But, ok, it is a little far-fetched to think that all of the relevant factors would have to come together. First, I need to confirm that CalTech actually has the apparatus and that it is in working order with all of the necessary auxiliary parts available. Then I would have to get permission to work with it, which is not impossible but somewhat unlikely. After that, I would have to get sufficient funding to fly out to California and live there for, I would think, about a month. Finally, I would have to weigh the costs and benefits of either being away from or uprooting my family for a good chunk of the summer.
Still, it's worth looking into. I emailed Paolo about my suspicion that CalTech has the apparatus, and he seemed intrigued. My evidence that they have it comes from two videos online. The first is a brief demonstration using an apparatus that looks just like Millikan's:
The second is an old educational video that was filmed in the same lecture hall, in which the lecturer points to an identical-looking apparatus in roughly the same spot on the same table and says explicitly that it is Millikan's own apparatus (about 21:40 in):
Come to think of it, it might actually be better for me if they have a replica of Millikan's apparatus, rather than the original one. The original would have a nice "gee-whiz" factor, but they might be more willing to let a grad student tinker with a replica.
I suggested that Paolo contact Jeff Cady, the demonstrator in the first video, because he is more likely to be taken seriously than I am. We'll see what happens!