Maybe this would be better suited for philosphy.se, if so, then let me know and i'll move it, but this seemed like a reasonable place to start.
Let's start with my motivations for asking such a bizarre question. I was watching a river flowing some years back when I started considering the individual water molecules that made up this river and where these particles would end up (in this case lake superior, and then eventually the ocean). So I had this idea, this river had a bunch of hydrogen atoms and a bunch of oxygen atoms, but each one of these particles was it's own particle. That is: each atom is surely its self and not another atom, and so I would say that each particle is unique. However, they're not, or are they? Each hydrogen atom is exactly the same(?), it has 1 proton and 1 electron. So fundamentally, two particles are exactly the same, yet they are unique. How do i remedy this paradox?
One answer I have thought of is this, sure each hydrogen is a proton and an electron, but two hydrogen atoms have different protons and electrons (they don't share the same proton or electron). So I would say the two hydrogen atoms are different. While they each have an electron and a proton, they are different electrons and protons and so the hydrogen atoms are different and not unique. but what if we go smaller?
Are there any differences between two separate electrons? These are fundamental particles, they consist only of themselves. So what is the fundamental difference between two separate electrons? If I lose my favorite electron when I vacation in florida, and then i try and find that electron later will i ever be able to tell which was my electron?
Is the only difference between two fundamental particles their location and momentum? Is there no way to keep track of a particle and know with certainty which, in a sea of particles, is the particle we're keeping track of?