  We present a general relativistic model of a spherical shell of matter with a
perfect fluid on its surface coupled to an internal oscillator, which
generalizes a model recently introduced by the authors to construct a
self-gravitating interferometer [1]. The internal oscillator evolution is
defined with respect to the local proper time of the shell, allowing the
oscillator to serve as a local clock that ticks differently depending on the
shell's position and momentum. A Hamiltonian reduction is performed on the
system, and an approximate quantum description is given to the reduced phase
space. If we focus only on the external dynamics, we must trace out the clock
degree of freedom, and this results in a form of intrinsic decoherence that
shares some features with a proposed "universal" decoherence mechanism
attributed to gravitational time dilation [2]. We note that the proposed
decoherence remains present in the (gravity-free) limit of flat spacetime,
emphasizing that the effect can be attributed entirely to proper time
differences, and thus is not necessarily related to gravity. Whereas the effect
described in [2] vanishes in the absence of an external gravitational field,
our approach bootstraps the gravitational contribution to the time dilation
decoherence by including self-interaction, yielding a fundamentally
gravitational intrinsic decoherence effect.
