## Best homework problem ever

Exercise 2.16 in Quantum Processes, Systems, and Information by Ben Schumacher and Mike Westmoreland refers to the Elitzur-Vaidman bomb test and reads, “If you do not find the previous paragraph strange and disturbing, re-read it.”

### 5 Responses to “Best homework problem ever”

1. That is a strange and disturbing gendanken, so I can see why that’s a good problem to assign. I like it!

2. sharone Says:

it would help if you jotted down the actual text. “if a train leaves albuqu…kerkay at 11am and the tracks are a piezoelectric somethingorother and the temperature is 27deg C, then something something let’s ride bikes something….

3. BlackGriffen Says:

I’m not seeing the weirdness here. It’s no different than if you put someone in a dark room and tell them that there’s a red ball either to their left or their right. To know the position of the ball they only have to shine their flashlight left (or right) because even if the ball isn’t there they can know where it is by discovering where it’s not.

This is similar to the algorithms for solving “scale puzzles” and the like ( some examples: http://www.mazes.com/scales/index.html ) – you don’t have to weigh/examine every individual object to figure out which one is the odd one out.

This particular application is, admittedly, quite interesting since you’re turning things on their heads and measuring a property of the detector. 🙂

4. It seems to me that the semi-classical way the apparatus is described serves to convert photonic engineering details into quantum mysteries … and students are better served IMHO to acquaint themselves with the photonic details.

E.g., even notions like “photon source”, “photon detector”, and “mirror” represent idealized elements, whose properties can only be approached (never realized) in the real world.

In particular, for each of these elements, as the limits of ideal dynamics are approached, renormalization effects diverge, and so the full apparatus of cavity QED is required to describe the dynamics. Thus it can happen that an “ideal” optical apparatus is not less complicated to analyze … it is more complicated … and this problem is (IMHO) one of those cases.

5. quantummoxie Says:

John makes an excellent point. It’s a great mental exercise but has little practical importance because no actual Mach-Zender interferometer is error-free; photons get absorbed throughout the apparatus and the interference pattern is hardly perfect.

Measuring the property of detectors is very interesting, though (as Sean pointed out), because this is precisely how you attack the thorny problem of the quantum-classical transition à la Niels Bohr. 🙂