Photons and interference
Physics Narrative for 14-16
A difficulty is that we only know where photons are when they no longer exist
There is a lurking difficulty here, that cuts to the core of what physicists know about radiating.
Both paths contribute, and these contributions add. The resultant sets the power at the detector. Yet the power at the detector can also be figured out in terms of the number of photons arriving each second. At very low intensities there may only be a single photon emitted over the trip times. So how do the two contributions come about from a single photon? This is the central mystery of quantum physics: it turns out that our picture of the world needs re-imagining. Things at this very small scale are just not like things at the human scale, if the experimental results are to be trusted, and so you ought to be very careful about what is
Paths helped us out before, when reasoning about the rules for rays. So let's think again about this interference situation, but this time with paths. The advantage for making sense of the core difficulty is that the paths are not physical: paths are just a way of scanning across possibilities.
For reflection and refraction you're looking for paths where the trip time is lowest.
For two beams that does not make much sense, as we need to consider the connections between the contributions of the paths. So here you'll look at differences in trip times – as the next simplest thing, and building on the ideas of being in and out of step.
Differences in trip times for paths is the key to figuring out contributions
This interactive focuses on difference in trip times for paths. The very first pane shows that where the difference in trip time is small, the number of photons arriving per second is large – that is a high intensity. You can connect this to the
real wave behaviour: where the difference in trip time was small, there the contributions from each source superposed constructively. Many photons are detected where the contributions add to give a large resultant amplitude. Where the resultant amplitude is close to zero, few photons are detected.
Yet there is nothing to suggest that we need to have only one path per slit. So the second pane of the interactive shows that three paths per slit predicts exactly the same result. If you are not convinced, you can of course do everything here with a piece of A3 paper and a sharp pencil: it's only geometry, trip time, and a bit of
do like me, but later to figure out contributions (which have both frequency and amplitude). So now you're working with a real stripped-down picture of what a wave is – a real mathematical model, applying to any physical wave.
The third pane shows something a little more interesting. It predicts that, if you have only one slit, the beam will spread. That's where we're going next, to look at the phenomenon of diffraction.