Paired accelerated arames: The perfect interferometer with everywhere smooth wave amplitudes

TL;DR

This paper explores a spacetime-based interferometer model derived from Rindler acceleration, analyzing wave packet behaviors across horizons and their implications for quantum and wave processes, including amplification and detector dynamics.

Contribution

It introduces a novel interferometer framework based on Rindler spacetime, describing wave packet histories with varying explosivity indices and their quantum mechanical implications.

Findings

Wave packets behave smoothly across horizons.

High explosivity index leads to non-trivial internal dynamics.

Application to wave amplification in inhomogeneous dielectrics.

Abstract

Rindler's 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. These processes are described in terms of amplitudes which behave smoothly across the event horizons of all four Rindler sectors. In this context there arises quite naturally a complete set of orthonormal wave packet histories, one of whose key properties is their "explosivity index". In the limit of low index values the wave packets trace out fuzzy world lines. 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 elucidate 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.