Reconciling the wave and photon models - sort of

Einstein's success with the photon model (explanation of Black-body radiation and the photoelectric effect) stands in striking contrast to what we thought we knew about light. Didn't Young and Fresnel kill the particle model with their demonstration that light interfered with itself and the wave model explained the observations beautifully? Even predicted new and surprising phenomena like Arago's bright spot? Can physics be so fickle?

Of course the phenomenon of interference still occurs. If we use a detector that measures our light intensity by basically counting photons, will we still see interference? The kind of detector that you have in your phone or digital camera should work. These are Charge-Coupled Devices — CCDs — fine grids that work by tthe photoelectric effect, converting photon energy to electric current. Much to our great relief, if you take a picture of an interference pattern with a CCD you still get a picture that looks like an interference pattern. So changing the detection method doesn't matter. But how does that work if there are photons?

One might suppose that somehow two photons might cancel each other producing interference — but that seems very strange. If a photon carries an energy of $hf$, how can two photons cancel each other? One way to test this might be to reduce the intensity of the light. We know how much energy a photon carries and we know the energy density of a light wave — it's proportional to the square of the electric field. A stronger electric field corresponds to a higher density of photons, each having the same energy. So if we make our light intensity very low, we ought to be able to reduce the intensity so that there is only one photon in the apparatus at a time. What does it look like if we collect our light through a double slit one photon at a time?

The result is a surprise and  complete game-changer! Each photon strikes one highly localized element in the detector, which is composed of a very large number of small sensing elements.  And here comes the interesting part:  Each photon can only be absorbed by one of the detector elements (pixels, if it's a camera).

So each photon is absorbed in a microscopic region — tiny compared to the size of the interference pattern. As the experiment runs, the points begin to appear randomly on the screen — or so it seems. But as time goes on, a pattern begins to build up and it builds up the interference pattern!

Somehow, each individual photon seems to know where to go and where not to go in the interference pattern. This means:

Photons show interference, but they are not interfering with other photons: they are interfering with themselves.

This is so strange that we haven't even bothered to mark it as a dangerous bend. This is more than a dangerous bend; this is an impossible disaster! The problem is: this is what happens.

What's worse, this is not only true of photons. It's true of electrons and atoms as well. But since the characteristic length scale of visible light is much larger than the characteristic length scales of atoms, these interference effects are much harder to see in double slit experiments. They were detected at much later times than interference in light. But you may have already encountered examples in chemistry.  Much of chemistry indeed can be modeled by some mix of the wave and particle model of electrons.  Do you recall examples where you had to think about electrons as a delocalized cloud or wave rather than a particle? Do you recall other examples in chemistry where thinking of electrons as particles is what you had to do?   

These results produce a complete change in the way we think about the character of the physical world. The microscopic elements of which our everyday matter is made are not just little pieces of ordinary matter. They have properties like nothing we see in our everyday lives. All we can do is put together partial models that allow us to think about some parts of each quantum phenomenon — kind of like the blind men and the elephant we encountered in our study of electric currents.

Interestingly enough, this did not turn into a disaster but rather an incredible success. Despite all odds, a theory of the phenomenon was developed and has continued to evolve. At this point, the quantum theory is one of the most successful physical theories in the history of humanity enabling all kinds of technology from lasers to transistors to information storage of incredible densities. We continue to try to find ways to think about what's happening. For photons, here's the best we have at present:

The electric and magnetic fields described classically by Maxwell's equations give an intensity for light and propagates like waves at the speed of light and does all the standard interference phenomena we have come to know. This intensity of the light at any point tells you the probability that you will find a photon there.

This may not be very satisfying, but it's the best interpretation we have. 

Joe Redish and Wolfgang Losert, 5/4/12 and 5/4/13