  Deciphering and understanding the small-scale magnetic activity of the quiet
solar photosphere should help to solve many of the key problems of solar and
stellar physics, such as the magnetic coupling to the outer atmosphere and the
coronal heating. At present, we can see only ${\sim}1%$ of the complex
magnetism of the quiet Sun, which highlights the need to develop a reliable way
to investigate the remaining 99%. Here we report three-dimensional radiative
tranfer modelling of scattering polarization in atomic and molecular lines that
indicates the presence of hidden, mixed-polarity fields on subresolution
scales. Combining this modelling with recent observational data we find a
ubiquitous tangled magnetic field with an average strength of ${\sim}130$ G,
which is much stronger in the intergranular regions of solar surface convection
than in the granular regions. So the average magnetic energy density in the
quiet solar photosphere is at least two orders of magnitude greater than that
derived from simplistic one-dimensional investigations, and sufficient to
balance radiative energy losses from the solar chromosphere.
