We employ the magnetic and velocity fields from turbulent dynamo simulations to synthesize the polarization of a typical photospheric line. The synthetic Stokes profiles have properties in common with those observed in the quiet Sun. The simulated magnetograms present a level of signal similar to that of the Inter-Network regions. Asymmetric Stokes V profiles with two, three, and more lobes appear in a natural way. The intensity profiles are broadened by the magnetic fields in fair agreement with observational limits. Furthermore, the Hanle depolarization signals of the Sr I λ4607 Å line turn out to be within the solar values. Differences between synthetic and observed polarized spectra can also be found. There is a shortage of Stokes V asymmetries, which we attribute to a deficit of structuring in the magnetic and velocity fields from the simulations as compared to the Sun. This deficit may reflect the fact that the Reynolds numbers of the numerical data are still far from solar values. We consider the possibility that intense and tangled magnetic fields, like those in the simulations, exist in the Sun. This scenario has several important consequences. For example, less than 10% of the existing unsigned magnetic flux would be detected in present magnetograms. The existing flux would exceed by far that carried by active regions during the maximum of the solar cycle. Detecting these magnetic fields would involve improving the angular resolution, the techniques to interpret the polarization signals, and to a lesser extent, the polarimetric sensitivity.