WKB analysis of relativistic Stern–Gerlach measurements

Spin is an important quantum degree of freedom in relativistic quantum information theory. This paper provides a first-principles derivation of the observable corresponding to a Stern–Gerlach measurement with relativistic particle velocity. The specific mathematical form of the Stern–Gerlach operator is established using the transformation properties of the electromagnetic field. To confirm that this is indeed the correct operator we provide a detailed analysis of the Stern–Gerlach measurement process. We do this by applying a WKB approximation to the minimally coupled Dirac equation describing an interaction between a massive fermion and an electromagnetic field. Making use of the superposition principle we show that the +1 and −1 spin eigenstates of the proposed spin operator are split into separate packets due to the inhomogeneity of the Stern–Gerlach magnetic field. The operator we obtain is dependent on the momentum between particle and Stern–Gerlach apparatus, and is mathematically distinct from two other commonly used operators. The consequences for quantum tomography are considered.     

Spin-polarization in a 3-terminal conductor induced by Rashba spin–orbit coupling

We investigate numerically the spin polarization of the current in the presence of Rashba spin–orbit interaction (RSOI) in a 3-terminal conductor. We use equation-of-motion method to simulate the time evolution of the wave packet and focus on single-channel transport. A T-shaped conductor with uniform RSOI proposed by Kiselev and Kim and a Y-shaped conductor with nonuniform RSOI are considered. In the T-shaped conductor, the strength of RSOI is assumed to be uniform. We have found that the spin polarization becomes nearly 100% with little loss of conductance for sufficiently strong spin–orbit coupling. This is due to the spin-dependent group velocity of electrons at the junction which causes the spin separation. In the Y-shaped conductor, the strength of RSOI is modulated perpendicular to the charge current. A spatial gradient of effective magnetic field due to the nonuniform RSOI causes the Stern–Gerlach type spin separation. The direction of the polarization is perpendicular to the current and parallel to the spatial gradient. Again almost 100% spin polarization can be realized by this spin separation.     

Classical Gravitational Interactions and Gravitational Lorentz Force

In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field.The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides,it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.     

Classical Gravitational Interactions and Gravitational Lorentz Force

In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field. The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides, it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field. The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.     

A testable prediction of the no-signalling condition using a variant of the EPR-Bohm example

Predictive power of the no-signalling condition (NSC) is demonstrated in a testable situation involving a non-ideal Stern–Gerlach (SG) device in one of the two wings of the EPR-Bohm entangled pairs. In this wing, for two types of measurement in the other wing, we consider the spin state of a selected set of particles that are confined to a particular half of the plane while emerging from the SG magnetic field region. Due to non-idealness of the SG setup, this spin state will have superposing components involving a relative phase for which a testable quantitative constraint is obtained by invoking NSC, thereby providing a means for precision testing of this fundamentally significant principle.     

Quantum theory as a description of robust experiments: Derivation of the Pauli equation

It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g. the Schrödinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Stern–Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments.     

Existence of the gravitomagnetic interaction

The point of view expressed in the literature that gravitomagnetism has not yet been observed or measured is not entirely correct. Observations of gravitational phenomena are reviewed in which the gravitomagnetic interaction—a post-Newtonian gravitational force between moving matter—has participated and which has been measured to 1 part in 1000. Gravitomagnetism is shown to be ubiquitous in gravitational phenomena and is a necessary ingredient in the equations of motion, without which the most basic gravitational dynamical effects (including Newtonian gravity) could not be consistently calculated by different inertial observers.     

Effects of atomic motion in a standing-wave laser field on the Rabi oscillations

We study the effects of the two-level-atom motion in a standing-wave laser field on the Rabi oscillations. In the presence of the resonance optical Stern–Gerlach effect, the atomic wave packet, centered initially at a node of the standing wave, is shown to evolve in such a way that the atomic population inversion remains zero when the initially de-excited atom moves between the nodes, then collapses to the ground level upon crossing the nodes, and practically returns to zero after that. This coherent population trapping is explained in the dressed-state picture. The Doppler–Rabi resonance, i.e., maximum Rabi oscillations at large values of the atom–field detuning, becomes possible if the detuning is equal to the Doppler shift. A simple formula for the population inversion is derived in the Raman–Nath approximation.     

Gravitomagnetic Effects on Collective Plasma Oscillations in Compact Stars

The effects of gravitomagnetic force on plasma oscillations are investigated using the kinetic theory of homogeneous electrically neutral plasma in the absence of external electric or magnetic field. The random phase assumption is employed neglecting the thermal motion of the electrons with respect to a fixed ion background. It is found that the gravitomagnetic force reduces the characteristic frequency of the plasma thus enhancing the refractive index of the medium. The estimates for the predicted effects are given for a typical white dwarf, pulsar, and neutron star.     

Gravitomagnetism in Metric Theories: Analysis of Earth Satellites Results, and Its Coupling with Spin

Employing the PPN formalism the gravitomagnetic field in different metheories is considered in the analysis of the LAGEOS results. It will be shown that there are several models that predict exactly the same effect that general relativity comprises. In other words, these Earth satellites results can be taken as experimental evidence that the orbital angular momentum of a body does indeed generate space–time geometry, nevertheless they do not endow general relativity with an outstanding status among metric theories. Additionally the coupling spin–gravitomagnetic field is analyzed with the introduction of the Rabi transitions that this field produces on a quantum system with spin 1/2. Afterwards, a continuous measurement of the energy of this system is introduced, and the consequences upon the corresponding probabilities of the involved gravitomagnetic field will be obtained. Finally, it will be proved that these proposals allows us, not only to confront against future experiments the usual assumption of the coupling spin–gravitomagnetism, but also to measure some PPN parameters and to obtain functional dependences among them.     

Gravitomagnetism and Non-commutative Geometry

Similarity between the gravitoelectromagnetism and the electromagnetism is discussed. We show that the gravitomagnetic field (similar to the magnetic field) can be equivalent to the non-commutative effect of the momentum sector of the phase space when one maintains only the first order of the non-commutative parameters. This is performed through two approaches. In one approach, by employing the Feynman proof, the existence of a Lorentz-like force in the gravitoelectromagnetism is indicated. The appearance of such a force is subjected to the slow motion and the weak field approximations for stationary fields. The analogy between this Lorentz-like force and the motion equation of a test particle in a non-commutative space leads to the mentioned equivalency. In fact, this equivalency is achieved by the comparison of the two motion equations. In the other and quietly independent approach, we demonstrate that a gravitomagnetic background can be treated as a Dirac constraint. That is, the gravitoelectromagnetic field can be regarded as a constrained system from the sense of the Dirac theory. Indeed, the application of the Dirac formalism for the gravitoelectromagnetic field reveals that the phase space coordinates have non-commutative structure from the view of the Dirac bracket. Particularly, the gravitomagnetic field as a weak field induces the non-trivial Dirac bracket of the momentum sector which displays the non-commutativity.     

The dual curvature tensors and dynamics of gravitomagnetic matter

Gravitomagnetic charge that can also be referred to as the dual mass or magnetic mass is the topological charge in gravity theory. A gravitomagnetic monopole at rest can produce a stationary gravitomagnetic field. Due to the topological nature of gravitomagnetic charge, the metric of spacetime where the gravitomagnetic matter is present will be nonanalytic. In this paper both the dual curvature tensors (which can characterize the dynamics of gravitational charge/monopoles) and the antisymmetric gravitational field equation of gravitomagnetic matter are presented. We consider and discuss the mathematical formulation and physical properties of the dual curvature tensors and scalar, antisymmetric source tensors, dual spin connection (including the low‐motion weak‐field approximation), dual vierbein field as well as dual current densities of gravitomagnetic charge. It is shown that the dynamics of gravitomagnetic charge can be founded within the framework of the above dual quantities. In addition, the duality relationship in the dynamical theories between the gravitomagnetic charge (dual mass) and the gravitoelectric charge (mass) is also taken into account in the present paper.     

From Kerr to Heisenberg

In this paper, we consider the space-time of a charged mass endowed with an angular momentum. The geometry is described by the exact Kerr–Newman solution of the Einstein equations. The peculiar symmetry, though exact, is usually described in terms of the gravito-magnetic field originated by the angular momentum of the source. A typical product of this geometry is represented by the generalized Sagnac effect. We write down the explicit form for the right/left asymmetry of the times of flight of two counter-rotating light beams along a circular trajectory. Letting the circle shrink to the origin the asymmetry stays finite. Furthermore it becomes independent both from the charge of the source (then its electromagnetic field) and from Newton’s constant: it is then associated only to the symmetry produced by the gravitomagnetic field. When introducing, for the source, the spin of a Fermion, the lowest limit of the Heisenberg uncertainty formula for energy and time appears.     

Detection of the gravitomagnetic field using an orbiting superconducting gravity gradiometer: principle and experimental considerations

The angular momentum of the Earth produces gravitomagnetic components of the Riemann curvature tensor, which are of the order of 10⁻¹⁰ of the Newtonian terms arising from the mass of the Earth. Due to the dragging of the local inertial frame by the spinning Earth, there are also secular terms, which grow in time. These fields can be detected in principle by a set of orbiting superconducting gravity gradiometers. The Riemann tensor components for various spacecraft orientations have been computed and the principle of detecting the gravitomagnetic tidal force has been published. In this paper, we review the conclusions of the earlier analyses and discuss the feasibility of the gravity gradiometer experiment.     

On the impossibility of using the longitude of the ascending node of GP-B for measuring the Lense–Thirring effect

The possibility of analyzing the node of the GP-B satellite in order to measure also the Lense–Thirring effect on its orbit is examined. This feature is induced by the general relativistic gravitomagnetic component of the Earth gravitational field. The GP-B mission has been launched in April 2004 and is aimed mainly to the measurement of the gravitomagnetic precession of four gyroscopes carried onboard at a claimed accuracy of 1%. of better. The aliasing effect of the solid Earth and ocean components of the solar K₁ tidal perturbations would make the measurement of the Lense–Thirring effect on the orbit unfeasible. Indeed, the science period of the GP-B mission amounts to almost one year. During this time span the Lense–Thirring shift on the GP-B node would be 164 milliarcseconds (mas), while the tidal perturbations on its node would have a period of the order of 10³ years and amplitudes of the order of 10⁵ mas.     

Letter: Sagnac Interferometry and Non–Newtonian Gravity

Sagnac interferometry has been employed in the context of gravity as a proposal for the detection of the so called gravitomagnetic effect. In the present work we explore the possibilities that this experimental device could open up in the realm of non–Newtonian gravitation. It will be shown that this experimental approach allows us to explore an interval of values of the range of the new force that up to now remains unexplored, namely, 10¹⁴ m.     

Local gravitomagnetism

In a simple two-body system, we calculate the gravitomagnetic components of the metric in the local quasi-inertial frame of one of the bodies. The local geometry in this frame which is freely falling along the geodesic but is directionally fixed with respect to distant stars is primarily denned by the gravitomagnetic components of the local metric. This metric serves to track down the various contributions from the local and distant source and thus provides further insight to the nature of gravitomagnetism. As a result we show that in the quasi-inertial frame geodetic precession is a gravitomagnetic phenomenon. Furthermore we establish a connection between local gravitomagnetic effects and Einstein's principle of equivalence.     

The Gravitational Interaction of Light: From Weak to Strong Fields

An explanation is proposed for the fact thatpp-waves superpose linearly when they propagateparallelly, while they interact nonlinearly, scatter andform singularities or Cauchy horizons if they areantiparallel. Parallel pp-waves do interact, but ageneralized gravitoelectric force is exactly cancelledby a gravitomagnetic force. In an analogy, theinteraction of light beams in linearized generalrelativity is also revisited and clarified, a new result isobtained for photon to photon attraction, and aconjecture is proved. Given equal energy density in thebeams, the light-to-light attraction is twice thematter-to-light attraction and four times the matter-to-matterattraction.     

A new approach to studying local gravitomagnetic effects on a superconductor

In this paper we introduce gravitomagnetic field equations into the investigation of gravitomagnetic effects on a superconductor. We point out that in the absence of an applied magnetic field, an applied gravitomagnetic field will induce twin currents, gravitational and electric supercurrents. The latter will create a magnetic field. The slightly modified Josephson, London, and London-type gravitomagnetic equations are obtained. Some applications of these equations are discussed.