If we want to know which way the photon went, we can't see the interference pattern. If we want to see an interference pattern, we can't ask to know which way the photon went.
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The problems only arise when we surrender to the urge to start imagining, once we know what the outcome of an experiment is,that we can deduce accurately what must have happened along the way. That is, if we see an interference pattern, we think the photon must have divided itself into separate pieces, whereas if we know the photon was detected along one pathway, that it must have actually gone down that pathway and not the other. But then when we do a delayed choice experiment, we find that insisting on one or the other of these two mutually exclusive interpretations leads us into trouble, because it appears that the photon must know in advance what is going to happen, so that it can choose the appropriate behavior to follow. But, and this is the fundamental point, those two possible behaviors are not actual behaviors that we know the photon must in fact have followed, but inferred, deduced, or (more accurately) speculated behaviors...
The lesson of the delayed choice experiment is that any hypothesis that forces the photon to adopt one or the other of two distinct and contradictory behaviors is, in fact, not reasonable.
And we should have known this in advance. What was the first thing we learned about quantum measurements from the Stern-Gerlach experiment? That the spin of an electron is strictly an undetermined quantity until an experiment yields a measurable value for it. And, moreover, that any attempt to say, having found the electron to be in an "up" orientation, that it must have been that way all along, is demonstrably incorrect.
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And the delayed choice experiment brings that point forcefully into the open. Seeing an interfrence pattern, or detecting a photon in one path or the other, is at bottom a simple measurement made on a complicated system. And any attempt to think that we know, once the measurement is done, what really went on inside the system (whether the photon went one way or the other, or both ways at once) is precisely an attempt to pin down the prior state of a system after a measurement has been made. It causes trouble and we musr resist the temptation to do it.
The minimal interpretation of quantum mechanics embedded in the first two sentences of this {quotation} is like a wise but stern parental injunction against certain kinds of teenage behavior: limiting, to be sure, but it keeps people out of danger.