Mach-Zehnder Interferometer

This goal here is to provide a simple explanation of a Mach-Zehnder interferometer.  Experiments with this device reveal fascinating facts about how the world works; counterintuitive to what you might think.  We’ll try to keep it as simple as possible, excluding details about the setup and practical problems that aren’t significant to the key idea.

A rough diagram of this interferometer is above.  The components of this interferometer are explained below.

1. One laser (L) which shoots photons, “one at a time” from left to right in the diagram. 
2. Two detectors (DA and DB) which “click” whenever a photon enters them.
3. Two beam splitters (BS1 and BS2).  What you need to know about a beam splitter follows.  If the detectors DA and DB were moved in front of the mirrors MA and MB in the diagram, then half the photons from L would end up in DA and half in DB.  This is sometimes described by saying half the photons are reflected and half are transmitted, but  that’s actually not equivalent to what was said in the previous sentence and it’s not quite true – it’s exactly what will be refuted by the experimental results below!
4. Two mirrors (MA and MB) which just reflect all the photons that come in contact, like a billiard ball bouncing off the edge of a pool table.
5. The horizontal and vertical lines in the diagram are not physical things in the interferometer; they just show all the locations where the photon would likely be detected (if we placed detectors at various places all over in the diagram).  It’s kind of like showing the possible trajectories of a photon, but the concept of a trajectory isn’t consistent with quantum mechanics as you'll see soon.

If the geometry of this interferometer is just right (we won’t get into those details here), all photons from L will end up at DA (DB won’t detect anything)!  If L fires 1000 photons, all 1000 will be detected by DA.

How is this possible?  You might think 500 of them should “follow the top-right path” and 500 should “follow the left-bottom path”.  Indeed, as stated in bullet 3 above, if you place detectors anywhere along those paths (before BS2) you will detect half the photons in each path. Additionally, if you placed the laser L just in front of BS2, firing photons parallel with the left-bottom path, then 50% of them will be found in each detector (and the same result again if you place the laser in front of BS2 parallel & along the top-right path).  So it may seem that, if you combine these facts you would get the following results.

• About 250 (half of half) of the photons go through the left-bottom half and to D1.
• About 250 of the photons go through the left-bottom half and to D2.
• About 250 of the photons go through the top-right half and to D1.
• About 250 of the photons go through the top-right half and to D2.

The problem with this conclusion is that those facts can’t be combined – when the photons interact with BS2 they did NOT come from a laser in either path, but from L.  In quantum mechanics things don’t behave like what you’re probably used to, you can’t say a photon followed this trajectory and then arrived at BS2, you have to consider that the photon came from both the upper-right AND left-lower path simultaneously, even if there’s just one photon fired at a time!  Although quantum mechanics predicts this behavior properly, no one can provide a deeper physical explanation of what’s forcing the photons into DA.   If you try to add detectors to investigate, the results will change!  This will be explained now.

If the experiment is repeated, but with a new detector DU placed in the upper path between BS1 and MA, the results will be different.  Half the photons (500) will be detected by DU (the expected behavior of BS1), 250 in DA, and 250 in DB!  So now, even if a photon is not detected by DU, it is somehow influenced by the presence of DU!  This paragraph applies analogously if the detector were placed in the left path below BS1.