Let me give another concrete example of where a physical system might be indistinguishable by one experiment, but has to be distinguishable regarding another.
Imagine heating a bose-einstein condensate with a laser, if all the atoms were truly indistinguishable, then there is no basis upon which an atom could be excited to a higher energy level while another one shouldn’t be. Trying to get one particle to be in a different state to the rest seems to be like trying to separate sand by sieving it, when all the sand particles are the same size.
Let me give another concrete example of where a physical system might be indistinguishable by one experiment, but has to be distinguishable regarding another.
Imagine heating a bose-einstein condensate with a laser, if all the atoms were truly indistinguishable, then there is no basis upon which an atom could be excited to a higher energy level while another one shouldn’t be. Trying to get one particle to be in a different state to the rest seems to be like trying to separate sand by sieving it, when all the sand particles are the same size.
I’m still thoroughly puzzled by quantum.