A. D'Abro on Max Planck

“There is no particular mystery about mathematical analysis; its only distinguishing feature is that it is more trustworthy, more precise, and permits us to proceed farther and along safer lines. Consider, for example, the well-known change of colour from red to white displayed by the light radiated through an aperture made in a heated enclosure, as the temperature increases. From this elementary fact of observation Planck, thanks to mathematical analysis, was able to deduce the existence of light quanta and thence the possibility that all processes of change were discontinuous, and that a body could only rotate with definite speeds. Obviously, commonplace reasoning unaided by mathematics would never have led us even to suspect these extraordinary results.”

“Inasmuch as both Rayleigh's and Wien's laws of radiation, though incorrect, appear to express facts correctly at opposite limits of temperature and frequency, we may presume that the correct law must have an intermediary form, passing over into Rayleigh's when [temperature] T is large and [frequency] ν small, and into Wein's when the reverse situation... Planck, guided by these considerations, devised a new theory of radiation which he called the "Quantum Theory." From this theory Planck was able to derive a radiation law which satisfied Wien's relation, ...the displacement law [when the temperature is increased, intensities of all the frequencies increase, while the radiation of maximum intensity is directly proportional to the absolute temperature] and Stefan's law, and which was in excellent agreement with experimental measurements at all temperatures.”