  Bright points (BPs) in the solar photosphere are radiative signatures of
magnetic elements described by slender flux tubes located in the darker
intergranular lanes. They contribute to the ultraviolet (UV) flux variations
over the solar cycle and hence may influence the Earth's climate. Here we
combine high-resolution UV and spectro-polarimetric observations of BPs by the
SUNRISE observatory with 3D radiation MHD simulations. Full spectral line
syntheses are performed with the MHD data and a careful degradation is applied
to take into account all relevant instrumental effects of the observations. It
is demonstrated that the MHD simulations reproduce the measured distributions
of intensity at multiple wavelengths, line-of-sight velocity, spectral line
width, and polarization degree rather well. Furthermore, the properties of
observed BPs are compared with synthetic ones. These match also relatively
well, except that the observations display a tail of large and strongly
polarized BPs not found in the simulations. The higher spatial resolution of
the simulations has a significant effect, leading to smaller and more numerous
BPs. The observation that most BPs are weakly polarized is explained mainly by
the spatial degradation, the stray light contamination, and the temperature
sensitivity of the Fe I line at 5250.2 \AA{}. The Stokes $V$ asymmetries of the
BPs increase with the distance to their center in both observations and
simulations, consistent with the classical picture of a production of the
asymmetry in the canopy. This is the first time that this has been found also
in the internetwork. Almost vertical kilo-Gauss fields are found for 98 % of
the synthetic BPs. At the continuum formation height, the simulated BPs are on
average 190 K hotter than the mean quiet Sun, their mean BP field strength is
1750 G, supporting the flux-tube paradigm to describe BPs.
