  To model the interior of a black hole, a study is made of a spin system with
long-range random four-spin couplings that exhibits quantum chaos. The black
hole limit corresponds to a system where the microstates are approximately
degenerate and equally likely, corresponding to the high temperature limit of
the spin system. At the leading level of approximation, reconstruction of bulk
physics implies that local probes of the black hole should exhibit free
propagation and unitary local evolution. We test the conjecture that a
particular mean field Hamiltonian provides such a local bulk Hamiltonian by
numerically solving the exact Schrodinger equation and comparing the time
evolution to the approximate mean field time values. We find excellent
agreement between the two time evolutions for timescales smaller than the
scrambling time. In earlier work, it was shown bulk evolution along comparable
timeslices is spoiled by the presence of the curvature singularity, thus the
matching found in the present work provides evidence of the success of this
approach to interior holography. The numerical solutions also provide a useful
testing ground for various measures of quantum chaos and global scrambling. A
number of different observables, such as entanglement entropy,
out-of-time-order correlators, and trace distance are used to study these
effects. This leads to a suitable definition of scrambling time, and evidence
is presented showing a logarithmic variation with the system size.
