Measurement disturbance - double slit

[namewills]

When electrons are passed through a double slit and can either display a wave-like interference pattern or a particle-like build-up pattern, is that because their momentum/direction is changed by the measuring device interacting with them, or due to some other feature associated with being recorded?

The first explanation makes more intuitive sense, but I seem to recall hearing that the interference pattern will still be visible despite the act of interacting with the electrons when detecting them, as long as the record (of which slit each electron passed through) is destroyed.

 

[Andeplane]

When electrons are passed through a double slit and can either display a wave-like interference pattern or a particle-like build-up pattern, is that because their momentum/direction is changed by the measuring device interacting with them, or due to some other feature associated with being recorded?

The first explanation makes more intuitive sense, but I seem to recall hearing that the interference pattern will still be visible despite the act of interacting with the electrons when detecting them, as long as the record (of which slit each electron passed through) is destroyed.

If we measure the position (i.e. what slit the electron passed through), the position gets sharply determined (and due to the uncertainty principle, the momentum is quite spread out). But now we know what slit the electron went through, so there isn't any superposition of the two slits anymore, and therefore we don't get the interference pattern (obviously since you need two waves to get that).

So if we know for sure where the electron went, then we would see a particle-like behavior as you described, with spread out intensity. And your second question; that record you are talking about, that could not be that a computer read out which slit the electron went through, and then deletes it from the hard-drive or anything like that, but rather if the measure outcome (slit 1 or slit 2) were a superposition state of the two possible outcomes, and that we did not measure (disturb the system) that, somehow destroy that information.

 

[namewills]

...if the measure outcome (slit 1 or slit 2) were a superposition state of the two possible outcomes, and that we did not measure (disturb the system) that, somehow destroy that information.

I'm not sure I know what you mean by superposition state of the two possible outcomes. Thanks.

 

[Andeplane]

Allright, say that you have the classical quantum mechanical example, a particle with spin up or down (for example an electron). Then it is possible to prepare the system (i have no idea how you do this in practice, but scientists are awesome) so that there is a 50/50 chance to measure spin up or spin down in one direction.

We then say that the electron is in a superposition state of the two outcomes. Both are possible, and with a repeated series of this experiment, you would end up getting both results.

Short comment on the expression 'superposition'; with waves that satisfy the superposition principle (http://en.wikipedia.org/wiki/Superposition_principle), if you have two waves moving and they meet in a point in space, the 'effective' wave one sees is simply the sum of the two amplitudes in that point. This is why we get intensity maxima and minima in interference experiments, at some points, the two waves cancel each other out, and some other points, they do in fact 'double up'.


So, back to the double slit experiment! When the electron moves towards the double slit, the reason why we get an interference pattern is that, well there is a chance that the electron will go through the left slit, and there is a chance that it will go through the right slit. Here we have a superposition of the two possible paths that the electron will go! Allright, then say that we choose to measure at what slit the electron passes through. Well, if we measure with some measurement device, we also have to check the device with our eyes what the result was! Because if we let the device measure the electrons wise choice, the measurement device could ALSO be in a superposition state, where BOTH left and right is possible!

We have sort of 'moved' the problem from the electron itself to the measurement device. But if we after the device did measure (but is in a superposition state, we have to check the device to force the Nature to choose what slit the electron chose), if we then just decided to drop to read out the result (this can be thought of as the destruction of the information, we just never measure), then we would still see wave behavior.

I haven't really read through this post again, might be really, really bad :p

 

[namewills]

Ok, I think I'm with you. So if you shift the problem from the electron to the measurement device, I see how you could still see wave behaviour by destroying the information/never forcing the device to choose a state. But what if you look at the screen first, note if it's an interference pattern or a particle-like build-up, and THEN choose to look at the read-out (forcing one of the two states)?

 

[venton]

Say we have a detector switched on which shows which slit it went through. We have no interference pattern.

We leave the detector switched on, but then we cut the wire to the display which shows which one it went through. Does the interference pattern reappear again - as we have no way of telling which one it went through?

I guess the interference pattern will not be there, because however the detector works, it collapses the superposition.

 

[Andeplane]

venton; yes, there is a conceptual problem, because it's not just to cut the wire and then the information is destroyed. It's not that since WE as human beings cannot tell (remember, we cut the wire), the interference pattern comes back to life.

But if we made this device that was completely quantum mechanical (which is possible), it wouldn't collapse the superposition of the electron since it would ITSELF be in a superposition of two outcomes.

And your suggestion namewills, say you first check the position of the electron, and then you check the measurement device. The problem is that when both the electron and the device is in a superposition state, they are also in an entangled state (if you measure one of them, the other will also collapse). And when you then let the electron hit the screen, hence collapsing the state, but NOT in the basis of left or right slit! So the information saved in the measurement device is now destroyed, and is not worth anything. I would guess that if you check the result from the measurement device, you would half the time get left slit, and the other half get right. But that information wouldn't mean anything.

 

[namewills]

Huh! I like it. Thanks, Andeplane! I will think about your answer for a bit.