Pop Quiz Answer

Yesterday’s Michelson Interferometer quiz was surprisingly popular– as of 8:30 pm Tuesday (when I’m writing this), just under 1500 people have voted in the poll, three and a half times as many as in the next most popular poll I’ve done. Who says there’s no audience for physics?

So, what’s the right answer, you ask?

The correct answer finished a distant second (as of 8:30 it has 21% of the votes, to 52% for the leading wrong answer). The answer is that the light goes back where it came from. Bob Hawkins and MattXIV have the right explanation: on the return trip, half of each beam goes to the screen, and half of each beam goes back to the laser. You get interference on each of those paths, and they complement one another– whatever fraction of the initial light goes to the screen, the remainder of the light goes back to the laser.

Another way to see this is by comparing the Michelson interferometer to everybody’s second favorite interferometer, the Mach-Zehnder. Here’s the Michelson again:


If you take the two mirrors, and turn them each by 45%, then insert a second beamsplitter, you get a Mach-Zehnder interferometer, which looks like this:


The Michelson is basically a Mach-Zehnder interferometer “folded” back on itself. If you look at the Mach-Zehnder interferometer, you can clearly see that there are two ways for the light to leave. When folded into the Michelson configuration, one of those paths leads to the detector screen, and the other goes back to the laser.

The other answers turned out to be even more distracting than I thought they would be, but they’re wrong. The light can’t simply be destroyed, because light carries energy, and energy can neither be created nor destroyed. All of the energy that flows into the interferometer has to end up going somewhere– it can’t just disappear.

It also can’t be absorbed by the beamsplitter, because we said it was an ideal 50/50 beamsplitter. If it were absorbing significant amounts of light, it wouldn’t be sending 50% into each arm of the interferometer. And the energy can’t be disappearing into parallel universes because this isn’t Star Trek, and the parallel “universes” of Many-Worlds aren’t real universes, but rather branches of a larger universal wavefunction.

Anyway, many thanks to “h” for proposing this question. I had no idea it would get such a huge response. It’s nice to see that interferometry has lots of fans.