The detector itself contaminating double slit? How do we know?

[atyy]

In the OP's sense, sure. But that is obviously not the general case. Generally, the detector is NOT the cause and that is what I wanted to make clear.

My case is the general case, and that makes it clear that there is something else at work. The OP is on the wrong track.

I think we all agree that some concepts in the initial posts were not quite correct. But couldn't the OP's idea be generalized to your case by saying that the different polarizer setting messed up the interference pattern?

 

[DrChinese]

I think we all agree that some concepts in the initial posts were not quite correct. But couldn't the OP's idea be generalized to your case by saying that the different polarizer setting messed up the interference pattern?

In my semantics, no. The original implication was that the detector's presence alone actively disturbs the interference.

In my storyline, it is the relationship between the polarizers that is central to the experiment. That is all that changes. So that should be the starting point of further discussion about when and why interference patterns emerge.

 

[Nugatory]

I think we all agree that some concepts in the initial posts were not quite correct. But couldn't the OP's idea be generalized to your case by saying that the different polarizer setting messed up the interference pattern?

Depends on whether you think of the polarizer setting as a controlled variable whose effect on the interference pattern is what you're trying to investigate, or an accidental uncontrolled input...

Yes, this is something of a quibble about wording, especially because when it comes to designing an experiment, it's natural enough to think of the interference pattern as something that is changed by the action of ("messed up by") the polarizer setting. But I still feel that that if we encourage people to start out thinking in those terms, they'll just have to unlearn them at some point.

 

[atyy]

In my semantics, no. The original implication was that the detector's presence alone actively disturbs the interference.

In my storyline, it is the relationship between the polarizers that is central to the experiment. That is all that changes. So that should be the starting point of further discussion about when and why interference patterns emerge.

I'm not so familiar with your set-up. Concretely, how would the polarizer settings be used to infer which path information?

 

[DrChinese]

I'm not so familiar with your set-up. Concretely, how would the polarizer settings be used to infer which path information?

That's a good question!

1. If you added an extra polarizer between the slits and the screen where the pattern appears, and orient it at a 45 degree angle: any photon arriving at the screen must have gone through the slit oriented at 45 degrees as well. You have gained which slit information.

2. If you next oriented that extra polarizer at a -45 degree angle: any photon arriving at the screen must have gone through the slit oriented at -45 degrees as well. You have gained which slit information.

3. Importantly: no extra polarizer is actually required for the interference to disappear when the slit polarizers are crossed per above. It is enough that you could have done it, regardless of whether you actually did.

 

[DrChinese]

Depends on whether you think of the polarizer setting as a controlled variable whose effect on the interference pattern is what you're trying to investigate, or an accidental uncontrolled input...

Yes, this is something of a quibble about wording, especially because when it comes to designing an experiment, it's natural enough to think of the interference pattern as something that is changed by the action of ("messed up by") the polarizer setting. But I still feel that that if we encourage people to start out thinking in those terms, they'll just have to unlearn them at some point.

I so agree!

 

[atyy]

That's a good question!

1. If you added an extra polarizer between the slits and the screen where the pattern appears, and orient it at a 45 degree angle: any photon arriving at the screen must have gone through the slit oriented at 45 degrees as well. You have gained which slit information.

2. If you next oriented that extra polarizer at a -45 degree angle: any photon arriving at the screen must have gone through the slit oriented at -45 degrees as well. You have gained which slit information.

3. Importantly: no extra polarizer is actually required for the interference to disappear when the slit polarizers are crossed per above. It is enough that you could have done it, regardless of whether you actually did.

Thanks!

Depends on whether you think of the polarizer setting as a controlled variable whose effect on the interference pattern is what you're trying to investigate, or an accidental uncontrolled input...

Yes, this is something of a quibble about wording, especially because when it comes to designing an experiment, it's natural enough to think of the interference pattern as something that is changed by the action of ("messed up by") the polarizer setting. But I still feel that that if we encourage people to start out thinking in those terms, they'll just have to unlearn them at some point.

I so agree!

What is the actual mathematical expression for this principle that the interference pattern depends on potential which path information? (I confess I have heard it, but I never use it, nor have I seen it as an equation. I always think the detector or polarizer is messing up the experiment. In the delayed choice quantum eraser experiment, I simply think different experimnents have different results, and different observables have different distributions, and it is no mystery to me.)

 

[atyy]

Also, looking up the polarizer action, it seems to be a projector, which is not so different from a measurement and collapse?

These notes all agree the polarizer is a projector:
http://www.physics.metu.edu.tr/~sturgut/p507/pol.pdf
http://ocw.mit.edu/courses/nuclear-...s-fall-2012/lecture-notes/MIT22_51F12_Ch3.pdf
http://web.stanford.edu/~rsasaki/AP226/text1.pdf
http://www.math.ru.nl/~maassen/lectures/Trieste.pdf

http://books.google.com/books?id=l-l0L8YInA0C&vq=polarizer&source=gbs_navlinks_s (p415) even makes an analogy between the polarizer and a measurement device, associating an observable to it, and eigenvectors.

 

[Cthugha]

Also, looking up the polarizer action, it seems to be a projector, which is not so different from a measurement and collapse?

Yes, a polarizer is a projector. However, in these measurements one usually places a lambda-half waveplate at the slits. It just rotates the polarization of the light beam passing through it. This is a completely reversible interaction.

 

[atyy]

Yes, a polarizer is a projector. However, in these measurements one usually places a lambda-half waveplate at the slits. It just rotates the polarization of the light beam passing through it. This is a completely reversible interaction.

Thanks! So there is a unitary operation which is just rotation to realize DrChinese's experiment.

Looking at the delayed choice quantum eraser the OP linked to earlier, it doesn't seem mysterious because the observable for which interference is observed or not observed is not even the same observable. So I would explain the "mysteries" by saying different setups yield different results, different observables yield different results. But is there a principle beyond that, a mathematical expression that formalizes the idea that potential which path information destroys the interference? I assume it's not just the [x,p] commutation relation?

 

[atyy]

Here's an an attempt to construct an argument against a change in the "potential to know" due to a known unitary operation. The basic idea is that a known unitary operation preserves information.

If the interference disappears due to a known unitary operation, then the interference can be made to appear by reversing the operation. It may be thought that this involves "doing something" as opposed to "doing nothing". However, "doing nothing" is also "doing something", because "doing nothing" is unitary evolution by a known Hamiltonian which happens to be free. To illustrate that that is doing something, consider the case where an atom is used and high vacuum is needed. The creation of the high vacuum is the creation of the known Hamiltonian, which happens to be chosen to be free, so it is not "doing nothing".