Compound double slit with measurement on only one

[Sting33]

This question relates to the double slit experiment where measurement affects whether an interference pattern is generated.

If an experiment were performed where electrons were sent through a double slit with another double slit behind the first double slit, and the measurement device measured which slit the electrons went through on the first double slit, but which slit the electrons went through on the second double slit was not measured, would the experiment still result in an interference pattern? Or would the collapsing of the wave function due to the observance of the first slit continue through to the second double slit as well?

Alternatively, what would happen if you measured only the results of the second double slit?

 

[PeroK]

This question relates to the double slit experiment where measurement affects whether an interference pattern is generated.

If an experiment were performed where electrons were sent through a double slit with another double slit behind the first double slit, and the measurement device measured which slit the electrons went through on the first double slit, but which slit the electrons went through on the second double slit was not measured, would the experiment still result in an interference pattern? Or would the collapsing of the wave function due to the observance of the first slit continue through to the second double slit as well?

Alternatively, what would happen if you measured only the results of the second double slit?

The simplest answer is that by measuring at the first double slit you effectively redefine the source of the electrons. What happens after that will be consistent with a single slit being the source of the electrons.

 

[David Byrden]

This question is a good example of why "collapse" interpretations are a bad thing. They lead to confusion.

Answering the question is not easy in any interpretation because you didn't indicate the distance between the screens. If close together, compared to the slit separation, they would behave almost as a single screen. If far apart, then an interference pattern could form on the second screen and we must ask if the slits fall in a bright or a dark band.

But here's a tool that will allow you to answer the question whatever the configuration:

If information about the path can reach you, by any route whatsoever, then you will see no interference.

 

[Mentz114]

This question is a good example of why "collapse" interpretations are a bad thing. They lead to confusion.

Answering the question is not easy in any interpretation because you didn't indicate the distance between the screens. If close together, compared to the slit separation, they would behave almost as a single screen. If far apart, then an interference pattern could form on the second screen and we must ask if the slits fall in a bright or a dark band.

But here's a tool that will allow you to answer the question whatever the configuration:

If information about the path can reach you, by any route whatsoever, then you will see no interference.

The complete answer is given by the complementarity of V ( fringe visibility), D (which path info or distinguishability) and C ( correlation, i.e. entanglement)

These are related by $V^2+D^2+C^2=1$. In the absence of C there is a trade-off between which path info and interference.
I have a proper reference somewhere.

 

[PeterDonis]

This question is a good example of why "collapse" interpretations are a bad thing. They lead to confusion.

I don't see how this question is a problem for collapse interpretations. In fact, the answer @PeroK gave in post #2, which works fine, is basically saying "collapse the electron wave function based on whichever slit of the first double slit the electron is measured to pass through".

 

[PeterDonis]

would the collapsing of the wave function due to the observance of the first slit continue through to the second double slit as well?

Why would it? The collapse at the first set of slits is because you're measuring which slit the electron went through. Since you're not measuring which slit at the second set of slits the electron went through, there won't be any collapse there.

 

[David Byrden]

I don't see how this question is a problem for collapse interpretations.

It seems to me that Sting33 wondered if "collapse" at the first slit somehow erased the electron's ability to do anything wavelike during the rest of its transit. He saw it as a permanent loss of wave-particle duality. A naive misinterpretation, but understandable.

 

[Sting33]

Thank you so much for all of your helpful explanations and setting my mind straight. I’ll probably be showing the extent of my naivity but I’d like try and see if I understand.

So if we send the electrons through the first double slit and don’t measure it the electrons will diffract into an interference pattern. Then if we set two more double slits on the edges of the interference pattern and measure only one of those second double slits, it seems to me the measured double slit would not create an interference pattern but unmeasured one would cause an interference pattern.

I guess to me it doesn’t make sense because some of the electron waves that went through the first slit would have hit both of the pairs of second slits and then when we measure if it went through one of the two secondary double slits we’ll measure that it did, and yet that same electron has made an interference pattern behind the unmeasured second double slit. Or perhaps that wouldn't be the result?

 

[PeterDonis]

if we send the electrons through the first double slit and don’t measure it the electrons will diffract into an interference pattern.

More precisely, they will show an interference pattern if you measure it after the first double slit, without the electrons doing anything else.

But if you don't put a detector after the first double slit and before a second double slit, then you can't say there is an interference pattern because you aren't measuring one.

if we set two more double slits on the edges of the interference pattern

What do you mean by "edges"? And how do you know where they are without measuring the pattern?

it seems to me the measured double slit would not create an interference pattern but unmeasured one would cause an interference pattern.

In your scenario as you describe it, which double slit is the "measured double slit" and which is the "unmeasured" one? You aren't describing a "which way" detector at either slit of any of the sets of double slits, so there's nothing to prevent interference anywhere.

some of the electron waves that went through the first slit

If you don't measure which slit an electron goes through at any of the double slits, then there are no such things as "electron waves that went through the first slit". All of the electron waves go through both slits.

It is true that once an electron has passed through the first double slit, its wave function is different, so the behavior after it passes through a second double slit and gets measured by a screen won't be the same as the behavior if it just passes through one double slit and gets measured by a screen. But the difference won't be a simple "interference" vs. "no interference". It will be different patterns of interference. (At least, that's what will happen if there are no "which slit" detectors anywhere, which is what I understand you to be describing.)

 

[Sting33]

Sorry, let me be more clear. Suppose an electron wave travels through a double slit. Typically without measurement I’d assume it would create an interference pattern on a screen. Now replace that screen with two different double slits and measure which slits the electron goes through on one of those double slits but not the other. And then put a screen in back of those. Would we just get an interference pattern behind one of the second double slits and not an interference pattern behind the other?

Another question: if you just have one double slit and you only measure which electrons go through one of the slits, how does it behave then?

 

[PeterDonis]

Suppose an electron wave travels through a double slit. Typically without measurement I’d assume it would create an interference pattern on a screen.

Meaning, without measurement of which slit it goes through? Detecting an interference pattern on a screen is a measurement; it's just not a measurement of which slit the electron goes through.

replace that screen with two different double slits and measure which slits the electron goes through on one of those double slits but not the other. And then put a screen in back of those. Would we just get an interference pattern behind one of the second double slits and not an interference pattern behind the other?

We already know that measuring which slit an electron goes through in a double slit means no interference pattern on a screen behind the double slit. Doesn't this answer your question?

if you just have one double slit and you only measure which electrons go through one of the slits, how does it behave then?

Putting a measuring device at one slit tells you which slit the electron goes through: if the measuring device registers no electron, and you see a dot on the screen where an electron lands, you know the electron went through the other slit. So there will be no interference.

 

[Sting33]

It’s amazing. I wish science was better at answering why questions though. It’s just so counterintuitive to me that it just seems like somethings wrong. Like the measurement device is messing with it. But I’m sure there have been sufficient experimentation to verify this is just how it behaves. I appreciate your comments and explanations!

 

[PeterDonis]

Like the measurement device is messing with it.

Measurements are interactions; of course measuring a system "messes with" it.

 

[Sting33]

Ok. Then this experiment isn’t as mysterious as I had previously thought. Of course if you interact with something things will change. I guess what they’re still trying to figure out is the mechanism for this change. And from other studies it looks like in one case the detector causes the electron to propagate as a spherical rather than cylindrical wave, and thus no interference pattern between the two waves. Thanks for your help.

 

[PeterDonis]

I guess what they’re still trying to figure out is the mechanism for this change.

The specific mechanism depends on the specific design of the electron detector. But whatever its design, to detect the electron, it has to interact with it. That interaction is the mechanism of the change.

from other studies it looks like in one case the detector causes the electron to propagate as a spherical rather than cylindrical wave

Where are you getting this from?

and thus no interference pattern between the two waves

Why would there be no interference pattern between spherical waves? Spherical waves can interfere.

 

[Sting33]

I should have been more clear. One type of detector caused inelastic scattering, which I don’t understand, but apparently the one slit acted more like a spherical wave that didnt interfere with the adjacent cylindrical wave. https://m.phys.org/news/2011-01-which-way-detector-mystery-double-slit.html

 

[PeterDonis]

One type of detector caused inelastic scattering, which I don’t understand, but apparently the one slit acted more like a spherical wave that didnt interfere with the adjacent cylindrical wave.

The full paper is behind a paywall and I can't find a preprint on arxiv.org, so I can't look at the actual math being used. The description in the phys.org article is in vague ordinary language and can't really support a proper analysis. Without seeing more of the technical details, all I can say is that the mechanism they are describing might be specific to this particular kind of which-way detector, not a general property of any which-way detector.

 

[David Byrden]

In everyday life, we're used to the notion that we can explain something by breaking it down into parts.

The car comprises engine, wheels etc.; the engine has casing, timing, pistons etc.; the timing circuit has wiring, chips, software etc; and so on in a seemingly unending sequence.

But at the quantum level we hit a wall.

Quantum mechanics gives us equations that predict behaviours, but we cannot explain them by breaking things down further. There is no further to go.

What we can do is " interpret" QM by imagining mechanisms that are comprehensible to us and that match the predicted behaviours (We hope). But when you assume, for example, collapse of the wave function, you will never see a wave function collapsing. It's not what "Really happens", it's more like a "story that I tell myself".

David

 

[David Byrden]

...some of the electron waves that went through the first slit would have hit both of the pairs of second slits and then when we measure if it went through one of the two secondary double slits we’ll measure that it did, and yet that same electron has made an interference pattern behind the unmeasured second double slit.

Ah, there's the rub!

Any single electron does not make a pattern. It makes a dot. It lands at one point.

David

 

[Sting33]

Ah, there's the rub!

Any single electron does not make a pattern. It makes a dot. It lands at one point.

David

Oh yeah! Of course. So only the electrons that traveled to the second measured slits would “choose” a slit and not cause an interference pattern. Like you and others have said, the new “source” becomes the second slits.

 

[PeroK]

Oh yeah! Of course. So only the electrons that traveled to the second measured slits would “choose” a slit and not cause an interference pattern. Like you and others have said, the new “source” becomes the second slits.

By focusing on the final outcome for many electrons in terms of an interference pattern or not, you may be distracting yourself from the main point. Each electron behaves probabilistically based on the paths available to it. An intermediate measurement reduces the available paths and the electron behaves According to a different set of probabilities.

Whether the eventual result is an "interference pattern" or not is a bit of a side issue - although the final pattern does, of course, correlate with the paths available to each electron.