Symbolism, Imagery, Allegory
If you didn't think that thought experiments dreamed up by an Austrian physicist could be romantic, think again. The ideas behind Schrödinger's cat come up quite a few times in this story. The band the Maybe Dead Cats is named after the theory, and Jane explains pretty well just what Edwin Schrödinger was up to with his fictional feline friend:
"Schrodinger was doing a thought experiment. Okay, so, this paper had just come out arguing that if, like, an electron might be in any one of four different places, it is sort of in all four places at the same time until the moment someone determines which of the four places it's in […]
"It totally doesn't make sense. It's mind-bendingly weird. So Schrodinger tries to point this out. He says: put a cat inside a sealed box with a little bit of radioactive stuff that might or might not—depending on the location of its subatomic particles—cause a radiation detector to trip a hammer that releases poison into the box and kills the cat […]
"So according to the theory that electrons are in all-possible-positions until they are measured, the cat is both alive and dead until we open the box and find out if it is alive or dead. He was not endorsing cat-killing or anything. He was just saying that it seemed a little improbable that a cat could be simultaneously alive and dead." (13.96, 98, 100)
Okay, so that might seem a bit dry and science-y, but it's actually a pretty awesome symbol for love. Will is in that in-between place; he doesn't know if he wants Jane or not. Maybe the relationship cat is dead or maybe it's alive. He doesn't know and he doesn't want to know, though; he just wants to keep that box closed and not deal with any of the feelings that will arise if the cat turns out to be dead after all.
Will realizes this big time once he finds out that Jane has that pesky boyfriend:
It seems to me that all the things we keep in sealed boxes are both alive and dead until we open the box, that the unobserved is both there and not. Maybe that's why I can't stop thinking about the other Will Grayson's huge eyes in Frenchy's: because he had just rendered the dead-and-alive cat dead. I realize that's why I never put myself in a situation where I really need Tiny, and why I followed the rules instead of kissing her when she was available: I chose the closed box. (13.101)
In the end, Will and Jane decide to open the box and give it a try. Things are alive for now, but who knows? In the future it might all fall apart. But that's okay—Will finally realizes that this stuff is all part of living and loving. He doesn't want to opt for closed boxes anymore. He wants to pull off those lids and take his chance with what's inside. Yay.