Except configurations have a position, that’s part of a configuration, and even something identical in all other parts of the configuration cannot be identical in the positional aspect, if it occupies exactly the same point in all dimensions and fits all other parts of the configuration then it is not a duplicate identical particle, or whatever the configuration represents, but the same thing. There’s not two of it, there’s just one.
With that in mind, that two things don’t have the same positional tag two things can never be identical, without being one thing.
Atom X has configuration of 4, 3 in substance, and 1, 1, 1, 1, 1 in position. Something with the identical substance 4, 3 but of position (say 1 second later) 1, 1, 1, 1, 2 is not identical, it would be classically, but not with configuration.
Atom X 4, 3 substance 1, 1, 1, 1, 1 is identical to Atom X 4, 3 substance 1, 1, 1, 1, 1, because it’s the same thing, but apart from that everything is completely different and unique. In fact, if they weren’t you wouldn’t be able to distinguish them to talk about them, if Electron 1 and Electron 2 is really Electron 1 twice you wouldn’t be able to test for them separately or do anything to one that you couldn’t do to another (like separate them as in your example). In fact, with your example you start of with two fundamentally not-identical things (by the fact that they both go to different places in different amounts which identical things would not do).
Identical is not the same is indistinguishable. Two electrons can be perfectly identical, but still distinguishable in hidden-variable theories for example, because there their position and velocity are precisely determined at each point in time.
Except configurations have a position, that’s part of a configuration, and even something identical in all other parts of the configuration cannot be identical in the positional aspect, if it occupies exactly the same point in all dimensions and fits all other parts of the configuration then it is not a duplicate identical particle, or whatever the configuration represents, but the same thing. There’s not two of it, there’s just one.
With that in mind, that two things don’t have the same positional tag two things can never be identical, without being one thing.
Atom X has configuration of 4, 3 in substance, and 1, 1, 1, 1, 1 in position. Something with the identical substance 4, 3 but of position (say 1 second later) 1, 1, 1, 1, 2 is not identical, it would be classically, but not with configuration.
Atom X 4, 3 substance 1, 1, 1, 1, 1 is identical to Atom X 4, 3 substance 1, 1, 1, 1, 1, because it’s the same thing, but apart from that everything is completely different and unique. In fact, if they weren’t you wouldn’t be able to distinguish them to talk about them, if Electron 1 and Electron 2 is really Electron 1 twice you wouldn’t be able to test for them separately or do anything to one that you couldn’t do to another (like separate them as in your example). In fact, with your example you start of with two fundamentally not-identical things (by the fact that they both go to different places in different amounts which identical things would not do).
Think that’s all.
Identical is not the same is indistinguishable. Two electrons can be perfectly identical, but still distinguishable in hidden-variable theories for example, because there their position and velocity are precisely determined at each point in time.