Sniping slits in double slit experiment?

[Jabbu]

Not if its position is known at one slit.

Thanks
Bill

Position would not be known generally, only starting position and the direction in which it was emitted, and location where it was detected.

Try what?

If you know the position for sure at one of the slits how can the state behind the slits be a superposition of position at both slits?

That's also true for those experiments where they place a detector in on of the slits, but aiming photons in known direction is much less intrusive way to know "which way", so wouldn't that be a better type of the same experiment?

 

[atyy]

Not if its position is known at one slit. If the tube exits at one slit you have blocked off the path to go through the other slit. If you move the exit back a bit and you have a path of traveling along the slit screen then through the other slit - yes it will go through both slits. But viewing it via Feymann's sum over histories approach the slight variation of that wild path will always cancel. Move the exit further back and that new path will cancel less and less so you get gradually more double slit interference.

Thanks
Bill

Yes, I agree. It's a matter of semantics. This is the same as blocking the other slit - in the sense that Jabbu cannot say 'this is a less intrusive way to know "which way" than placing a detector in one of the slits'.

 

[atyy]

That's also true for those experiments where they place a detector in on of the slits, but aiming photons in known direction is much less intrusive way to know "which way", so wouldn't that be a better type of the same experiment?

The "which way" language is a confusing language, even though you will see it often in the peer-reviewed literature. Electrons do not have any way which is a way governed by equations that are the classical limit of the quantum equations. So we cannot ask "which way" the electron went - unless you measure the electron's position at every point in the electron's trajectory - but these experiments do not do that - they only measure position at a few points.

 

[bhobba]

Position would not be known generally, only starting position and the direction in which it was emitted, and location where it was detected.

If you know direction you know momentum and hence its not spread over space and can't go through both slits. To go through both slits it must be in a superposition of direction.

That's also true for those experiments where they place a detector in on of the slits, but aiming photons in known direction is much less intrusive way to know "which way", so wouldn't that be a better type of the same experiment?

If you place a detector at one slit the state behind the slit screen is not a superposition of position for both slits.

Read the link I gave. See equation 9 and its assumption - 'Assuming the source-slit geometry does not favor one slit is over the other, the state vector is the superposition of position eigenvectors'. But if you have a detector at one slit y1 or y2 in that equation is not a Dirac Delta function - its a big fat zero - so the analysis is as per the single slit.

Thanks
Bill

 

[atyy]

Why can we not be more precise when shooting stuff through the double slit, so that we know if it goes in the direction of one slit or the other? By the way, is there any significant difference in workings between single and double slit interference?

There is no fundamental difference between the single and double slit interference. Even with a single slit you get an interference pattern. The double slit experiment is just a single slit experiment in which the slit has a weird shape.

 

[Jabbu]

The "which way" language is a confusing language, even though you will see it often in the peer-reviewed literature. Electrons do not have any way which is a way governed by equations that are the classical limit of the quantum equations. So we cannot ask "which way" the electron went - unless you measure the electron's position at every point in the electron's trajectory - but these experiments do not do that - they only measure position at a few points.

What about photons and lenses? Can we not direct photons through lenses with enough precision to be sure it went towards one slit and not the other?

 

[bhobba]

What about photons and lenses? Can we not direct photons through lenses with enough precision to be sure it went towards one slit and not the other?

Its very annoying coming up with some hand-wavey type proposal such as can we vaguely have some lens arrangement to vaguely do something or another that may allow us to violate basic premises of QM.

If you want to go down that path make an exact proposal, with a detailed experimental arrangement, and it can be exactly analysed.

Thanks
Bill

 

[atyy]

What about photons and lenses? Can we not direct photons through lenses with enough precision to be sure it went towards one slit and not the other?

Strictly speaking you cannot, but approximately you can. Let's just think about classical light - it is spread out in space, so it will always go through all the open slits. But sometimes with lenses and classical geometrical optics, we can treat light approximately as rays and say it went through a slit without bending. When can we do that? We can do that if the slit and the distance between the slit is big compared to the wave length of the light.

But again, I stress that even if an electron or photon goes through one slit, it is a wave, and there will be an interference pattern.

 

[bhobba]

But again, I stress that even if an electron or photon goes through one slit, it is a wave, and there will be an interference pattern.

Yes - but its a different sort associated with the finite width of the slit:
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslitd.html

The paper I linked to on the correct analysis of the double slit experiment analyses that situation as well.

Thanks
Bill

 

[Jabbu]

There is no fundamental difference between the single and double slit interference. Even with a single slit you get an interference pattern. The double slit experiment is just a single slit experiment in which the slit has a weird shape.

Photons interfere with themselves in a single slit experiment as well?

Can we say those photons which ended up in between the slits are not involved in interference and fringe pattern forming? And can we say then the photons that do make interference pattern must have therefore been directed more towards one or the other slit and away from the middle point between them?

Its very annoying coming up with some hand-wavey type proposal such as can we vaguely have some lens arrangement to vaguely do something or another that may allow us to violate basic premises of QM.

I'm not proposing anything, I'm asking. What is the reason we can not focus individual photons through lenses with enough precision to be sure they went towards one slit and not the other?

 

[atyy]

Photons interfere with themselves in a single slit experiment as well?

Yes. As an example, you can see the interference pattern formed by neutrons in a single slit experiment in Fig. 2, 3 and 4 of http://www.unicamp.br/~vitiello/f6892s04/nw.pdf.

Can we say those photons which ended up in between the slits are not involved in interference and fringe pattern forming? And can we say then the photons that do make interference pattern must have therefore been directed more towards one or the other slit and away from the middle point between them?

Within quantum mechanics, photons, neutrons and electrons simply do not have trajectories that are described by the classical equations of motion. The do not have definite positions when their position is not observed.

However, can one assign photons, neutrons and electrons trajectrories that are described by different equations from the classical equations of motion? There are many ways of doing so, corresponding to the many variants of Bohmian mechanics. If one is prepared to assume a particular one of these theories, then yes, by looking at where the electron ended up on the screen, even if there is an interference pattern, one can say which slit it came from.

So to stress again: in quantum mechanics, particles do not have simultaneously well defined position and momentum - they do not have trajectories described by classical equations of motion. If one assumes some variant of Bohmian mechanics, one can assign simultaneously well defined Bohmian position and "Bohmian momentum" (not a standard term). This does not contradict the non-existence of simultaneous position and momentum, because Bohmian position and Bohmian momentum (as a pair) are not the same as the position and momentum (as a pair) of quantum mechanics. As an example of Bohmian trajectories in an interference pattern, take a look at http://scienceblogs.com/principles/2011/06/03/watching-photons-interfere-obs/.

 

[Cthugha]

I'm not proposing anything, I'm asking. What is the reason we can not focus individual photons through lenses with enough precision to be sure they went towards one slit and not the other?

Ehm...if you do not insist on single photons, you can do just that by using incoherent light. Just place a standard light bulb very close to the slits. It is so incoherent that you could determine in principle which path each photon went through. Just try it and you will not see an interference pattern. You could use unfiltered light from the sun, too.

 

[Jabbu]

Yes. As an example, you can see the interference pattern formed by neutrons in a single slit experiment in Fig. 2, 3 and 4 of http://www.unicamp.br/~vitiello/f6892s04/nw.pdf.

Dimensions of those slits are part of the equation, so why would we say a photon interacts with itself instead of photon interacts with the slit?

So to stress again: in quantum mechanics, particles do not have simultaneously well defined position and momentum - they do not have trajectories described by classical equations of motion. If one assumes some variant of Bohmian mechanics, one can assign simultaneously well defined Bohmian position and "Bohmian momentum" (not a standard term). This does not contradict the non-existence of simultaneous position and momentum, because Bohmian position and Bohmian momentum (as a pair) are not the same as the position and momentum (as a pair) of quantum mechanics. As an example of Bohmian trajectories in an interference pattern, take a look at http://scienceblogs.com/principles/2011/06/03/watching-photons-interfere-obs/.

I hear you. But if we can focus a light beam to a sharp point of 0.1mm size, why would we think not all of the photons actually end up within that 0.1mm focus point? Is this technical limit or theoretical uncertainty, or QM and optics give different results, or something else?

 

[Dale]

The OPs question has been answered over and over. There is plenty of information about single slit experiments.