The reason why we are supposed to be able to prove, that two particles are identical, is because quantum mechanics allows us to make an experiment, which has a certain outcome only! if the two particles taking part in the experiment are identical (the amplitudes add up). However, there is no prove that the amplitudes of “P1 at L1, P2 at L2” and “P1 at L2, P2 at L1″ can’t add up, even if P1 and P2 are different particles. Its only what quantum mechanics tells us.
Because, although quantum mechanics is a brilliant and most successful model of the real world, it is still a model. Therefore the particles could have different properties, which are ignored by quantum mechanics but which are very real. Consequently the experiment still only “fails to establish a difference” as Bob said.
The reason why we are supposed to be able to prove, that two particles are identical, is because quantum mechanics allows us to make an experiment, which has a certain outcome only! if the two particles taking part in the experiment are identical (the amplitudes add up). However, there is no prove that the amplitudes of “P1 at L1, P2 at L2” and “P1 at L2, P2 at L1″ can’t add up, even if P1 and P2 are different particles. Its only what quantum mechanics tells us. Because, although quantum mechanics is a brilliant and most successful model of the real world, it is still a model. Therefore the particles could have different properties, which are ignored by quantum mechanics but which are very real. Consequently the experiment still only “fails to establish a difference” as Bob said.