(For context, Sheldon is discussing the famous double-slit experiment in physics.)
Using "each" instead of "either" would change the meaning of the sentence.
Let's work with a simpler version of the sentence:
If either slit is observed, the photon will not go through both slits.
In context, "either" implies a choice between two options. During the experiment, a person may choose to look at the first slit only, or at the second slit only. The outcome will be the same in both cases: "the photon will not go through both slits."
Now, let's look at the alternative:
If each slit is observed, the photon will not go through both slits.
"Each" does not imply a choice between options. This sentence says that if a person looks at the first slit, and a person looks at the second slit, then afterwards "the photon will not go through both slits". (Perhaps one person should look at the first slit and a different person should look at the second slit, or perhaps a single person may look at both of the slits in turn, one after the other. It is not clear from context.)
Let me give another example:
Here is a red marker, and here is a green marker. Take either marker and draw a picture.
This means that I want you take one of the two markers and draw one picture. I do not care whether you use the red marker or the green marker.
Here is a red marker, and here is a green marker. Take each marker and draw a picture.
This means that I want you to draw two pictures. One picture should be drawn with the red marker, and the other picture should be drawn with the green marker. I do not care about the order; you may draw the red picture first and the green picture second, or the green picture first and the red picture second.