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The concept of information transmission in a multiple antenna channel with scattering objects is studied from first physical principles. The amount of information that can be transported by electromagnetic radiation is related to the space-wavenumber and the time-frequency spectra of the system composed by the transmitting antennas and the scattering objects, and to the spatial extension of the receiving domain. The spatial information content of the field is related to the number of relevant communication modes of the channel. It is shown that for narrow-band frequency transmission space and time can be decoupled, leading to a space-time information duality principle in the computation of the capacity of the radiating system. In contrast, in the case of wide-band frequency transmission, it is shown that time and space cannot be decoupled and they jointly characterize the wave's information content.