24 research outputs found
Gyroscope deviation from geodesic motion: quasiresonant oscillations on a circular orbit
General relativistic spin-orbit interaction leads to the quasiresonant
oscillation of the gyroscope mass center along the orbital normal. The beating
amplitude does not include the speed of light and equals the ratio of the
intrinsic momentum of the gyroscope to its orbital momentum. The modulation
frequency equals the angular velocity of the geodetic precession that prevents
the oscillation from resonance. The oscillation represents the precession of
the gyroscope orbital momentum. Within an acceptable time the oscillation
amplitude reaches the values that are amenable to being analyzed
experimentally. Taking into account the source oblateness decreases the beating
amplitude and increases the modulation frequency by the factor that is equal to
the ratio of the quadrupole precession velocity to the geodetic precession
velocity. The period of the quadrupole precession turns out to be a quite
sufficient time to form a measurable amplitude of the oscillation.Comment: 5 pages, LaTeX2e, 1 eps figure, to appear in J. Exp. Theor. Phy
Ultrarelativistic decoupling transformation for generalized Dirac equations
The Foldy--Wouthuysen transformation is known to uncover the nonrelativistic
limit of a generalized Dirac Hamiltonian, lending an intuitive physical
interpretation to the effective operators within Schr\"{o}dinger--Pauli theory.
We here discuss the opposite, ultrarelativistic limit which requires the use of
a fundamentally different expansion where the leading kinetic term in the Dirac
equation is perturbed by the mass of the particle and other interaction
(potential) terms, rather than vice versa. The ultrarelativistic decoupling
transformation is applied to free Dirac particles (in the Weyl basis) and to
high-energy tachyons, which are faster-than-light particles described by a
fully Lorentz-covariant equation. The effective gravitational interactions are
found. For tachyons, the dominant gravitational interaction term in the
high-energy limit is shown to be attractive, and equal to the leading term for
subluminal Dirac particles (tardyons) in the high-energy limit.Comment: 10 pages; RevTeX; Phys. Rev. A, in pres