I have talked about some of the strange quantum mechanics effects before. An example is the two-slit experiment. If we fire photons (particles of light) at a pair of slits, and then measure where they appear on the other side of the slits, we get a two-slit diffraction pattern – exactly what we’d get if the photon travelled as a wave. We can conclude from that that the photon has travelled through BOTH slits – not one or the other – since if it went through just one it would give a different diffraction pattern. But now if we try to measure which slit it went through (by putting a detector just by one of the slits) we do indeed see that it goes through one or the other – but what is more, the pattern we get is not a two-slit diffraction pattern – it is the combination of the two one-slit patterns. The conclusion then: That if we measure which slit the photon goes through, it does indeed go through a single slit. But if we don’t measure it, it goes through both. The act of measuring it has fundamentally changed what it does.

Now, earlier this week my colleague Michael Cree gave a good seminar on some quantum effects, and included this neat development on the two-slit experiment. It’s a bit silly, as presented, but the idea can be developed into something useful. The problem goes like this:

Suppose we have developed a bomb that can be triggered by just a single photon of light (Yes, this is silly, but bear with me). If it gets hit by just one photon, it blows up. Now, we have a production line to manufacture these bombs, but we know from experience that it’s not a very good line: about half our bombs are duds and fail to detonate when we give them a photon. Now, suppose we want to test which bombs are duds and which work. On the face of it, that’s impossible without blowing up the working ones. We shine photons at them, and those that are duds do nothing, and those that aren’t, blow up. True, we identify which are the duds and which aren’t, but we have blown up all the working ones in the process.

The two-slit phenomenon allows us to make some progress though. Imagine shining a photon through the two slits. We take the bomb we want to test, and put it by one of the slits – call it slit A. If the bomb is a working one, this process measures which slit the photon goes through – if it goes through A the bomb blows up; if it goes through B, the bomb doesn’t. But if the bomb is a dud, it cannot make this measurement, and so the photon will go through both slits. So let’s (in our imagination) take a bomb (which might or might not be a dud) and put it by slit A. After shining the photon at the two slits, the bomb will either have exploded or not. If it has exploded we conclude that the bomb was working and the photon went through slit A. If it didn’t explode we can conclude EITHER the bomb is a dud, OR the bomb was working but the photon went through slit B.

Let’s suppose we have a bomb that didn’t explode. Now, IF the bomb were a dud, where would the photon end up? It would end up somewhere consistent with a two-slit diffraction pattern, since it would go through both slits. IF the bomb were live, then the photon has gone through slit B, and it would end up somewhere consistent with a one-slit diffraction pattern from slit B. These two patterns are different. Specifically, there are places on the two-slit diffraction pattern for which there is zero probability of finding the photon. SO, if we happen to see the slit at one of these zeros, we can conclude that it couldn’t possibly have gone through both slits, and therefore the bomb cannot be a dud. It is live. That means we have made a measurement of what could have happened (it could have exploded), but didn’t.

Our experience of the everyday world says you can’t measure something that didn’t happen. But in some cases, you can.

This video presents the same, but in a slightly different arrangement.