The Thomas Precession and the Transformation to Rotating Frames

The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of v/c, important differences in the predicted angle of precession appear, depending on the transformation used. For smaller values of v/c these differences might be measured by extending the time of observation.     

The Sagnac Vortex Optical Effect

It is shown that the Sagnac phenomenon observed experimentally is in conflict with special (and also general) relativity. The calculation of the magnitude of the Sagnac effect within the framework of a relativistic theory results in a paradox. Thus, for the moving relativistic observer, the simultaneous events of meeting of ± rays with the radiant are nonsimultaneous for the events of meeting of the radiant with ± rays. Here, the index + denotes a ray propagating in the direction of motion of the observer, while the index – denotes a ray propagating against the motion. The paradox is resolved within the framework of the theory of a luminiferous ether at rest.     

The Foucault Pendulum and the Sagnac Effect

Russian Physics Journal -     

Relativistic Sagnac Effect and Ehrenfest Paradox

There seems to exist a dilemma in the literature as to the correct relativistic formula for the Sagnac phase-shift. The paper addresses this issue in the light of a novel, kinematically equivalent linear Sagnac-type thought experiment, which provides a vantage point from which the effect of rotation in the usual Sagnac effect can be analyzed. The question is shown to be related to the so-called rotating disc problem known as the Ehrenfest paradox. The relativistic formula for the Sagnac phase-shift seems to depend on the way the paradox is resolved. Kinematic resolution of the Ehrenfest paradox proposed by some authors predicts the usually quoted formula for the Sagnac delay but the resolution itself is shown to be based upon some implicit assumptions regarding the behaviour of solid bodies under acceleration. In order to have a greater insight into the problem, a second version of the thought experiment involving linear motion of a special type of a non-rigid frame of reference is discussed. It is shown by analogy that the usually quoted special relativistic formula for the Sagnac delay follows, provided the material of the disc matches the special type.     

New Perspectives on the Relativistically Rotating Disk and Non-Time-Orthogonal Reference Frames

The rotating disk problem is analyzed on the premise that proper interpretation of experimental evidence leads to the conclusion that the postulates upon which relativity theory is based, particularly the invariance of the speed of light, are not applicable to rotating frames. Different postulates based on the Sagnac experiment are proposed, and from these postulates a new relativistic theory of rotating frames is developed following steps similar to those initially followed by Einstein for rectilinear motion. The resulting theory agrees with all experiments, resolves problems with the traditional approach to the rotating disk, and exhibits both traditionally relativistic and non-relativistic characteristics. Of particular note, no Lorentz contraction exists on the rotating disk circumference, and the disk surface, contrary to the assertions of Einstein and others, is found to be Riemann flat. The variable speed of light found in the Sagnac experiment is then shown to be characteristic of non-time-orthogonal reference frames, of which the rotating frame is one. In addition, the widely accepted postulate for the equivalence of inertial and non-inertial standard rods with zero relative velocity, used liberally in prior rotating disk analyses, is shown to be invalid for such frames. Further, the new theory stands alone in correctly predicting what was heretofore considered a spurious non-null effect on the order of 10^–13 found by Brillet and Hall in the most accurate Michelson-Morley type test to date. The presentation is simple and pedagogic in order to make it accessible to the non-specialist.     

Spacetime without Reference Frames: An Application to Synchronizations on a Rotating Disk

Nonstandard synchronizations of inertial observers in special relativity and synchronizations with respect to a uniformly rotating observer are investigated in a setting which avoids coordinates and transformation rules and so removes some misunderstandings.     

Sagnac Effect in the Kerr-Newman and Reissner-Nordstrom Fields

By means of a formal analogy with the Aharonov-Bohm effect, the Sagnac time delay and the corresponding Sagnac phase shift in the Kerr-Newman and Reissner-Nordstrfm spacetimes are discussed. We find that the effect depends on the properties of the source of the gravitational field. The contributions made by the electric charge of the gravitational source can be employed to weaken it in the Kerr-Newman spacetime, even if a phase shift and a time delay still appear. This is due to the properties of the rotating source of the gravitational field.     

The Sagnac effect: 20 years of development in matter-wave interferometry

Since the first atom interferometry experiments in 1991, measurements of rotation through the Sagnac effect in open-area atom interferometers have been investigated. These studies have demonstrated very high sensitivity that can compete with state-of-the-art optical Sagnac interferometers. Since the early 2000s, these developments have been motivated by possible applications in inertial guidance and geophysics. Most matter-wave interferometers that have been investigated since then are based on two-photon Raman transitions for the manipulation of atomic wave packets. Results from the two most studied configurations, a space-domain interferometer with atomic beams and a time-domain interferometer with cold atoms, are presented and compared. Finally, the latest generation of cold atom interferometers and their preliminary results are presented.     

The Effect of Rotating Cylindrical Langmuir Probes in Magnetron Plasmas

Using a cylindrical Langmuir probe, the plasma properties (ion density, electron temperature, floating and plasma potentials) in a magnetron sputter source have been investigated, along one particular line‐of‐sight, but for different probe‐orientations with respect to the B‐field. The plasma in the region hosen for observation is haracterised by electrons, which are magnetised (Larmor radius r_le < both the electron mean‐free‐path λ_e, and plasma extension L) and ions, which are not (their Larmor radius r_I > L, λ_I). Through the development of a simple expression for the electron saturation current at different probe angles relative to the local B‐field, it is possible to correct for the diminished electron currents due to their restricted transport across the field. The results indicate that the measured ion density, electron temperature, floating and plasma potentials are unaffected by the probe orientation, however the electron saturation current is attenuated when the probe is aligned along the B‐field. A simple model for the collection of electrons indicates that classical electron diffusion may not operate in the magnetron, with cross‐field electron transport dominated by anomalous, possibly Bohm, diffusion.     

Quadratic Sagnac Effect Recorded by an Observer in the Laboratory Frame

Optics and Spectroscopy - The quadratic Sagnac effect, recorded by an observer in the laboratory frame of reference (inertial frame), relative to which the Michelson interferometer moves, has been...     

The Sagnac Phase Shift Suggested by the Aharonov-Bohm Effect for Relativistic Matter Beams

The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a formal analogy with the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and Newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.     

Quantum Interference Effect in General Rotating Systems

As the mechanical counterpart of the Aharonov-Bohm effect and the Aharonov-Cashier effect in a magnetic field, the existence and possibility of observation of a quantum interference effect between the split paths of a coherent particle beam in a uniformly rotating frame have been studied previously. The discussion is now generalized to the case of a reference frame rotating at arbitrary time varying angular velocity about a fixed center. The phase difference between the split beams of particles and the resulting interference pattern depend not only upon the speed, but also upon the orientation of the axis of rotation. The conclusion may have, therefore, inferences on gyroscopic applications.     

Materials for Electrodes of Li-Ion Batteries: Issues Related to Stress Development

Presently, rechargeable Li-ion batteries, possessing highest energy densities among all batte-ries, are used in a major fraction of all portable electronic devices. However, for bestowing the Li-ion batteries suitable for such advanced applications, further improvements in the energy densities (Li-capacities) and in the cycle life are essential. In a broader sense, this can be achieved by replacing the presently used electrode materials by materials possessing higher Li-capacities and minimization of the degradation of such materials with electrochemical cycling. It has been realized that the major reason for degradation in battery performance in terms of capacity with cycling is the disintegration/fragmentation of the active electrode materials due to stresses generated during Li-intercalation/de-intercalation in every cycle. Such stresses arise from the reversible volume changes of the active electrode materials during Li-insertion and removal. In quest of higher energy densities, replacement of the presently used graphitic carbon by potentially higher capacity metallic anode materials (like Si, Sn, and Al) is likely to further accrue this stress related disintegration due to ～30 times higher volume changes experienced by such materials. It has also been recently realized that passivating layer formed on the surface of the electrodes also contributes toward the stress development. After briefly introducing the mechanistic aspects of Li-ion batteries, this article focuses on the reasons and consequences associated with stress developments in different electrode materials, highlighting the various strategies, in terms of designing new electrode com-positions or reducing the microstructural scale, that are being presently adopted to address the stress-related issues. Considering that experimental determination of such stresses is essential toward further progress in Li-ion battery research, this article introduces a recently reported technique developed for real-time measurement of such stresses. It finally concludes by raising some critical issues that need to be resolved through further research in this area.     

Letter: Axial Torsion-Dirac Spin Effect in Rotating Frame with Relativistic Factor

In the framework of spacetime with torsion and without curvature, the Dirac particle spin precession in the rotational system is studied. We write out the equivalent tetrad of the rotating frame, in the polar coordinate system, through considering the relativistic factor, and the resultant equivalent metric is a flat Minkowski one. The obtained rotation-spin coupling formula can be applied to the high speed rotating case, which is consistent with the expectation.     

Reference Frames and Rigid Motions in Relativity: Applications

The concept of rigid reference frame and of constricted spatial metric, given in the previous work [Class. Quantum Grav. 21, 3067 (2004)] are here applied to some specific space-times: in particular, the rigid rotating disc with constant angular velocity in Minkowski space-time is analyzed, a new approach to the Ehrenfest paradox is given as well as a new explanation of the Sagnac effect. Finally the anisotropy of the speed of light and its measurable consequences in a reference frame co-moving with the Earth are discussed.     

Rotating spiral waves in excitable media: The analytical results

In this paper we calculate the rotation frequency of spiral waves as a function of the parameters of the excitable medium. We give the complete analytical solution in the special case of the Rinzel-Keller model and suggest an analytical procedure for general two-component relaxational reaction-diffusion models. This procedure is based on the Greenberg equation and stability analysis; it is applicable when the core of a spiral wave is large as compared with the characteristic diffusion length. Construction of spiral wave solutions for the waves inside ring channels, circular regions, or around holes is discussed. Multi-armed spiral waves are investigated.     

Polyakov Soldering and Second-Order Frames: The Role of the Cartan Connection

The so-called ‘soldering’ procedure performed by Polyakov (Int J Math Phys A5, 833–842, 1990) for a -gauge theory is geometrically explained in terms of a Cartan connection on second-order frames of the projective space P¹. The relationship between a Cartan connection and the usual (Ehresmann) connection on a principal bundle allows to gain an appropriate insight into the derivation of the genuine ‘diffeomorphisms out of gauge transformations’ given by Polyakov himself. Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités Aix-Marseille I, Aix-Marseille II et de l’Université du Sud Toulon-Var. Unité affiliée à la FRUMAM Fédération de Recherche 2291.     

Separability and Entanglement in the Hilbert Space Reference Frames Related Through the Generic Unitary Transform for Four Level System

Quantum correlations in the state of four-level atom are investigated by using generic unitary transforms of the classical (diagonal) density matrix. Partial cases of pure state, X-state, Werner state are studied in details. The geometrical meaning of unitary Hilbert reference-frame rotations generating entanglement in the initially separable state is discussed. Characteristics of the entanglement in terms of concurrence, entropy and negativity are obtained as functions of the unitary matrix rotating the reference frame.