Double-slit experiment, determining which slit an electron passed thru

[tade]

I was reading Feynman's lecture on the double-slit experiment, the attempts to determine which slit an electron passes through.
https://www.feynmanlectures.caltech.edu/III_01.html#Ch1-S6

And the key part is when Feynman says, "Then a terrible thing happens.", about the low optical resolutions of long wavelengths.

However, if the separation distance between the two slits is long enough, would it be possible to determine which slit an electron passes through while still having the set-up produce an interference pattern?

 

[PeroK]

However, if the separation distance between the two slits is long enough, would it be possible to determine which slit an electron passes through while still having the set-up produce an interference pattern?

Why would that happen?

 

[tade]

Why would that happen?

to be cautious, if i am allowed to explain my thinking in order to answer your question, because the long distance would make up for the low optical resolution, and then, because Feynman said that:

And it is just with light of this color that we find that the jolts given to the electron are small enough so that P′12 begins to look like P12—that we begin to get some interference effect.

 

[PeroK]

to be cautious, if i am allowed to explain my thinking in order to answer your question, because the long distance would make up for the low optical resolution, and then, because Feynman said that:

If the slits are far enough apart there is no interference in the first place. No electrons get through unless you point the electron gun at one particular slit, whereupon it becomes effectively a single-slit experiment.

 

[tade]

If the slits are far enough apart there is no interference in the first place. No electrons get through unless you point the electron gun at one particular slit, whereupon it becomes effectively a single-slit experiment.

what if the electron beam is wide enough to cover both slits

 

[PeroK]

what if the electron beam is wide enough to cover both slits

You'll get two separate single-slit interference patterns.

 

[PeroK]

... I'm not sure what this has to do with detecting the electron?

 

[tade]

... I'm not sure what this has to do with detecting the electron?

making up for the low optical resolutions of long wavelengths

 

[PeroK]

making up for the low optical resolutions of long wavelengths

To get an significant interference pattern the slits must be close together. That's fundamental.

 

[tade]

You'll get two separate single-slit interference patterns.

if the two separate diffractions overlap, will they produce a double-slit interference pattern

 

[PeroK]

if the two separate diffractions overlap, will they produce a double-slit interference pattern

Not really. You may get simply two single-slit patterns with a weak interference on the small overlap region, where few electrons are detected in any case.

There is a quantitative point about these experiments that must be addressed if you are intent on subverting the UP. It is always possible to get a bit of indeterminate interference, coupled with significant which-way detection.

It's not a black and white, one thing or the other.

 

[tade]

There is a quantitative point about these experiments that must be addressed if you are intent on subverting the UP. It is always possible to get a bit of indeterminate interference, coupled with significant which-way detection.

It's not a black and white, one thing or the other.

oh i see, that seems to be quite different from Feynman's striking declarations in the text.

Not really. You may get simply two single-slit patterns with a weak interference on the small overlap region, where few electrons are detected in any case.

by the way how does the slit spacing affect the strength of the interference pattern

because in those diagrams demonstrating double-slit interference, they don't define the slit-spacing in terms of absolute magnitudes

 

[PeroK]

oh i see, that seems to be quite different from Feynman's striking declarations in the text.

Please quote some specific statements in context.

by the way how does the slit spacing affect the strength of the interference pattern

because in those diagrams demonstrating double-slit interference, they don't define the slit-spacing in terms of absolute magnitudes

View attachment 316224

This diagram may be purely illustrative. If those two slits were further apart then eventually all the beam would be absorbed or reflected by the barrier. And nothing or almost nothing would get through.

 

[tade]

If those two slits were further apart then eventually all the beam would be absorbed or reflected by the barrier. And nothing or almost nothing would get through.

could this be compensated by increasing the rate of electrons of the electron beamor, on the other hand, say if its an experiment of the cumulative interference pattern of one electron at a time

 

[PeroK]

could this be compensated by increasing the rate of electrons of the electron beam

Again, you're not thinking quantitatively. Probabilities drop off to negligible numbers very quickly. The slits must be relatively close together. That's a basic part of the experiment. If you have slits 100m apart and fire a beam of electrons at the midway point, then noting gets through. The numbers matter.

 

[tade]

Again, you're not thinking quantitatively. Probabilities drop off to negligible numbers very quickly. The slits must be relatively close together. That's a basic part of the experiment. If you have slits 100m apart and fire a beam of electrons at the midway point, then noting gets through. The numbers matter.

oh, cos i had said, "what if the electron beam is wide enough to cover both slits"

 

[PeroK]

oh, cos i had said, "what if the electron beam is wide enough to cover both slits"

Let me describe what I think you are saying. We have two slits, let's say 10m apart. We have a beam of electrons that covers both slits. And, let's have a very weak electron detection behind both slits that fairly reliably detects which slit, without significantly affecting the electron.

Now, you say, we have which-way information and an interference pattern. And the UP disappears in a puff of qualitative logic.

Now, let's describe what would happen. The slits are so far apart that there is no interfence pattern to begin with. There are effectively two single-slit patterns.

So, you say, let's make the slits extremely narrow, so that the single-slit patterns overlap. Now, we have a very faint beam on the far side of the barrier, because the slits are so narrow that very few electrons make it through. Moreover, not many of these electrons are diffracted by the required 5m in order to overlap. So, we have an extraordinarily faint interference pattern directly between the slits (and mostly single-slit patterns on either side). And, that central interference pattern is now destroyed by any detection of the electron - because it's so faint and delicate, and hangs by a thread (as it were).

Your idea is a common attempt to circumvent the UP. If you don't think too carefully or think quantitaively, then it appears the UP must fail. But, once yiou subject your thought experiment to a careful and perhaps quantitative analysis, you find that the UP re-asserts itself.

 

[PeroK]

PS Reading the Feynman lecture, he covers this point clearly and more coherently than I have in this thread. There is no implication that we get interference or not as an all-or nothing phenomenon. He gives examples where a mixture of interfence and not is the result of the experiment.

 

[tade]

The slits are so far apart that there is no interfence pattern to begin with. There are effectively two single-slit patterns.

I see, I think that this takes us back to #12.

Now, we have a very faint beam on the far side of the barrier, because the slits are so narrow that very few electrons make it through. Moreover, not many of these electrons are diffracted by the required 5m in order to overlap. So, we have an extraordinarily faint interference pattern directly between the slits (and mostly single-slit patterns on either side). And, that central interference pattern is now destroyed by any detection of the electron - because it's so faint and delicate, and hangs by a thread (as it were).

So, say the pattern is faint due to the number of electrons being small. However, are the mechanics of the detection a quantized interaction of a single photon with a single electron?

 

[PeterDonis]

would it be possible to determine which slit an electron passes through while still having the set-up produce an interference pattern?

No. This is never possible. The two things are mutually exclusive; you can only have one or the other.

Notice that I didn't even quote the qualifier you gave, because it is irrelevant to the question. The answer to the question, exactly as quoted above, is always no, regardless of any other aspects of the scenario. So the same answer applies to all the other versions of the same question that you keep asking with different qualifiers. None of the qualifiers matter.

 

[tade]

No. This is never possible. The two things are mutually exclusive; you can only have one or the other.

Notice that I didn't even quote the qualifier you gave, because it is irrelevant to the question. The answer to the question, exactly as quoted above, is always no, regardless of any other aspects of the scenario. So the same answer applies to all the other versions of the same question that you keep asking with different qualifiers. None of the qualifiers matter.

so if it is always no, is this because there is a mathematical proof which covers all possible circumstances and scenarios

 

[PeterDonis]

if it is always no, is this because there is a mathematical proof which covers all possible circumstances and scenarios

The "mathematical proof" is called quantum mechanics. Once you understand how the math of QM works for the double slit experiment, the general statement I made is obvious.

 

[tade]

The "mathematical proof" is called quantum mechanics. Once you understand how the math of QM works for the double slit experiment, the general statement I made is obvious.

And so say an experiment with all of the qualifiers is attempted, what do you predict will occur, how will it all "play out", and, what will "go wrong"

 

[StevieTNZ]

And so say an experiment with all of the qualifiers is attempted, what do you predict will occur

You seem to be relitigating a question which you've already received an answer to - multiple times. You marked this thread as 'I', so we're assuming you have some background (undergraduate) knowledge already.

 

[tade]

You seem to be relitigating a question which you've already received an answer to - multiple times. You marked this thread as 'I', so we're assuming you have some background (undergraduate) knowledge already.

uhh, i think i haven't actually received a particular answer, which is connected to #19 as well

So, say the pattern is faint due to the number of electrons being small. However, are the mechanics of the detection a quantized interaction of a single photon with a single electron?

as I'm interested in the details of the experimental setup, how it will all "play out"

 

[vanhees71]

You'll get two separate single-slit interference patterns.

Only if the coherence length of the beam is not large enough. Otherwise there should be two-slit interference patterns (of course superimposed by the single-slit patterns as well).

 

[PeterDonis]

say an experiment with all of the qualifiers is attempted, what do you predict will occur, how will it all "play out", and, what will "go wrong"

This is unanswerable because there are many different possible experiments.

I'm interested in the details of the experimental setup

Then you need to describe the details of the experimental setup you are interested in. And you would be much better served by first learning the math so that you can figure out for yourself "how it plays out" in whatever experiment you dream up.

Basically it seems like you want answers, but you don't want to do any work yourself to get them. That's not how it works.

Thread closed.