delayed-choice experiment
The delayed-choice experiment is a thought experiment proposed by John Wheeler, and since carried out for real, in which the decision of whether to look for wave-like or particle-like behaviour is postponed until after the particle has already passed the slits or beam-splitter. Common sense whispers that the particle must have 'decided' on the way in whether to behave as a wave or a particle. Wheeler's setup makes the choice only after that point, seemingly too late.
What the experiments find is that the outcome always matches the measurement actually performed, regardless of how late the choice is made: arrange to detect interference and you get fringes; arrange to detect the path and you get definite paths. There is no sign that the particle pre-commits to a nature at the slits and then gets caught out by a last-second switch. The naive idea that the particle 'was already' a wave or a particle simply does not survive.
Wheeler's lesson is that it is meaningless to assign a wave or particle nature to the particle before the full experiment, including the final choice, is fixed. This is not the future rewriting the past, and it sends no signal backward in time. It is a vivid statement of complementarity: which property is real is settled by the whole experimental arrangement, and asking what 'really happened' apart from that arrangement is asking an unanswerable question.
Deciding late which question to ask makes no difference: the result fits the measurement made.
Delayed choice is not retrocausation: nothing travels backward in time and no message can be sent to the past. It shows only that a quantum object has no fixed wave-or-particle identity until the whole experiment is complete.