But suppose you ran the experiment, measured which slit each photon passed through, and measured where each photon struck the distant screen, but before you look at the results, you destroy the data on which slit each photon passes through. In other words, you make a delayed choice about the experiment. What would happen? On the one hand, the measurements were made, so the photons should act like particles.
When this was first proposed as a thought experiment in the early 20th century, it caused a great deal of debate, but it wasn’t until 1999 that this kind of experiment was done. It didn’t involve a double slit, but it did involve choosing what is known about the photons after the experiment is committed. What we found was that the delayed choice really does determine the outcome of the earlier experiment. In our double slit experiment, that would mean destroying the data about the photons going through the slit would give the “wave” interference pattern, even though the “particle” data was collected at the time.