system
Given the following post, respond as if you're commenting on Reddit:
human
What is the closest that we can push two electrons together?

I just want to get a better understanding of electromagnetic forces. How close can we bring two together? How much energy would it take? What would happen?
gpt
They can actually almost be in the exact same place, quantum mechanically, if they are in what's called the "singlet" state. As long as they have opposite spins, the Pauli Exclusion Principle will allow them to both occupy the same state. For example, two electrons in the ground state orbital of helium (the 1s2 state) are actually described by a difference of products of their wave functions. 

Okay, that was a lot of jargon. Imagine it like this. The electron is a wave, right? It's spread out over some space, like the surface water sloshing around in a bucket. Now pour another cup of water into the bucket. The water sloshes differently now, and you can identify that it's "two cups of water" sloshing, but you can't point to an exact ripple on the surface of the water and say "this is the original cup of water" or "this is the added cup of water." All you can do is describe the ripples as they are with either two cups of water in the bucket, or one cup of water in the bucket. The bucket is like the atom, and the sloshing is like the electron wavefunctions for different orbitals and electron occupancies.