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.
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.