The discussions between Bragg and Barkla in Britain, and between Stark and Sommerfeld in Germany, encouraged attempts to determine how much spatial concentration of radiant energy was demanded by ionization, and how much was compatible with classical electromagnetic theory. Mirroring the different perceptions of and approach to the problems of x-ray absorption in Britain and in Germany, there were two parallel responses. J. J. Thomson recognized that the paradoxes applied equally to all forms of radiation. He influenced important experimental tests of energy localization, and concluded that the classical ideal of symmetry of the electric field around an electron would have to be abandoned. Arnold Sommerfeld took no refuge in the alteration of the physical interpretation of Maxwell's theory. He pressed formal electrodynamics to its extreme to show that the energy of y-rays might be localized to an extent compatible with recent experiments.

But neither Thomson's nor Sommerfeld's treatment addressed the most compelling problem raised by Bragg and Stark. The energy transferred from a wave to an electron does not seem to change when the distance from the source changes. No matter how severely limited in angular extent the energy of x-rays and γ-rays might be according to Thomson or Sommerfeld, that energy is still diluted in strength as the rays traverse space. Neither of them therefore confronted the issues in quite the same way as did Bragg, who had never intended his neutral-pair hypothesis to apply to ordinary light.