B What constitutes a measurement of which slit - double slit

[Negatratoron]

In the double slit experiment, when you measure which slit your photon passes through, it will land in the corresponding location on the photosensitive film at the end of the apparatus. If, however, you don't measure which slit it goes through, an interference pattern will appear on the film.

If the film is sensitive enough to show two distinct blobs vs an interference pattern, why does it not constitute a measurement of which slit the photon went through? I.e. why is there ever an interference pattern?

 

[andrewkirk]

Experiments have been done in which the photon flow is so sparse that the film (or other sensing device) is marked by distinct blobs one by one. When there have been slit-detection apparatus operating, the little blobs gradually build up a pattern of two big smudges, one opposite each slit. When there is no slit-detection apparatus operating, the little blobs gradually paint an interference pattern, in a pointilliste sort of fashion. The latter case demonstrates that individually marking the arrival of each photon on the film does not give any information about which slit was traversed.

 

[Negatratoron]

Experiments have been done in which the photon flow is so sparse that the film (or other sensing device) is marked by distinct blobs one by one. When there have been slit-detection apparatus operating, the little blobs gradually build up a pattern of two big smudges, one opposite each slit. When there is no slit-detection apparatus operating, the little blobs gradually paint an interference pattern, in a pointilliste sort of fashion. The latter case demonstrates that individually marking the arrival of each photon on the film does not give any information about which slit was traversed.

Consider just the film (or other sensing device). If each photon brightens a certain area, doesn't that alone constitute a measurement of which slit it went through?

 

[Negatratoron]

What materials were actually used to conduct the two-slit experiment? I feel like my misunderstanding comes from using these ideal abstractions like "film" etc.

 

[Negatratoron]

You know, it seems like the reason the film would not constitute a measurement, is because you actually can't use it to tell which slit any given photon passed through. The slit-detection apparatus makes a difference because it increases sensitivity.

 

[bhobba]

You know, it seems like the reason the film would not constitute a measurement,

It does constitute a measurement.

You need to see a better analysis of the experiment than is given in beginner texts
https://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

If you do a measurement of which slit it goes through it has an exact position at that slit and is exactly the same as a single slit experiment.

Thanks
Bill

 

[Negatratoron]

It does constitute a measurement.

You need to see a better analysis of the experiment than is given in beginner texts
https://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

If you do a measurement of which slit it goes through it has an exact position at that slit and is exactly the same as a single slit experiment.

Thanks
Bill

Thanks, that's a good PDF.

Let's say you have a device, and you're not sure whether or not it detects photons. Can you test it by putting it in front of one slit, and checking whether there's interference? It sounds like you could...

 

[bhobba]

Let's say you have a device, and you're not sure whether or not it detects photons. Can you test it by putting it in front of one slit, and checking whether there's interference? It sounds like you could...

Of course you could. But its not a good way to see if it detects photons.

Thanks
Bill

 

[vanhees71]

It's not the photoscreen which causes the interference pattern but the photon-distribution has this pattern itself. So no matter how good the resolution of your detector, you'll always have this distribution. A single photon, of course, makes only one spot on the screen, but the probability, where it appears there is determined by the interference pattern, and according to quantum theory (QT) there's nothing else than these probabilities that can be known about the appearance of the single photon on the screen, and this probability distribution is calculated using quantum electrodynamics or in very good approximation the intensity of classical electromagnetic waves subject to the boundary conditions given by the double slit.

Now to the question concerning "which-way information". One way to gain which-way information is to use polarized single photons, which you can get using polarization-entangled photon pairs and using one of the photons to filter such that you consider only the second photon in the pair that is polarized in a certain direction, say in $x$-direction (the double-slit plane may be in the $xy$ plane).

Now you put quarter-wave plates into each slit, one oriented $+45^{\circ}$ and the other $-45^{\circ}$ relative to the polarization direction of your photons. After passing the slits the photon is circularly polarized but left-circularly polarized if going through one and right-circularly polarized if it goes to the other. Thus after passing the slits the polarization of the photons tell you through which slit it came. Since the two circular polarization states are orthogonal to each other, there's no interference between the photon running through the one or the other slit anymore. Thus gaining sure which-way information killt the interference pattern completely.

 

[andrewkirk]

You know, it seems like the reason the film would not constitute a measurement, is because you actually can't use it to tell which slit any given photon passed through.

That's correct, because the waves travel in all directions when they come through a slit, so looking at where a photon hits the screen cannot tell us anything about which slit it came from.

The slit-detection apparatus makes a difference because it increases sensitivity.

It doesn't increase sensitivity. What it does is change the waves going through the two slits in different ways so they cannot interfere with one another and make an interference pattern.

 

[Tollendal]

In June 2011 the Canadian scientist Aephraim Steinberg measured one photon both position and momentum, verifying that it behaves as an wave even when it traverses just one single slit (http://phys.org/news/2011-06-quantum-physics-photons-two-slit-interferometer.html). Double slits are desnecessary.

 

[Norbert Fnord]

It's not the photoscreen which causes the interference pattern but the photon-distribution has this pattern itself. So no matter how good the resolution of your detector, you'll always have this distribution. A single photon, of course, makes only one spot on the screen, but the probability, where it appears there is determined by the interference pattern, and according to quantum theory (QT) there's nothing else than these probabilities that can be known about the appearance of the single photon on the screen, and this probability distribution is calculated using quantum electrodynamics or in very good approximation the intensity of classical electromagnetic waves subject to the boundary conditions given by the double slit.

Now to the question concerning "which-way information". One way to gain which-way information is to use polarized single photons, which you can get using polarization-entangled photon pairs and using one of the photons to filter such that you consider only the second photon in the pair that is polarized in a certain direction, say in $x$-direction (the double-slit plane may be in the $xy$ plane).

Now you put quarter-wave plates into each slit, one oriented $+45^{\circ}$ and the other $-45^{\circ}$ relative to the polarization direction of your photons. After passing the slits the photon is circularly polarized but left-circularly polarized if going through one and right-circularly polarized if it goes to the other. Thus after passing the slits the polarization of the photons tell you through which slit it came. Since the two circular polarization states are orthogonal to each other, there's no interference between the photon running through the one or the other slit anymore. Thus gaining sure which-way information killt the interference pattern completely.

To me the electromagnetic radiation is a propagating wave until it is detected. So with the standard double slit it propagates through both slits as a probability and interferes with itself producing an interference pattern of probabilities and therefore produces the multiple bands on the screen. If detected at one of the parallel slits it is reduced to a photon particle and proceeds in a more or less straight line.
In the case of the above experiment, it will still be a wave propagation but due to polarization there is only one slit open to the wave and it can only go through one slit, so no interference can occur.
It would be interesting to know that if a detector was placed on one of the slits, whether or not the spread of the two bands would be any narrower.

 

[Tollendal]

As we know, difraction is the bending of wave rays when they meet an obstacle to propagation .

Suppose an wave propagating in a medium until it meet a slit in an opaque barrier.

In 1924, Louis DeBroglie made an important discovery. Considering Einstein's relation

lambda = h/p ( is Plank's constant and p is momentum),

he demonstraded that the relation faculted the determination of the wave length of any material object. For this equation he earned the Nobel prize in 1929. The hypothesis was confirmed in 1927 by Clinton Davisson and Lester Germer.

Yet the habit of treating with corpuscles hinders until today that people understand that DeBroglie really has demonstrated particles inexistence. There is no duality, as generally affirmed, but only waves. A wave, as the photon, that manifests itself in a limited space, will seem to the observer a particle.

 

[vanhees71]

To me the electromagnetic radiation is a propagating wave until it is detected. So with the standard double slit it propagates through both slits as a probability and interferes with itself producing an interference pattern of probabilities and therefore produces the multiple bands on the screen. If detected at one of the parallel slits it is reduced to a photon particle and proceeds in a more or less straight line.
In the case of the above experiment, it will still be a wave propagation but due to polarization there is only one slit open to the wave and it can only go through one slit, so no interference can occur.
It would be interesting to know that if a detector was placed on one of the slits, whether or not the spread of the two bands would be any narrower.

No, it cannot go only through one slit, because it's linearly polarized, and the quarterwave plates just make a left- and right-polarized when the wave goes through. Nothing is absorbed by the quarter-wave plates! So the wave goes through two slits here too, but since the parts going through slit 1 is orthogonally polarized to those going through slit 2 there is no interference term. If you have single photons, you can in principle determine with certainty through which slit it has gone by measuring whether it's left or right-circularly polarized. That's an example for the fact that you can know which-way information (whether really observed or not is unimportant) with certainty excludes an interference pattern.

 

[StevieTNZ]

In June 2011 the Canadian scientist Aephraim Steinberg measured one photon both position and momentum, verifying that it behaves as an wave even when it traverses just one single slit (http://phys.org/news/2011-06-quantum-physics-photons-two-slit-interferometer.html). Double slits are desnecessary.

That experiment used 'weak measurements'. I don't think they count as proper measurements of position and/or momentum -- only an average over many photons. I think weak measurements are a bit controversial in the QM academia, given what information they purport to give. Someone can correct me if I am mistaken, though.