  One of the key research problems in stellar physics is to decipher the
small-scale magnetic activity of the quiet solar atmosphere. Recent
magneto-convection simulations that account for small-scale dynamo action have
provided three-dimensional (3D) models of the solar photosphere characterized
by a high degree of small-scale magnetic activity, similar to that found
through theoretical interpretation of the scattering polarization observed in
the Sr I 4607 \AA\ line. Here we present the results of a novel investigation
of the Hanle effect in this resonance line, based on 3D radiative transfer
calculations in a high-resolution magneto-convection model having most of the
convection zone magnetized close to the equipartition and a surface mean field
strength ${\langle B \rangle}{\approx}170$ G. The Hanle effect produced by the
model's magnetic field depolarizes the zero-field scattering polarization
signals significantly, to the extent that the center-to-limb variation of the
calculated spatially-averaged polarization amplitudes is compatible with the
observations. The standard deviation of the horizontal fluctuations of the
calculated scattering polarization signals is very sensitive to the model's
magnetic field and we find that the predicted spatial variations are
sufficiently sizable so as to be able to detect them, especially with the next
generation of solar telescopes. We find that at all on-disk positions the
theoretical scattering polarization signals are anti-correlated with the
continuum intensity. To facilitate reaching new observational breakthroughs, we
show how the theoretically predicted polarization signals and spatial
variations are modified when deteriorating the signal-to-noise ratio and the
spectral and spatial resolutions of the simulated observations.
