Self-gravitating interferometry and intrinsic decoherence

To investigate the possibility that intrinsic gravitational decoherence can be theoretically demonstrated within canonical quantum gravity, we develop a model of a self-gravitating interferometer. We search for evidence in the resulting interference pattern that would indicate coherence is fundamentally limited due to general relativistic effects. To eliminate the occurrence of gravitational waves, we work in spherical symmetry, and construct the “beam” of the interferometer out of WKB states for an infinitesimally thin shell of matter. For internal consistency, we encode information about the beam optics within the dynamics of the shell itself, by arranging an ideal fluid on the surface of the shell with an equation of state that enforces beam splitting and reflections. We then determine sufficient conditions for (interferometric) coherence to be fully present even after general relativistic corrections are introduced, test whether or not they can be satisfied, and remark on the implications of the results.

Figure 1

Schematic representation of the splitting, reflecting, and recombining that occur in our shell interferometer. $R$ and $T$ are effective reflection and transmission coefficients for the beam splitter.

Figure 2

A sample equation of state represented by (60).

Figure 3

A sample mass function $\widehat{M}$ is plotted with respect to the shell radius $X$. The approximate step function near $X=2$ serves as a beam splitter, and the steep quadratic sides correspond to the inner and outer reflectors of the interferometer.

Figure 4

Sample interference pattern, for $M_{+}=15$, $v_{+}=0.003$, $X_{-}=5000$, $L_{-}=20$, and $M_{-}$ chosen to satisfy (92), plotted against the outer mirror position, $X_{+}$.

Figure 5

Sample interference pattern, for $M_{+}=15$, $v_{+}=0.01$, $X_{-}=200$, $L_{-}=20$, and $M_{-}$ chosen to satisfy (92), plotted against the outer mirror position, $X_{+}$.

Figure 6

Sample interference pattern, for $M_{+}=0.05$, $v_{+}=0.0001$, $X_{-}\approx 1$, $L_{-}\approx 0.997$, and $M_{-}$ chosen to satisfy (92), plotted against the outer mirror position, $X_{+}$.