218 research outputs found
Quantum Theory in Accelerated Frames of Reference
The observational basis of quantum theory in accelerated systems is studied.
The extension of Lorentz invariance to accelerated systems via the hypothesis
of locality is discussed and the limitations of this hypothesis are pointed
out. The nonlocal theory of accelerated observers is briefly described.
Moreover, the main observational aspects of Dirac's equation in noninertial
frames of reference are presented. The Galilean invariance of nonrelativistic
quantum mechanics and the mass superselection rule are examined in the light of
the invariance of physical laws under inhomogeneous Lorentz transformations.Comment: 25 pages, no figures, contribution to Springer Lecture Notes in
Physics (Proc. SR 2005, Potsdam, Germany, February 13 - 18, 2005
Nonlocality of Accelerated Systems
The conceptual basis for the nonlocality of accelerated systems is presented.
The nonlocal theory of accelerated observers and its consequences are briefly
described. Nonlocal field equations are developed for the case of the
electrodynamics of linearly accelerated systems.Comment: LaTeX file, no figures, 9 pages, to appear in: "Black Holes,
Gravitational Waves and Cosmology" (World Scientific, Singapore, 2003
Acceleration and Classical Electromagnetic Radiation
Classical radiation from an accelerated charge is reviewed along with the
reciprocal topic of accelerated observers detecting radiation from a static
charge. This review commemerates Bahram Mashhoon's 60th birthday.Comment: To appear in Gen. Rel. Gra
Gravitomagnetic Effects in the Propagation of Electromagnetic Waves in Variable Gravitational Fields of Arbitrary-Moving and Spinning Bodies
Propagation of light in the gravitational field of self-gravitating spinning
bodies moving with arbitrary velocities is discussed. The gravitational field
is assumed to be "weak" everywhere. Equations of motion of a light ray are
solved in the first post-Minkowskian approximation that is linear with respect
to the universal gravitational constant . We do not restrict ourselves with
the approximation of gravitational lens so that the solution of light geodesics
is applicable for arbitrary locations of source of light and observer. This
formalism is applied for studying corrections to the Shapiro time delay in
binary pulsars caused by the rotation of pulsar and its companion. We also
derive the correction to the light deflection angle caused by rotation of
gravitating bodies in the solar system (Sun, planets) or a gravitational lens.
The gravitational shift of frequency due to the combined translational and
rotational motions of light-ray-deflecting bodies is analyzed as well. We give
a general derivation of the formula describing the relativistic rotation of the
plane of polarization of electromagnetic waves (Skrotskii effect). This formula
is valid for arbitrary translational and rotational motion of gravitating
bodies and greatly extends the results of previous researchers. Finally, we
discuss the Skrotskii effect for gravitational waves emitted by localized
sources such as a binary system. The theoretical results of this paper can be
applied for studying various relativistic effects in microarcsecond space
astrometry and developing corresponding algorithms for data processing in space
astrometric missions such as FAME, SIM, and GAIA.Comment: 36 pages, 1 figure, submitted to Phys. Rev.
Effects of Space-Time Curvature on Spin-1/2 Particle Zitterbewegung
This paper investigates the properties of spin-1/2 particle Zitterbewegung in
the presence of a general curved space-time background described in terms of
Fermi normal co-ordinates, where the spatial part is expressed using general
curvilinear co-ordinates. Adopting the approach first introduced by Barut and
Bracken for Zitterbewegung in the local rest frame of the particle, it is shown
that non-trivial gravitational contributions to the relative position and
momentum operators appear due to the coupling of Zitterbewegung frequency terms
with the Ricci curvature tensor in the Fermi frame, indicating a formal
violation of the weak equivalence principle. Explicit expressions for these
contributions are shown for the case of quasi-circular orbital motion of a
spin-1/2 particle in a Vaidya background. Formal expressions also appear for
the time-derivative of the Pauli-Lubanski vector due to space-time curvature
effects coupled to the Zitterbewegung frequency. As well, the choice of
curvilinear co-ordinates results in non-inertial contributions in the time
evolution of the canonical momentum for the spin-1/2 particle, where
Zitterbewegung effects lead to stability considerations for its propagation,
based on the Floquet theory of differential equations.Comment: 22 pages, no figures; slight revisions; accepted for publication in
Classical and Quantum Gravit
The Generalized Jacobi Equation
The Jacobi equation in pseudo-Riemannian geometry determines the linearized
geodesic flow. The linearization ignores the relative velocity of the
geodesics. The generalized Jacobi equation takes the relative velocity into
account; that is, when the geodesics are neighboring but their relative
velocity is arbitrary the corresponding geodesic deviation equation is the
generalized Jacobi equation. The Hamiltonian structure of this nonlinear
equation is analyzed in this paper. The tidal accelerations for test particles
in the field of a plane gravitational wave and the exterior field of a rotating
mass are investigated. In the latter case, the existence of an attractor of
uniform relative radial motion with speed is pointed
out. The astrophysical implications of this result for the terminal speed of a
relativistic jet is briefly explored.Comment: LaTeX file, 4 PS figures, 28 pages, revised version, accepted for
publication in Classical and Quantum Gravit
Spin-Gravity Coupling in a Rotating Universe
The coupling of intrinsic spin with the nonlinear gravitomagnetic fields of
Goedel-type spacetimes is studied. We work with Goedel-type universes in order
to show that the main features of spin-gravity coupling are independent of
causality problems of the Goedel universe. The connection between the
spin-gravitomagnetic field coupling and Mathisson's spin-curvature force is
demonstrated in the Goedel-type universe. That is, the gravitomagnetic
Stern--Gerlach force due to the coupling of spin with the gravitomagnetic field
reduces in the appropriate correspondence limit to the classical Mathisson
spin-curvature force.Comment: 37 page
Nonlocal Electrodynamics of Rotating Systems
The nonlocal electrodynamics of uniformly rotating systems is presented and
its predictions are discussed. In this case, due to paucity of experimental
data, the nonlocal theory cannot be directly confronted with observation at
present. The approach adopted here is therefore based on the correspondence
principle: the nonrelativistic quantum physics of electrons in circular
"orbits" is studied. The helicity dependence of the photoeffect from the
circular states of atomic hydrogen is explored as well as the resonant
absorption of a photon by an electron in a circular "orbit" about a uniform
magnetic field. Qualitative agreement of the predictions of the classical
nonlocal electrodynamics with quantum-mechanical results is demonstrated in the
correspondence regime.Comment: 23 pages, no figures, submitted for publicatio
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