Grad school and a major (good) event in my personal life have been gobbling huge swaths of time, hence the comparative silence around here. I’m afraid we may be down to a few times a week for the next few months. I hope y’all’ll bear with me. (“Y’all’ll” is of course the standard contraction for “you all will”, is it not?)
Still, there’s always time for some physics now and then. Say you’re presented with a box with two holes in the side. From one opening, a laser beam – say, HeNe red – from a laser in the box emerges. From the other, the light from a red hot object in the box emerges. But there’s a filter in front of the hot object, so it only lets red light at the HeNe wavelength emerge from the hot object.
Assuming you don’t know which light comes from which opening, is there any way to distinguish the two? Just to make our life a little harder, let’s say the thermal light is appropriately focused and collimated so that the actual beam profile is indistinguishable from the profile of the laser beam. In other words, what we’re asking is if there’s some difference between laser light and ordinary light of the same frequency.
We might be tempted to see which light source is coherent, but classically speaking monochromatic light is also coherent. If both the laser and the thermal light span the same narrow frequency range, we’re probably stuck here. Coherence is, of course, the property a light wave has when it maintains a regular constant phase. Light from a thermal source like a light bulb hasn’t got it unless it’s filtered:
The image is from a great site at Ryerson University; I’m pretty sure using it here is educational fair use, but to be safe I’m thumbnailing it with a link to the great full image and explanation at their site.
Anyway, checking for classical coherence is out. Can we distinguish the beams by other methods? We can. We can stick a photon counter in front of each beam as look at the rate at which they hit the detector. For the coherent laser source, the photons are emitted randomly in a way that obeys Poisson statistics – these are the statistics followed by events which are unrelated to one another. The events consisting of a car passing a particular interstate mile marker on an interstate with very light traffic is pretty much Poissonian, for instance. But the light from the thermal source exhibits different statistics – in particular, the photons tend to come in clusters. To demonstrate this mathematically is much more difficult than is realistic here, as it requires some rather serious quantum mechanics. The American physicist Roy Glauber got a Nobel Prize for doing it, after all.
If you were to measure the photons with your detector, you could see which beam exhibited the most photon bunching and distinguish between the light in that way. This is more dramatic than it sounds, because this effect is entirely non-classical. Classical or semi-classical theories treating light only as a wave would leave you stuck.