IL: But the experiment doesn’t prove that the two photons are really identical, it just proves that the photons are identical as far as the configurations are concerned. The photons could still have tiny tags with a number on them, but for some reason the configurations don’t care about tags.
Yes, that’s the part where the observed universe is a lie.
I have difficulty expressing in words exactly how fundamental is the notion of configurations. Now that we know about them, our old ideas about particles have gone away, or rather, been made strictly emergent in configurations… what you just said is the same probability as discovering that apples aren’t made of atoms after all, but are in fact fundamental apples.
The configurations are reality, the underlying fundamental from which the appearance of individual particles emerges; they are not something tacked on.
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.
You assume that the wave-functions are ontic, or close enough. In hidden-variable theories of QM the particles have a definite position and velocity at each point in time, and I don’t see a problem with adding a hidden variable each particle that makes them nonidentical, except that this would violate occam’s razor, but that is a probabilistic argument, not an absolute.
And while hidden-variable theories are not falsifiable, you could have “slightly-hidden-variable” theories, which would need to be ruled out by experiements.
You could argue that the added hidden variable is not part of the particle, but then your particles would be identical by definition, which makes this whole discussion moot.
IL: But the experiment doesn’t prove that the two photons are really identical, it just proves that the photons are identical as far as the configurations are concerned. The photons could still have tiny tags with a number on them, but for some reason the configurations don’t care about tags.
Yes, that’s the part where the observed universe is a lie.
I have difficulty expressing in words exactly how fundamental is the notion of configurations. Now that we know about them, our old ideas about particles have gone away, or rather, been made strictly emergent in configurations… what you just said is the same probability as discovering that apples aren’t made of atoms after all, but are in fact fundamental apples.
The configurations are reality, the underlying fundamental from which the appearance of individual particles emerges; they are not something tacked on.
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.
You assume that the wave-functions are ontic, or close enough. In hidden-variable theories of QM the particles have a definite position and velocity at each point in time, and I don’t see a problem with adding a hidden variable each particle that makes them nonidentical, except that this would violate occam’s razor, but that is a probabilistic argument, not an absolute. And while hidden-variable theories are not falsifiable, you could have “slightly-hidden-variable” theories, which would need to be ruled out by experiements.
You could argue that the added hidden variable is not part of the particle, but then your particles would be identical by definition, which makes this whole discussion moot.