What is the result of putting a detector on both slits in the 2 slit experiment?

[drl]

In the 2 slit experiment , what would be the result if we put a dedector on both slits? would we get an interference patern?

 

[drl]

i.e. Does using a detector at one slit alter the wave function of the wave so that it is no longer interference capable with the wave function passing thru the 2`nd slit?

 

[lekh2003]

Interference would no longer be possible since you have collapsed the wave function. You would see two plain lines of whatever you were passing through the two slits.

Point of advice: don't reply to yourself, your thread will no longer be in the unanswered section which usually gets answers faster than if it looks like your thread is already replied to.

 

[drl]

Where my problem comes in is if a polarizer is placed at each of the 2 slits and the polarizers are parallel we get an interference pattern. If the polarizers are in crossed position , the interference pattern disappears. I would have assumed that if we used detectors at both slits we would have obtained the same result. please explain.

 

[lekh2003]

Where my problem comes in is if a polarizer is placed at each of the 2 slits and the polarizers are parallel we get an interference pattern. If the polarizers are in crossed position , the interference pattern disappears. I would have assumed that if we used detectors at both slits we would have obtained the same result. please explain.

Ok I'm not too sure about polarization. I would assume that polarisations of light which are not in line with each other would not interfere.

It would help to wait for some other responses.

 

[Khashishi]

what would be the result if we put a dedector on both slits?

English is ambiguous here. Do you mean two detectors, one on each slit? Or do you mean one detector that spans both slits?
If the detector can provide "which way" information, then it will destroy the interference. But if the detector counts the particles that pass either slit without telling which slit the particles pass through, then it can preserve the interference, provided it is not possible in principle to tell which slit they passed through.

 

[lekh2003]

English is ambiguous here. Do you mean two detectors, one on each slit? Or do you mean one detector that spans both slits?
If the detector can provide "which way" information, then it will destroy the interference. But if the detector counts the particles that pass either slit without telling which slit the particles pass through, then it can preserve the interference, provided it is not possible in principle to tell which slit they passed through.

How is it possible to have individual photons pass through slits and have two separate detectors and at the same time have no clue which went through which? The act of knowing something went through something allows you to figure out where it went.

You can't have two detectors telling you that one photon went through both of them. The detectors will have already collapsed the wave function.

 

[Khashishi]

As long as you are measuring something that cannot provide which way information, it doesn't have to break the interference. Also, it's possible to restore the interference after a which way measurement if the measurement is erased by a quantum eraser.

Let us consider how an actual detector experiment would work. For the most part, you can't detect photons without blocking some of them. For example, you can detect vertical polarization by using a polarizer, but that will block out half the light.

If you set up a double slit, and you put a horizontal polarizer in front of one slit and a vertical polarizer in front of the other, there will be no interference on the screen. The polarizers act as detectors, encoding the "which way" information into the polarization of the light.
Now if you put a diagonal polarizer between the screen and slits, you can restore the interference pattern, because it removes the "which way" information. Of course, this can all be explained in terms of classical optics. But the point is that you could do something similar with electrons if you wanted to.

The main difficulty is trying to devise what you can actually use as a detector in an experiment.

 

[PeterDonis]

@drl there is no need to shout. I have deleted your post for that reason. Feel free to post again in answer to my question below, but please do so without using all caps.

Where my problem comes in is if a polarizer is placed at each of the 2 slits and the polarizers are parallel we get an interference pattern. If the polarizers are in crossed position , the interference pattern disappears.

Can you give a reference that gives this experimental result, and more details about how it was achieved?

 

[vanhees71]

Hm, I don't know whether Walborn et al checked putting the polarizers in parallel orientation, but it's very clear that then you get the full-contrast 2-slit interference as if there where no polarizers (of course with a factor 1/2 reduced intensity, because half the photons are absorbed by the polarizers). Of course then you don't gain any which-way information whatsoever. For 90-degree relative orientation your interference pattern is completely gone (and you gain complete which-way information). This case is indeed verified in the original paper:

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, PRA 65 033818 (2002)

Of course for an arbitrary relative angle of the polarizers you get any contrast in between and correspondingly more or less certain which-way information.

 

[PeterDonis]

it's very clear that then you get the full-contrast 2-slit interference as if there where no polarizers (of course with a factor 1/2 reduced intensity, because half the photons are absorbed by the polarizers). Of course then you don't gain any which-way information whatsoever. For 90-degree relative orientation your interference pattern is completely gone (and you gain complete which-way information).

Perhaps it might help to clarify why you get which-way information from 90-degree relative orientation but not from parallel orientation. I would say it's because "which-way information" means the degree to which the states of the photons coming from each slit are orthogonal, and can therefore be reliably distinguished by further measurements. For the 90-degree relative orientation, the photon states coming from the two slits are exactly orthogonal; for the parallel orientation, the photon states coming from the two slits are identical (i.e., exactly "non-orthogonal"), and for intermediate orientations, the photon states coming from the two slits are partly orthogonal and partly not.

 

[DrChinese]

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, PRA 65 033818 (2002)

Adding to what you and PeterDonis are discussing (which also references the above):

http://sciencedemonstrations.fas.ha...-demonstrations/files/single_photon_paper.pdf

An apparatus for a double-slit interference experiment in the single-photon regime is described. The apparatus includes a which-path marker that destroys the interference as well as a quantum eraser that restores it. We present data taken with several light sources, coherent and incoherent and discuss the efficacy of these as sources of single photons.

 

[drl]

It seems to me that when you say which way information cannot be recorded. that this is a nonscientific assumption. Can it be that when we use a detector at one slot only, the wave function at that slot is altered to the extent that it becomes incompatible with the unaltered wave function from the other slot to achieve an interference pattern? When we use polarizers, both in parallel position we get interference pattern because the wave functions coming thru both slots have both been altered to the same extent? When we cross the polarizers , we have altered the compatibility of both wave functions to produce the interference pattern. That is why I suggested using a detector at both slots to see if the wave functions would both be altered to a compatible state. Thanks for your help.

 

[Nugatory]

wave function at that slot is altered to the extent that it becomes incompatible with the unaltered wave function from the other slot to achieve an interference pattern?

You'd have to provide a clear mathematical definition of what you mean by the wave function "at that slot" and how it is that anything can be "incompatible with" anything else when there's only one wave function involved.

This being a B-level thread, there are two books that you might want to try: Feynman's "QED: The strange theory of light and matter"; and Giancarlo Girardi's "Sneaking a look at god's cards". The first will go a long way towards understanding how the possible paths the light could have taken affects the interference pattern (detectors tell you something about which paths are possible). The second will get you started on how to think about which slits the particle "goes through" in the double-slit experiment.

 

[drl]

It seems to me that a single wave function in superposition goes to the 2 slits.where the detector at one of the slits alters the wave function so that it is different from the other wave function at the other slit.I assume that in order to get an interference pattern the wave functions at both slits have to be the same. The crossed polarizers at the slits indicates there is . no interference pattern until the wave functions are the same, as when an eraser is used. Hope I don't annoy you!

 

[PeroK]

It seems to me that a single wave function in superposition goes to the 2 slits.where the detector at one of the slits alters the wave function so that it is different from the other wave function at the other slit.I assume that in order to get an interference pattern the wave functions at both slits have to be the same. The crossed polarizers at the slits indicates there is . no interference pattern until the wave functions are the same, as when an eraser is used. Hope I don't annoy you!

There is only one wave function. You should also know that you have single-slit interference. Try, for example:

https://www.khanacademy.org/science...nce-of-light-waves/v/single-slit-interference

 

[drl]

O.K. It seems to me that that the idea that you cannot transmit whichway information has some sort of mystical origin which I find difficult to accept. Again, could it be that any attempt to find whichway information alters the wave function where the detector is used so that it is not compatible (out of phase) with the wave function from the other slit. At rate, if it has not been attempted as yet, why not give a detector at both slits a try..

 

[PeroK]

O.K. It seems to me that that the idea that you cannot transmit whichway information has some sort of mystical origin which I find difficult to accept. Again, could it be that any attempt to find whichway information alters the wave function where the detector is used so that it is not compatible (out of phase) with the wave function from the other slit. At rate, if it has not been attempted as yet, why not give a detector at both slits a try..

First, I think you are confusing theory with experiment. The experiments that lead to an interference pattern and the ones that do not are well established. Do you really think that in almost 100 years no one has thought to put a detector at both slits? And run the experiment so that every particle gets detected?

The theory is how to explain this. There is only ever one wavefunction. If you do not detect the particle, then it behaves in a certain way and you get a double slit interference pattern. If you do detect the particle, then that constitutes a measurement of the particle which resets the wave function and you get single slit interference. There is no interchange of information between two wave functions.

 

[Mentz114]

O.K. It seems to me that that the idea that you cannot transmit whichway information has some sort of mystical origin which I find difficult to accept. Again, could it be that any attempt to find whichway information alters the wave function where the detector is used so that it is not compatible (out of phase) with the wave function from the other slit. At rate, if it has not been attempted as yet, why not give a detector at both slits a try..

As PerOK has said you have a misconception about this situation. In quantum mechanics, if there is more than one way for something to happen then all the ways must be taken into account in calculating probabilities of outcomes. Combining amplitudes can cause interference if the parts remain coherent.

Some things one can do will diminsh or destroy the coherence. All this is well known and understood. It is the phrase 'which-path information' which is mis-used that leads to confusion and your use of the word 'mystical'.

 

[drl]

O.K. Perok says "Do you really think that in almost 100 yrs. no one has thought to put a detector at both slits. Hey, that was my very first question in this thread." If it was done what were the results? Perhaps my volcabulary was off and the further question should have been if the detector could alter that part of the wave function crossing the detectors slit so that its waves were no longer coherent with the wave function going thru the other slit! Somehow I feel as if I`m missing something or I`m not getting across.

 

[Mentz114]

O.K. Perok says "Do you really think that in almost 100 yrs. no one has thought to put a detector at both slits. Hey, that was my very first question in this thread." If it was done what were the results? Perhaps my volcabulary was off and the further question should have been if the detector could alter that part of the wave function crossing the detectors slit so that its waves were no longer coherent with the wave function going thru the other slit! Somehow I feel as if I`m missing something or I`m not getting across.

What do you think will happen if there is a detector at both slits ? Remember that the more accurately the detector can locate the particle the more will be the decoherence.

 

[Nugatory]

Perhaps my volcabulary was off and the further question should have been if the detector could alter that part of the wave function crossing the detectors slit so that its waves were no longer coherent with the wave function going thru the other slit! Somehow I feel as if I`m missing something or I`m not getting across.

You're still saying things like "the wave function going through the other slit" and "that part of the wave function crossing the detectors slit". But that's not how it works. The wave function is a function, a mathematical formula into which you plug four input numbers (time and position along each of three spatial dimensions) to calculate a single complex output number. Talking about it moving or going through a slit makes no more sense than talking about hitting the quadratic formula with a hammer, or boiling Newton's third law in a kettle, or... You get the idea.

If you aren't up for taking on a college-level intro QM textbook, you might want to give Giancarlo Ghirardi's book "Sneaking a look at God's cards" a try. It's one of very few layman-friendly but not misleading explanations of what quantum mechanics is about.

 

[Nugatory]

Hey, that was my very first question in this thread.

It was, and "What happens?" was answered by @Khashishi in post #6 of the thread.

One thing to remember is that in quantum mechanics the words "detection" and "observation" (Khashishi also said something cautionary about English being imprecise) mean something closer to "thermodynamically irreversible interaction"; so you are really asking if the experiment has been done with the particle interacting no matter which slit as it passes through. The answer to that pretty much has to be "yes", because that's what usually happens when something encounters a screen with a slit. For a truly trivial example: every time that you enter a building with two doors and leave via one or the other (thus interacting with the air molecules in that doorway)... You've just done the equivalent of a double slit experiment with detectors at both slits. It takes fairly heroic measures with subatomic particles to put together an experiment in which we do observe interference, so those are the ones that get all the press.

(And an aside - Do not confuse the quantum mechanical double slit experiment with Young's 1801 experiment involving light and interference patterns. That's a different double-sit experiment involving light waves, and has little to do with quantum mechanics).

 

[lekh2003]

You're still saying things like "the wave function going through the other slit" and "that part of the wave function crossing the detectors slit". But that's not how it works. The wave function is a function, a mathematical formula into which you plug four input numbers (time and position along each of three spatial dimensions) to calculate a single complex output number. Talking about it moving or going through a slit makes no more sense than talking about hitting the quadratic formula with a hammer, or boiling Newton's third law in a kettle, or...

 

[vanhees71]

A very thorough discussion on these issues can be found in the introductory chapter of vol. 3 of the Feynman lectures, which are completely online for free:

http://www.feynmanlectures.caltech.edu/III_01.html#Ch1-S1

 

[drl]

Getting confused Let's put it this way.There has to be 2 coherent waves each of which goes thru one of the slits to get an interference pattern. Some how the particle creating these coherent waves can only go thru one of these slits at any time and we still get an interference pattern. It is only when we try to detect the which way that it took that we get a wave function collapse. So again I`m asking if this a result of some mystical thinking that some how which way information is forbidden or can it be the result of the detectors effect on the wave passing thru to alter its coherency to the wave at the other slit? Sorry to be a pain. Thanks for your efforts.

 

[Mentz114]

Getting confused Let's put it this way.There has to be 2 coherent waves each of which goes thru one of the slits to get an interference pattern. Some how the particle creating these coherent waves can only go thru one of these slits at any time and we still get an interference pattern. It is only when we try to detect the which way that it took that we get a wave function collapse. So again I`m asking if this a result of some mystical thinking that some how which way information is forbidden or can it be the result of the detectors effect on the wave passing thru to alter its coherency to the wave at the other slit? Sorry to be a pain. Thanks for your efforts.

There is nothing mystical about the interference. In quantum mechanics all the possible ways of something happening have to be included in the outcome, by adding amplitudes. It is all predicted and explained by quantum theory. Loss of the interference is caused by decoherence which results from partial or full position detection at the slits.

There is a report of an experiment here

Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences
P. Grangier, G. Roger and A. Aspect

If you want to try it yourself read this !
The theory is also given in the above.