A critical remark on Planck's model of black--body

We reexamine the model of matter--radiation interaction considered by Planck in his studies on the black--body problem, and point out that it is, in our opinion, inconsistent. The key point is that Planck's model deals in principle with a system of $n$ material resonators interacting with the field, but in fact Planck actually deals with a single forced resonator, because he explicitly makes the assumption that the resonators act {\it independently of one another}, i.e. perform incoherent motions. We show that this assumption is inconsistent when the contribution of all the resonators is taken into account. Moreover we point out that, in view of the long range character of the electrodynamical forces, it would be more appropriate to deal from the start with the dynamics of the complete system, with the mutual interaction of matter and radiation taken into account, looking for solutions of a coherent or correlated type (normal modes).