Can You Prove Two Particles Are Identical?

I've read this post several times, as well as the previous three posts, and I still can't see how the theory guarantees the indistinguishability of any two particles. Admittedly, I'm weak on the math, so maybe there was a really clear mathematical explanation that was wasted on me (I take it that the amplitude equations were supposed to rule out distinguishability in virtue of difference in, say, spin values at the 100th decimal place, but I couldn't tell for sure).

But, much like our stubborn philosopher Bob, I still think that the theory is insufficientl... (read more)

Mitchell, the essence of indistinguishability is NOT "that if you were to get the two particles and move them around so that they occupied the other position, that would count as the same configuration, quantum mechanically." Bob doesn't care about a version of indistinguishability that restricts the relevant properties to those important for QM. QM-indistinguishability is not indistinguishability. So if that's the notion of indistinguishability at play here, then Bob could accept that QM can determine that two electrons are QM-indistinguishab... (read more)