# Another double slit question

by Fiziqs
Tags: double, slit
 P: 113 I realize that the people here must be sick of answering stupid questions about the double slit experiment, and different ways of setting it up, but if I may, I have a question about what you would expect to see if the double slit experiment were set up in a slightly different manner, and why. First, I am assuming that in the classic double slit experiment we need only put a detector at one slit in order to destroy the interference pattern. But this leaves me with a question. Is it the fact that we then know which slit the particle went through that destroys the interference pattern, or is it the fact that we interacted with the probability wave that destroyed the interference pattern? In other words, could we destroy the probability wave without knowing which slit the particle went through. So my question is, what if, instead of setting up the double slit experiment in the way that I usually see it portrayed, with something that looks like a laser pointed at a wall with two slits in it, but instead we set it up with a light positioned in the center of a box with a pair of slits on each of the six opposing walls, and a screen positioned behind each pair of slits. I assume that absent any detectors we would expect to see an interference pattern on all six of the screens. But what if we then put a detector on just one of the twelve slits? Would that one detector be sufficient to destroy the interference pattern on all six of the screens? Or would it only destroy the interference pattern on the screen positioned behind the wall with the detector? What would you expect to see with such a setup, and why? Thanks to everyone for considering my question.
 Sci Advisor Thanks P: 1,741 I'm never sick about answering (or at least trying to answer) such questions. I always find these ideas on which-way information vs. the observation of an interference pattern quite vague. One should clearly specify the experiment and analyse it. Then most of the quibbles with quantum theory vanish usually in a natural way. One must also state clearly which interpretation of quantumt theory one follows. I'm using the minimal statistical interpretation. Now let's consider the usual double-slit experiment. Let's use single photons of a well-defined linear polarization and frequency. Hitting the double slit without any device to determine through which of the slits the photon has gone with very many of such prepared photons, you'll find the double-slit interference pattern on the detection screen. Now the question is, how you can (at least in principle) gain "which-way information" for each single photon with certainty. This is only possible by somehow "tagging" each photon with the information through which slit it might have come. This can be easily achieved by, e.g., putting quarter-wave plates into the slits. Such a quarter-wave plate transforms the linear-polarization state into an elliptically polarized state. If we choose the orientation of the quarter-wave plates to be $45^{\circ}$ in the one slit and $-45^{\circ}$ in the other, with the angle measured relative to the polarization direction of the incoming photon, then any photon, coming through slit 1 becomes left-circular (helicity -1) and any photon coming through slit 2 becomes right-singular (helicity +1) polarized. These polarization states are completely disinguishable, because the corresponding state kets are orthogonal to each other. Now, orthogonal states can never interfere, and thus you won't see any two-slit interference pattern anymore, because the two ways a photon can run to hit the screen are now completely distinguishable, because this information is inherent in any photon behind the double slit. Thus the possibibilities cannot interfere anymore, and thus you don't see an interference pattern. There are very clever setups of this kind, using entangles photon pairs, where you can choose, whether you want to see the interference pattern or not by looking on subensembles of the complete ensemble after the whole experiment has been performed and the data on the position of each photon hitting the screen are fixed. Thus you can "erase" the which-way information for a subensemble of the whole ensemble such that the subensemble shows the interference pattern again. See this publication for details: S. P. Walborn, M. O. Terra Cunha, S. Pádua, C. H. Monken, Double-slit quantum eraser, Phys. Rev. A 65, 033818 (2002) http://link.aps.org/abstract/PRA/v65/e033818 It's also nicely described on the following website: http://grad.physics.sunysb.edu/~amarch/ Concerning your alternative setup, I don't see how the six double-slit experiments should be correlated. By just putting a light source into the box, for sure they are not related in any way.
Mentor
P: 9,585
 Quote by Fiziqs Would that one detector be sufficient to destroy the interference pattern on all six of the screens? Or would it only destroy the interference pattern on the screen positioned behind the wall with the detector? What would you expect to see with such a setup, and why?
You would destroy the interference pattern where you destroy coherency between the two slits - at the side of your detector only.

P: 113

## Another double slit question

 Quote by mfb You would destroy the interference pattern where you destroy coherency between the two slits - at the side of your detector only.
If I may bother you further, what is the mechanism by which the detector introduces decoherence between the two slits?

In the classic double slit experiment, with a detector at both slits, how do the detectors introduce decoherence?

Dumb question I know.
 Mentor P: 9,585 The detectors interact with the wave function "in some way" (enough to cause decoherence, i.e. a phase shift which cannot be predicted).
P: 113
 Quote by mfb The detectors interact with the wave function "in some way" (enough to cause decoherence, i.e. a phase shift which cannot be predicted).
Now when you say "in some way", do you mean that it depends upon the method being used, or do you mean that we really don't know exactly how the detector interacts with the wave to cause decoherence?
 Mentor P: 9,585 It interacts according to the laws of physics, which are well-known for usual detectors. It depends on the precise quantum-mechanical state of the detector (which we usually do not know), and the used method of course.
 P: 55 "Now, orthogonal states can never interfere, and thus you won't see any two-slit interference pattern anymore, because the two ways a photon can run to hit the screen are now completely distinguishable, because this information is inherent in any photon behind the double slit. Thus the possibilities cannot interfere anymore, and thus you don't see an interference pattern." This is exactly a point I wanted to ask about. If orthogonal states can never interfere anyway, then that and that alone is the reason for the lack of fringes. We don't need to say simply knowing or not knowing which slit the photon came through is reason for the state of the photon. It is the quarter-wave polarizers that destroy the interference pattern. In other words, even if the photon went through both slits as a probability wave, and not just one as a particle, the interference pattern would still be destroyed. So, how does this experiment prove anything at all?
P: 719
 Quote by marksesl If orthogonal states can never interfere anyway, then that and that alone is the reason for the lack of fringes. We don't need to say simply knowing or not knowing which slit the photon came through is reason for the state of the photon.
Yes. Interference occurs when there is a possibility to reach the same exact final state by each of two different paths. If you alter one of the paths so that that it no longer reaches the same final state, the interference goes away. I agree that this is a much simpler way of talking about it, and should probably be preferred to langauge that seems to attribute special properties to "measuring devices" or "knowledge."

So why do people say that measuring "which path" information destroys the interference? The interference is destroyed because if you measure which path information, you change the paths so that they reach different final states. One final state is "electron hits the wall at x=5 and the detector reads 'left path,'" while the other final state is "electron hits the wall at x=5 and the detector reads 'right path.'" Since these final states are different, the two paths can't interfere. This sort of thing is going to happen no matter how you detect which path the electron took, so in general "which path" measuring devices destroy the interference pattern.

This also makes it clear that it's not just deliberate measurements that destroy interference. If there's a single stray photon that scatters off the electron if it takes the right path, but not the left path, then this will lead to different final states: "electron hits the screen at x=5 and photon was scattered" vs "electron hits the screen at x=5 and photon was not scattered." So this single stray photon will destroy the interference pattern. Of course, you can think of the photon as performing a crude and accidental "measurement" of which path the electron took.
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P: 5,055
 Quote by marksesl This is exactly a point I wanted to ask about. If orthogonal states can never interfere anyway, then that and that alone is the reason for the lack of fringes. We don't need to say simply knowing or not knowing which slit the photon came through is reason for the state of the photon. It is the quarter-wave polarizers that destroy the interference pattern. In other words, even if the photon went through both slits as a probability wave, and not just one as a particle, the interference pattern would still be destroyed. So, how does this experiment prove anything at all?
There is a direct relationship between the relative orientation of the polarizers and the knowledge of the which-slit. If the polarizers were oriented at 45 degrees, for example, there would be some interference and the possibility of some knowledge of the slit.

So we are saying that the wave function for a single photon describes something which is physically real (according to your interpretation of course), and that wave traverses both slits - not just one.
P: 55
 Quote by DrChinese There is a direct relationship between the relative orientation of the polarizers and the knowledge of the which-slit. If the polarizers were oriented at 45 degrees, for example, there would be some interference and the possibility of some knowledge of the slit. So we are saying that the wave function for a single photon describes something which is physically real (according to your interpretation of course), and that wave traverses both slits - not just one.
Yes, but it appears that knowledge of which slit is just an illusion caused by the experiment. The very act of distinguishing one slit from the other is what causes wave function collapse giving the impression that the particle behaves differently just because we are looking, implying some profound mystery. But, it is the very mechanism involved in looking that causes the wave to collapse, rather than just human awareness. There is no legitimate knowledge of which-way because the particle always traverses both slits until we ourselves screw with it. I believe I'm correct in this. The delayed erasure is still a mystery to me though. If we mess with the signal photon's cousin "idler" photon after the "signal" photon as already struck, then how can the fringes reappear?
P: 3,180
 Quote by marksesl Yes, but it appears that knowledge of which slit is just an illusion caused by the experiment. [..] The delayed erasure is still a mystery to me though. If we mess with the signal photon's cousin "idler" photon after the "signal" photon as already struck, then how can the fringes reappear?
It's a similar illusion caused by the way people describe the experiment. That was discussed here: www.physicsforums.com/showthread.php?t=402497
In particular starting from post #21

Mentor
P: 9,585
 Quote by marksesl The delayed erasure is still a mystery to me though. If we mess with the signal photon's cousin "idler" photon after the "signal" photon as already struck, then how can the fringes reappear?
The order of measurements does not matter - they can even be spacelike separated, so different reference frames will see different time-orderings of the measurements.
If you use collapse interpretations, you have to "wait" with the full collapse until the whole process is done.
P: 671
 Quote by The_Duck Yes. Interference occurs when there is a possibility to reach the same exact final state by each of two different paths. If you alter one of the paths so that that it no longer reaches the same final state, the interference goes away. I agree that this is a much simpler way of talking about it, and should probably be preferred to langauge that seems to attribute special properties to "measuring devices" or "knowledge." So why do people say that measuring "which path" information destroys the interference? The interference is destroyed because if you measure which path information, you change the paths so that they reach different final states. One final state is "electron hits the wall at x=5 and the detector reads 'left path,'" while the other final state is "electron hits the wall at x=5 and the detector reads 'right path.'" Since these final states are different, the two paths can't interfere. This sort of thing is going to happen no matter how you detect which path the electron took, so in general "which path" measuring devices destroy the interference pattern. This also makes it clear that it's not just deliberate measurements that destroy interference. If there's a single stray photon that scatters off the electron if it takes the right path, but not the left path, then this will lead to different final states: "electron hits the screen at x=5 and photon was scattered" vs "electron hits the screen at x=5 and photon was not scattered." So this single stray photon will destroy the interference pattern. Of course, you can think of the photon as performing a crude and accidental "measurement" of which path the electron took.
I think this is an accurate description of how it works. I too have a semantics problem with the "know which path" concept (the word "know" or "identify" has too many connotations). If anything happens that makes the final state from one path different from (orthogonol to) the other then the interference cannot occur. Only to the extent that the final states are identical can like mixed terms from the product cause reinforcement or cancellation.
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