  The near-field Lienard-Wiechert potential solution of a longitudinally
oscillating electrical field produced by an oscillating charge is presented,
and the results are compared to the R. P. Feynman multipole far-field solution.
The results indicate that the phase speed of a longitudinally oscillating
electrical field is much faster than the speed of light in the near field. A
similar analysis is presented for a longitudinally oscillating gravitational
field produced by a vibrating mass. The result also indicates that the phase
speed of a longitudinally oscillating gravitational field is also much faster
than the speed of light in the near-field. The possibility of measuring the
group speed of a longitudinally oscillating electrical field and a
longitudinally oscillating gravitational field, which is commonly thought to be
equal to the speed of light, is now being considered. The basic idea is to
amplitude-modulate the longitudinal vibration of a charge or a mass and to
measure the resultant longitudinal vibration of a nearby charge or a mass due
to electrical or gravitational interaction. The modulation signal can then be
extracted using a diode detector and the group speed can then be determined
from the oscillation frequency, the separation distance between the masses, and
the measurement of the phase shift of the modulation signal. If the group speed
is equal to the speed of light, then phase shifts on the order of 1 microdegree
could be generated with a typical experimental set-up. An analysis using the
classical definition of group velocity for a longitudinally oscillating
electrical field is presented, and the results indicate that the group speed is
also much faster that the speed of light in the near field, which should not be
possible due to causality violation.
