Consider the classic two slit experiment (which really is an enormously powerful demonstration often undervalued until you've though about it several times), but let's do two things...
- Lets use a really good CCD or a multichannel plate for the image plane detector (rather than a white screen or phosphor field or something). The important thing here is that this is a discrete, digital device capable or registering single photons on many small spatial areas.
- Turn the intensity way down so that on average there is only one photon in transit at a time.
Two things become obvious.
- The CCD registers a single photon at a time, each landing on a single pixel of the detector.
- If we wait long enough we still get the interference pattern.
These results mean that the device is not registering some smear of values for over the whole region, at most it registers a smear over one pixel; and the second one means that it registers on each pixel with a frequency consistent with the probabilistic interpretation.