One day Merle had read in the Hartford Courant about a couple of professors at the Case Institute in Cleveland who were planning an experiment to see what effect, if any, the motion of the Earth had on the speed of light through the luminiferous Æther.
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"Hartford Courant"
This Connecticut newspaper is apparently the oldest continuously published newspaper in the United States, beginning its life as the Connecticut Courant in 1764. Merle would have been a reader of this paper as we learned, from his association with Heino Vanderjuice, he was a Connecticut resident. Merle, interested in light and photography, had a mechanical aptitude which he used to help build machines for Professor Vanderjuice back at Yale.
"a couple of professors at the Case Institute in Cleveland"
Physicists Albert Michelson and Edward Morley. The Case Institute wasn't actually known as the Case Institute of Technology until 1947. At the time, it would have been the Case School of Applied Science. But don't be too hard on Pynchon about that. It's not like I would have known any better if I didn't have the Internet to help me understand every single reference Pynchon makes.
"were planning an experiment"
The experiment described in this passage took place between April and July of 1887.
"to see what effect, if any, the motion of the Earth had on the speed of light through the luminiferous Æther"
This experiment is just one of the major changes happening around the liminal space of 1890. Being that Against the Day is one of Pynchon's four great novels he had within him (the others being Mason & Dixon, Gravity's Rainbow, and, well, um, I don't know. Has he done the fourth?! Are the three I named even three of the four?! You'd think I'd do some outside research on shit like this), it takes place at a pivotal place in history (especially the history of Western Civilization, or at least through its perspective, and particularly the American perspective), science, economics, and any other academic subject you can think of.
While meant to determine motions effect on the speed of light, what the experiment actually presented was strong evidence that Æther didn't exist. So we have the world before 1887 where science simply took for granted that a substance or medium must exist within vacuums and all around us that enables light waves to pass through (as waves through water or sound through air/water), dubbing the mystery substance Æther, and the time after where an entirely new understanding of what light might be and how it works was needed. So just as the Frontier was disappearing, changing the entire landscape of America and our relationship with it and each other, Æther was disappearing as well, turning the physics of light on its head.
Reading about the failed experiment reminds one of reading Gravity's Rainbow due to all the talk of sine waves and zeroes. I don't think they ever mention beyond the zero though! But beyond this experiment, which was pretty much the nail in the coffin for ether (both physicists themselves ceasing their experimentation into the nature of Æther and concentrating instead on light's properties) and opened up the scientific world for accepting the idea of special relativity. Whatever that is, amirite?! I think that just means light doesn't go faster if a train turns on its headlights because it just phase shifts to red or something (unless it's blue!).