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##

Double Slit Interference

The third property of the radiation process is that it highlights the
interference between the waves coming from Rindler sectors and
. The interference pattern, which is recorded on a hypersurface of
synchronous time , has fringes whose separation
yields the separation between the two localized in and .
Let these sources be located symmetrically at

and let them have equal proper frequency and hence (in
compliance with the first term of the wave Eq.(27) equal Rindler coordinate frequency

Consequently, they are characterized by their amplitudes and their
phases. Indeed, their form is

Thus the full scalar field, Eq.(54), expresses two waves. Both propagate in the expanding
inertial frame, which is coordinatized by
. Their
respective wave crests are located in compliance with the constant
phase conditions
Consequently, one wave
travels into the -direction with amplitude , the other
into the -direction with amplitude . They have well-determined phase velocities.
Together, these two waves form an interference pattern of standing waves,

The amplitude of this interference pattern is ,
and there is a uniform background of amplitude
.
At synchronous time the interference fringes along the -direction
can be read off the factor

in Eq.(56). Consequently, the fringes are
spaced by the amount

This means that, analogous to a standard optical interference pattern,
the fringe spacing is inversely proportional to the distance
between the two sources. Furthermore, the position of this
interference pattern depends on the phase of source relative to
source [#!phase!#]. It is difficult to find a more welcome way
than the four Rindler sectors for double slit interference.
These observations lead to the conclusion that (i) the four Rindler
sectors quite naturally accommodate a *double slit
interferometer*, and that (ii) the spatial as well as the temporal
properties of the interference fringes, together with the magnitude of
the travelling background wave, are enough to reconstruct every aspect
of the two sources, Eq.(55).

** Next:** The Rindler Interferometer
** Up:** RADIATION: PHYSICAL RELATION TO
** Previous:** Spatial Structure of the
Ulrich Gerlach
2001-10-09