Aims: We study the observational signature of flux emergence in the photosphere using synthetic data from a 3D MHD simulation of the emergence of a twisted flux tube. Methods: Several stages in the emergence process are considered. At every stage we compute synthetic Stokes spectra of the two iron lines Fe I 6301.5 Å and Fe I 6302.5 Å and degrade the data to the spatial and spectral resolution of Hinode's SOT/SP. Then, following observational practice, we apply Milne-Eddington-type inversions to the synthetic spectra in order to retrieve various atmospheric parameters and compare the results with recent Hinode observations. Results: During the emergence sequence, the spectral lines sample different parts of the rising flux tube, revealing its twisted structure. The horizontal component of the magnetic field retrieved from the simulations is close to the observed values. The flattening of the flux tube in the photosphere is caused by radiative cooling, which slows down the ascent of the tube to the upper solar atmosphere. Consistent with the observations, the rising magnetized plasma produces a blue shift of the spectral lines during a large part of the emergence sequence. Figure 3 is only available in electronic form at http://www.aanda.org