In Wheeler's delayed choice experiment (http://en.wikipedia.org/wiki/Wheeler%27s_delayed_choice_experiment) When the experimental apparatus does not contain a final interfering mirror, the photon is said to have been observed to travel as a particle because... there is no interference?
Even if the photon were to be traveling as a wave, I don't see why there would be interference without the mirror.
I.e., to take this passage from wikipedia: "Observing that photons show up in equal numbers at the two detectors, experimenters generally say that each photon has behaved as a particle from the time of its emission to the time of its detection, has traveled by either one path or the other, and further affirm that its wave nature has not been exhibited."
But just because the wave nature has not been "exhibited", does not mean it's not there. This seems like touching an apple with your eyes closed and saying "the visual properties of this apple haven't been exhibited, so it must be transparent to visible light".
I know that I'm wrong, but I can't figure out where I'm wrong. In my QM classes, experiments like this made more sense when one of the paths was blocked.
I think the problem I'm having is that I can't think of any specifically particle-like properties that are being exhibited in this experiment.