What happens to the missing intensity in a Mach-Zehnder interferometer?

[Wanderbiker]

I am new to quantum physics and mostly self taught. Please forgive me for what is probably a very naïve question.

Here's the way I understand it.

A beam of photons is directed into a Mach-Zehnder interferometer (two beam splitters, two regular mirrors, and two detectors). At the first splitter, the beam is split into two beams (1/2 intensity each). At the second beam splitter, each of the two beams is split again. This results in four beams (each of 1/4 intensity). At one detector, two beams display constructive interference, resulting in a detection of 1/2 intensity (1/4 + 1/4). At the other detector, the two beams display destructive interference, resulting in a detection of zero intensity (1/4 - 1/4).

Here's my problem:
If this is all true, where did half of the intensity go? Energy doesn't just disappear.

Other explanations I have heard say that full intensity is detected at the constructive interference detector. They don't, however, explain how this can be when half the intensity of the original beam ended up at the destructive interference detector.

Please help me understand.
Thanks.

 

[jtbell]

With constructive interference of two equal-amplitude beams, the resulting beam has twice the amplitude of either incoming beam. Energy is proportional to the square of the amplitude, so the resulting has four times the energy (intensity) of either incoming beam.

 

[Wanderbiker]

Thank you. I knew there had to be a simple answer.