic function in terms of the spherical moments. It is shown that the Wigner-Weyl distribution function turns out to be a distribution over the sphere in the classical limit.

Wigner’s famous 1939 classification of positive energy representations, combined with the more recent modular localization principle, has led to a significant conceptual and computational extension of renormalized perturbation theory to interactions involving fields of higher spin. Traditionally the clash between pointlike localization and the the Hilbert space was resolved by passing to a Krein space setting which resulted in the well-known BRST gauge formulation. Recently it turned out that maintaining a Hilbert space formulation for interacting higher spin fields (...) requires a weakening of localization from point- to string-like fields for which the d = s + 1 short distance scaling dimension for integer spins is reduced to d = 1 and and renormalizable couplings in the sense of power-counting exist for any spin. This new setting leads to a significant conceptual change of the relation of massless couplings with their massless counterpart. Whereas e.g. the renormalizable interactions of s = 1 massive vectormesons with s \ 1 matter falls within the standard field-particle setting, their zero mass limits lead to much less understood phenomena as “infraparticles” and gluon/quark confinement. It is not surprising that such drastic conceptual changes in the area of gauge theories also lead to a radical change concerning the Higgs issue. (shrink)

The problem of the electromagnetic coupling for spin-3/2 particles is discussed. Following supergravity and some previous researches in the field of classical supersymmetric particles, we found that the electromagnetic coupling must not obey a minimal coupling in the sense of coupling the electromagnetic potential, but some kind of an electromagnetic field strength.

The orthodox presentation of quantum theory often includes statements on state preparation and measurements without mentioning how these processes can be achieved. The often quoted projection postulate is regarded by many as problematical. This paper presents a systematic framework for state preparation and measurement. Within the existing Hilbert space formulation of quantum mechanics for spinless particles we show that it is possible (1)to prepare an arbitrary state and (2)to reduce all quantum measurements to local position measurements in an asymptotic way (...) by unitary evolution processes without recourse to the projection postulate. A generalization to spin-1/2particles is also given. The theory presented provides a general mathematical and theoretical foundation for many practical schemes for state preparation and measurement. (shrink)

This chapter contains sections titled: Etching Awesomeness on the Top Tube in Three Pedal Strokes Free Riding with the Bhagavad Gita Coming Full Circle Notes.

In this paper I aim to answer two questions: Can spin be treated as a determinable? Can a treatment of spin as a determinable be used to understand quantum indeterminacy? In response to the first question I show that the relations among spin number, spin components and spin values cannot be captured by a single determination relation; instead we need to look at spin number and spin value separately. In response to the second (...) question I discuss three ways in which the determinables model might be modified to account for indeterminacy, and argue that none of them is fully successful in helping us to understand quantum indeterminacy. (shrink)

In this essay, I consider the question of whether women have an obligation to confront men who sexually harass them. A reluctance to be guilty of blaming the victims of harassment, coupled with other normative considerations that tell in favor of the unfairness of this sort of obligation, might make us think that women never have an obligation to confront their harassers. But 1 argue that women do have this obligation, and it is not overridden by many of the considerations (...) that can override other obligations to confront wrongdoers. (shrink)

In this essay, I consider the question of whether women have an obligation to confront men who sexually harass them. A reluctance to be guilty of blaming the victims of harassment, coupled with other normative considerations that tell in favor of the unfairness of this sort of obligation, might make us think that women never have an obligation to confront their harassers. But 1 argue that women do have this obligation, and it is not overridden by many of the considerations (...) that can override other obligations to confront wrongdoers. (shrink)

In this review paper, we discuss how gravity and spin can be obtained as the realization of the local Conformal-Affine group of symmetry transformations. In particular, we show how gravitation is a gauge theory which can be obtained starting from some local invariance as the Poincaré local symmetry. We review previous results where the inhomogeneous connection coefficients, transforming under the Lorentz group, give rise to gravitational gauge potentials which can be used to define covariant derivatives accommodating minimal couplings of (...) matter, gauge fields (and then spin connections). After we show, in a self-contained approach, how the tetrads and the Lorentz group can be used to induce the spacetime metric and then the Invariance Induced Gravity can be directly obtained both in holonomic and anholonomic pictures. Besides, we show how tensor valued connection forms act as auxiliary dynamical fields associated with the dilation, special conformal and deformation (shear) degrees of freedom, inherent to the bundle manifold. As a result, this allows to determine the bundle curvature of the theory and then to construct boundary topological invariants which give rise to a prototype (source free) gravitational Lagrangian. Finally, the Bianchi identities, the covariant field equations and the gauge currents are obtained determining completely the dynamics. (shrink)

A new approach to developing formulisms of physics based solely on laws of mathematics is presented. From simple, classical statistical definitions for the observed space-time position and proper velocity of a particle having a discrete spectrum of internal states we derive u generalized Schrödinger equation on the space-time manifold. This governs the evolution of an N component wave function with each component square integrable over this manifold and is structured like that for a charged particle in an electromagnetic field but (...) also includes SU(N) gauge field couplings. This construction reveals a new hasis for gauge invariance and new insight into the appearance of spin and other such properties in relativistic quantum mechanics and suggests a new charged particle model. (shrink)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor 2s belongs to the exchange wave function when this function is constructed so as to get (...) the spinor ambiguity under control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

The paper provides a briefintroduction to the biotechnology revolutionand its impact upon biological researchrelevant to military uses. It describes thestatus of biological weapons today, and currentefforts to strengthen the Biological WeaponsConvention with a legally binding complianceprotocol. Specific modifications ofmicro-organisms that may be of military use arediscussed. Three examples of dual-use researchactivities are then used to highlight issuesand dilemmas in ethical decision making.

The Middle Eastern trouble continues, in part, from a jumbling of names for the two parties. But social science requires precise delineation as each belligerent streamlines a modus operandi. “Terrorist” commonly means “relating to what presently is causing terror”. Therefore, so to term those insurgents is to concede victory to them, without further struggle. One must map the nicknames for each of the tactical variants. In so doing, we find several dozen overlapping terms, such as identity thief, agent provocateur, and (...) scorpion. Most analogies, however, are anthropomorphized by the characteristics of snakes. Therefore, some existing analogy for the insurgents would better be reimaged by terming them “slitherites”. Our Goal Is to Name the Phases of the Middle Eastern Struggle. (shrink)

The algebraic structure of the 8-spinor formalism is discussed, and the general form of the 8-component wave equation, equivalent to the second-order 4-component one, is presented. This allows a canonical formulation that will be the first stage of the future Clebsch parametrization, i.e., a relativistic generalization of the Bohm-Schiller-Tiomno pioneering work on the Pauli equation.