THE PERFECT INTERFEROMETER

WITH

EVERYWHERE SMOOTH WAVE AMPLITUDES

**ULRICH H. GERLACH
Department of Mathematics, Ohio State University,
Columbus, OH 43210, USA**

**November 11, 1997**

In the absence of gravitation the distinguishing feature of any
linearly and uniformly accelerated frame is that it is one member of
a pair moving into opposite directions. This pairing partitions
Minkowski spacetime into four mutually exclusive and jointly
exhaustive domains whose boundary consists of the future and past
event horizons relative to each of the two frames. This
acceleration-induced partitioning of spacetime leads to a
nature-given interferometer. It accomodates quantum mechanical and
wave mechanical processes in spacetime which in (Euclidean) optics
correspond to wave processes in a ``Mach-Zehnder'' interferometer:
amplitude splitting, reflection, and interference. The spacetime
description of these processes is given in terms of amplitudes which
are defined globally as well as locally in each of the four Rindler
spacetime domains. It is found that these amplitudes behave smoothly
across the event horizons. In this context there arises quite
naturally a complete set of orthonormal wave packet histories, one
of whose key properties is their *explosivity index*. It
measures the rate at which the wave packets collapse and reexplode.
In the limit of low index values the wave packets trace out fuzzy
world lines. For large mass this fuzziness turns into the
razor-sharpness of classically determinate world lines of the
familiar Klein-Gordon scalar particles. By contrast, in the
asymptotic limit of high index values, there are no world lines, not
even fuzzy ones. Instead, the wave packet histories are those of
entities with non-trivial internal collapse and explosion dynamics.
Their details are described by the wave processes in the
above-mentioned Mach-Zehnder interferometer. Each one of them is a
double slit interference process. These wave processes are applied
to illucidate the amplification of waves in an accelerated
inhomogeneous dielectric. Also discussed are the properties and
relationships among the transition amplitudes of an accelerated
finite-time detector.

PACS numbers: 04.62.+v, 03.65.Pm, 42.25.Hz, 42.25.Fx