I'll be getting back to walking with Planck, specifically on the subject mentioned above, the division of 2-dimensional phase space into cells of area h, which is thoroughly discussed in The Theory of Heat Radiation. This was not something Planck did in his original papers of October and December 1900. As discussed at length in my previous post, he used Boltzmann's combinatorial formula for the sum of the number of complexions in the logarithm for the entropy of a resonator (electromagnetic oscillator), and from that found the average value of the resonator's energy, which is where he found that emission of discrete packets of e.m. energy fit the curves of the recently measured black-body radiation spectrum. He only figured out the phase space thing later.
See my thesis for a discussion of electromagnetic mass, which is supposedly an entirely different type of infinite energy problem (evidently solved by renormalization techniques).
