It's not necessarily controversial that Millikan set out to disprove Einstein's work. After all, this is how the scientific method actually works: by falsifying possibilities to arrive at theory, and in the case of events that are absolutely predictable given particular conditions, law (like the ultra-famous Law of the Conservation of Energy, per Lumen). It's simply ironic that Millikan wound up winning a Nobel Prize in part because he had a distaste for another guy's Nobel Prize-winning work — in this case, Einstein's.
And to be sure, Millikan did have a distaste for it, as discussed on Science Blogs. Millikan was an ardent pragmatist who replied on experimental design to arrive at conclusions, and Einstein's work on the photoelectric effect was largely theoretical. In a January 1916 paper, Millikan starts off by saying, somewhat derisively, "Einstein's photoelectric equation for the maximum energy of emission of a negative electron under the influence of ultra-violet light... cannot in my judgment be looked upon at present as resting upon any sort of a satisfactory theoretical foundation."
Einstein's work, in this case, revolved around the now-commonly known nature of light: It behaves like a wave and a particle. In 1905, as the American Physical Society (APS) tells us, Einstein postulated that light traveled not in a continuous wave, but in "packets" — photons — that moved like waves, but retained the attributes of particles. Millikan thought that this sounded like rubbish, and set out to disprove it.
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