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A thing called a "Mach-Zehnder Interferometer" takes a beam of light from a source, like a laser, and uses a half-silvered mirror to split it into two beams that travel at right-angles to each other. These two beams then reflect off two further mirrors that bring them back together again. They then hit another half-silvered mirror, as shown here.
- The Interferometer setup
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(I'm only allowed to attach 3 illustrations! So imagine the picture above but with detector B in the dark.)
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How does physics attempt to describe this observed behaviour?
Well, the idea that light might be a wave seems to work quite well. We know from examining various types of waves, like those that we see on the surface of water or those that travel through air as sound, that when two waves cross paths with each other they "interfere". If a peak of the first wave coincides with a peak of the second, we get one big peak. The peaks add up. If a peak of the first wave coincides with a trough of the second, we get nothing. They cancel each other out.
If we carry this experience of waves with peaks and troughs either doubling or cancelling over to the behaviour of light, it seems to work quite well. If we think of that beam of light in the interferometer as a little line of peaks and troughs then we could imagine it splitting into two little lines of peaks and troughs and then recombining. We can then see how changing the length of one of those paths relative to the other would affect what happens when they meet again. If, when they meet, a peak is aligned with a trough we'll get no light. If it's peak-with-peak and trough-with-trough, adding to each other, we'll get all the light.
- Light travelling down both paths as waves
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OK, well before deciding for sure, let's test our theory with some different light levels. Suppose we dim the light a bit. When we do that, we find that whatever's coming out the other end gets dimmed by the same amount. So far so good. Perhaps our little waves just got a bit smaller.
But if we keep dimming the light some more we find that something different gradually starts to happen. The detectors start to see the light in uneven flashes, rather than as a smooth continuous stream. We still get the phenomenon whereby changing those path lengths changes which detector receives the most flashes. But flashes they are, nevertheless. This new behaviour is modeled by thinking of the light not as a continuous stream of waves but as little packets called photons. Again, as with the wave idea, we can't actually see these little photon things. All we see, using our detectors, is the flashes. But the idea of light travelling along these paths as little discrete packets would seem, on the face of it, to explain what we're seeing.
Think of the illustration at the top but with little dots along the path representing our idea of what photons "look like"
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But how can we use this new idea of little packets of light to continue to correctly describe the interference effects; the thing that we managed before so successfully to describe using the wave idea? Well, perhaps we could say that these little photons are like little packets of waves and that when two photons hit that last mirror together they interfere with each other? Sometimes re-enforcing each other; sometimes cancelling each other out.
Think of the illustration with the waves on the path but with little packets of waves
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We can test this new theory by turning the light down even further. Suppose we turn it down so that only one single flash of light is seen per hour. That way, if these supposed photons really do exist and aren't just a figment of our imaginations, the interference should surely disappear. After all, with only one photon at a time there is nothing for that one photon to interfere with, is there?
If we do that what we find is that the interference remains, just as before. Strange.
OK, perhaps that single photon divides in two when it travels down those separate paths, and those two halves then interfere at the end? Well we can test that by putting detectors not at the end of the apparatus but somewhere along those paths so that we can see this happening.
- Observing which path the supposed photon takes
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One of the strange consequences of this is what happens, with this ultra-low light level, in the situation of "peak-meets-trough" that was mentioned earlier. This is the situation where the lengths of the paths are arranged such that we get absolutely no light detected by one of our two detectors. Our old wave idea tried to model this by imagining the two beams of light waves meeting each other at the end with the peaks of one beam lined up with the troughs of the other.
That worked fine for a continuous stream of light, and it still seems to work with just one little bit of light - one photon - at a time. But what then happens if we block one of the paths is that interference disappears and we now do get light detected where previously there was none. That's ok when we're simply thinking of it as waves. But how can that possibly work with these single photons that we've already observed to be travelling down only one path or the other but not both? How does that one photon find its way to the detector with just one path open but fails to find its way there when both are open? That's the opposite of what common sense would tell us about a single object travelling down one of two possible paths! Restricting the photon's options actually allows it travel. Removing those restrictions stops it from travelling.
Weird.
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So what is actually happening along those paths?
This is where the philosophy finally comes in. All of the above is simply a description of what has been observed. The question of what is "really" happening is what is debated.
Some people say that it is meaningless to even ask what is happening along those paths when we're not looking at them. All we can meaningfully talk about, they claim, is the world as we observe it, not the world that we assume to exist when we are not looking. Naturally, this has proved philosophically problematic because it implies that there is a sense in which the world is created by the act of observing it. And it invites the question: what do we class as an "act of observation"? Has the detector performed such an act even if we don't look at its output? Does it need to be a conscious observer? Since we've used that word, what exactly do we mean by "conscious"? It's a philosophical can of worms.
Some others go for the so-called "many worlds" solution. This proposes that the photon does actually travel down both paths, but does so in two completely separate universes. We, occupying just one of those universes, only observe one. The interference happens as a result of interference between those two universes, but when we make a measurement we only see one of them. A lot of people would see this as pretty unsatisfactory too!
So, now it's up to you. Can you think of a way of thinking about this which is both philosophically satisfying and crucially which fits all of this observed evidence?
Suppose that the photon (previous disclaimer) is a discrete field not a wave. A field is always in all possible places simultaneously. I'm thinking of a field kind of like the air in a balloon. When the balloon is punctured the energy is released (becomes visible). The field is collapsed (punctured) in the detector (eyeball) and seen. We can make the field with nothing more than energy and speed through time or simply contain it in space-time depending on whatever works. We have them both handy.
The name comes from my work and proclivities. I spent a lot of time in my working life reverse engineering things that didn't work. Now my hobby is reverse engineering the universe in order to figure out how it works. 
It might not get much better!
