What Would Happen If We Set Up the Double Slit Experiment Differently?

[Fiziqs]

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.

 

[vanhees71]

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.

 

[mfb]

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.

 

[Fiziqs]

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.

 

[mfb]

The detectors interact with the wave function "in some way" (enough to cause decoherence, i.e. a phase shift which cannot be predicted).

 

[Fiziqs]

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?

 

[mfb]

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.

 

[marksesl]

"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?

 

[The_Duck]

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 language 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.

 

[DrChinese]

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.

 

[marksesl]

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?

 

[harrylin]

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

See also links to similar discussions at the bottom of that page.

 

[mfb]

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.

 

[meBigGuy]

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 language 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.

 

[DrChinese]

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?

The truth is that these are alternative ways to describe the same thing. It is true that orthogonal states do not interfere. If you then accept that the superposition consists of many states (when interference is seen), you have accepted the standard interpretation. If you insist there is no superposition ever (there is only a single unknown state), then your description does not work.

So the upshot is: if you accept the conventional interpretation and join the scientific consensus, and you can call it whatever you want. Even an "illusion".

 

[stewart brands]

On what evidence,or why,does everyone assume that the photon leaves the source? Why does everyone assume that the photon is an autonomous entity before it entangles with the destination?

If people use the double slit experiment to prove for themselves that the photon is in 2 places,why then are they comfortable with having the photo a SEPERATE! entity from the source?

 

[stewart brands]

Could the photon not be a long quivering filament of energy attached to the source,only becoming a particle when entanglement occurs?It would be this filament that passes through the slit,and not the entire photon(until it hits the screen(entanglement)?

 

[mfb]

You can know that a photon left the source (with a proper single-photon source), close the source, and only then let your photon go through the double slit. That does not change anything, and I don't see the relevance for the double slit experiment.

 

[DrChinese]

Could the photon not be a long quivering filament of energy attached to the source,only becoming a particle when entanglement occurs?It would be this filament that passes through the slit,and not the entire photon(until it hits the screen(entanglement)?

If so, your "filament" would need to pass through *both* slits to allow for the interference.

Most people think of the thing you call "filament" as one possible path. And then (possibly infinitely) many of those form the particle wave function which evolves from source to a target (and the various paths can interfere). Various targets have various probabilities of occurrence. One of those is randomly selected (no one can say how) and that is what is detected. This explains the results and is consistent with known experiments.

 

[vanhees71]

Again, the whole trouble is the wrong idea of photons as a kind of particle. It's not! It's a single-photon Fock state! A photon doesn't even have a position observable in the strict sense and picturing it as a "minature billard ball" is even more wrong than such a picture for massive elementary "particles". I prefer the word "quanta" to make very clear that one is dealing with entities that in general cannot neither be described as "classical particles" nor "classical fields".

If you have a setup ("preparation"), where you observe interference effects as in the double-slit experiment you have a situation, where for sure a particle description is inadequate. It's closer to a wave/field description. However, if you really deal with single-photon states (which are not easy to prepare, by the way, it's not enough to simply dim down a classical light source or even a laser as is unfortunately also claimed in some popular texts), also the classical-field description is not entirely correct.

The quantum-theoretical state just gives the detection probabilities for photons behind the double slit. Sending many equally prepared single-photons through this setup you get an interference pattern that looks like the intensity pattern of classical electromagnetic waves going through the double slit. This interpretation of the quantum state makes the idea of "wave-particle duality" of the "old quantum mechanics" consistent, and it's the only way known today to get this consistency! Thus one should not stick to the old-fashioned picture of "old quantum theory" which has been obsolete since the discovery of "modern quantum theory" by Heisenberg, Jordan, Born and Schrödinger, and Dirac!

 

[stewart brands]

"If so, your "filament" would need to pass through *both* slits to allow for the interference."

Granted that comes from the pattern created. So the question is do the possible paths(vibrating filament) pass the slits simultaneously or is there perhaps an oscillation at the slits of this filament(causing the wave pattern). The distance"in time" between the slits would be immeasurably short given the tiny filament oscillations also have c in addition to vector path c to the destination.
Certainly the number of paths is infinite,but considering we are discussing a loci around the slits, is this infinity set not then constrained to this area and therefore calculable?

But my first question is, does the community see the photon as a distinct entity, separate from the source and why?

 

[stewart brands]

Not to belabour the point too much,however, every explanation of the interference pattern assumes that the light wave/particle is distinct from the source. As far as I can see this distinctness from the source is an assumption.Not even an hypothesis. Where is the hard evidence that the source ceases to be a factor in the slit paradox? Where is the evidence that the source and destination are not connected for an immeasurably short time?

 

[marksesl]

The truth is that these are alternative ways to describe the same thing. It is true that orthogonal states do not interfere. If you then accept that the superposition consists of many states (when interference is seen), you have accepted the standard interpretation. If you insist there is no superposition ever (there is only a single unknown state), then your description does not work.

So the upshot is: if you accept the conventional interpretation and join the scientific consensus, and you can call it whatever you want. Even an "illusion".

I agree. In order for this experiment to even make any since, one must assume there is no such thing as the probability wave, and that a photon can only enter one or the other slit, so in that case it is the fringe pattern that must be a type of illusion.

One or the other is an illusion though. It seems so self-evident that a single photon can traverse both slits though, that finding the photon to have gone through only one slit is where the illusion lies.

The experiment just seems fundamentally flawed. There is no way to test to see if the photon goes through both slits because if it does the polarizing filters are bound to cancel the interference. The very act of determining which way the photon went precludes any other alternative than it only went through one slit, and must just assume the fuzziness of the photon is something that just can't be explained.

 

[stewart brands]

Is it not possible that the photon is a filament of oscillating energy from the source to its destination? Is it not possible that the oscillation of this filament of energy(at c "speed") would enter each slit at different times and subsequently interfere with itself. The distance between the slits is tiny,but the velocity huge therefore any time differences could not be measured. The time to transverse a mm at c for instance.
Is it not the case that the photon passing both slits simultaneously is an assumption in disregard other possible realities, designed to prove a theory?
Perhaps the appearance of an interference pattern does not prove that the photon did go through both slits but is used to prove the hypotheses that it did.
The assumption that the photon is distinct at time t from the source is also ,it would appear,to be an unfounded assumption.
I am unaware of any experiment whereby a single photon is contained. Perhaps a photon cannot be distinct because it is attached to the source until it entangles. Hence the proposal of a stretched out vibration"filament" of huge period relative to the collapsing wavelength("colour")

 

[DrChinese]

Where is the evidence that the source and destination are not connected for an immeasurably short time?

The "immeasurably short time" part doesn't make any sense to me. Light moves at c. You can construct experiments to demonstrate it is

On the other hand, the normal interpretation is that an excitation of the EM field flows from source to target. So you could say there is a connection. However, that "connection" is usually called a "photon".

 

[stewart brands]

The immeasurably short time refers to the time it would take for this "filament still attached to the source" to enter one slit and then the other.In other words say a mm at c

 

[DrChinese]

One or the other is an illusion though. It seems so self-evident that a single photon can traverse both slits though, that finding the photon to have gone through only one slit is where the illusion lies.

The experiment just seems fundamentally flawed. There is no way to test to see if the photon goes through both slits because if it does the polarizing filters are bound to cancel the interference. The very act of determining which way the photon went precludes any other alternative than it only went through one slit, and must just assume the fuzziness of the photon is something that just can't be explained.

As mentioned, if you start with the idea that the photon is a wave: then interference makes perfect sense. But that same photon is quantized and appears at a single point only, giving it particle-like properties. So there are elements of both.

Your reasoning is circular about the importance of the experiment though. You can see that the behavior is fundamentally different when you cannot determine which of 2 slits the light traverses. Such matches the classical view of light as a wave, and what you make of that is up to you. I appreciate that all of this is "self-evident" to you but that is hardly the case for most. For example, the classical view of light as a wave is strictly ruled out in this experiment:

http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf

Not so obvious.

 

[DrChinese]

The immeasurably short time refers to the time it would take for this "filament still attached to the source" to enter one slit and then the other.In other words say a mm at c

Light travels about a foot in a nanosecond. For modern high speed detectors, it is possible to distinguish distances (differences in arrival times) of much smaller than this.

But again, I am not really sure of your point. Since all possible paths contribute to the observed pattern and related intensities (probability amplitudes), the filament idea doesn't really address this. That's because the filament now must have something like polarization in order to match experiment. Which is what a photon is, so why not just call it a photon like everyone else?

 

[DennisN]

Even though The Duck mentioned it in post #9, I'd like to jump in and point out that interference can be observed with massive particles too, e.g. electrons and even objects as large as C-60 (bucky-balls), see e.g.

• Double-slit experiment (Hitachi)
  
• An Experiment on Electron Interference (O. Donati, G. P. Missiroli, and G. Pozzi, 1973)
  
• The Merli–Missiroli–Pozzi Two-Slit Electron-Interference Experiment (article by Rodolfo Rosa, 2012)
  
• http://www.univie.ac.at/qfp/research/matterwave/c60/ (University of Vienna)
  
• Wave-particle duality of C60

 

[stewart brands]

I ponder the filament idea because of the assumption that a photon is a distinct entity in space with a beginning and an end separate from source and entanglement. The contrary would indicate connection to the source until entanglement,thereby indicating a physical connection. This would lead to different interpretations of the experiment with 2 slits would it not?
My point is that when anyone discusses the slit experiment,the apparent assumption is that the source is no longer a factor when the light traverses the slit. I am simply wondering if this is a proper assumption and what is the experimental evidence that it is true.

 

[mfb]

stewart brands: Did you see my previous post? You can block, or even destroy the photon source if you like, before you do the double slit experiment. It does not matter.

 

[DrChinese]

I ponder the filament idea because...

Your filament is a photon. What you are asking is whether photons have (or not) existence independent of the source and detector. This has nothing to do whatsoever with the double slit experiment. As previously mentioned by several others, you can get interference from things other than photons.

Your speculative idea (which is not really appropriate) calls for the photon to act the same as usual, but there is also this previously unknown connection too. As mfb says, this cannot be something which in any ways is detectible. Ergo it is excess baggage.

 

[marksesl]

Is it not possible that the photon is a filament of oscillating energy from the source to its destination? Is it not possible that the oscillation of this filament of energy(at c "speed") would enter each slit at different times and subsequently interfere with itself. The distance between the slits is tiny,but the velocity huge therefore any time differences could not be measured. The time to transverse a mm at c for instance.
Is it not the case that the photon passing both slits simultaneously is an assumption in disregard other possible realities, designed to prove a theory?
Perhaps the appearance of an interference pattern does not prove that the photon did go through both slits but is used to prove the hypotheses that it did.
The assumption that the photon is distinct at time t from the source is also ,it would appear,to be an unfounded assumption.
I am unaware of any experiment whereby a single photon is contained. Perhaps a photon cannot be distinct because it is attached to the source until it entangles. Hence the proposal of a stretched out vibration"filament" of huge period relative to the collapsing wavelength("colour")

We know from the De Broglie equation that all particles should and do have a wave property. So, why should we need some special explanation for how a photon can manage to get through both slits at the same time? Even electrons and some molecules exhibit the same behavior. The maxima of the various particles tested correspond to their mass with the frequency going up and the fringes getting closer. It's case closed, small particles do go through both slits simultaneously, by virtue of their wave ccharacteristics.

 

[welcomeblack]

For my explanation, you need to know some elementary QM. The probability to go from initial state to final state is the probability amplitude squared. This probability amplitude is denoted <f|i>, so P(i→f)=|<f|i>|². The total probability amplitude is the sum of all indistinguishable paths between final state and intial state. If the paths are distinguishable, then it is the probabilities that are summed. Now, let's set up the double slit in the following way:

Let |i> represent the initial state at the source, and |f> represent the state at the detector. We denote the particle passing through slit one by the state |1>, and the particle passing through slit two by |2>.

The probability amplitude for the particle to be emitted by the source and to go through slit one is <1|i>. The probability amplitude for the particle to travel from slit one to the detector is <f|1>. Thus the probability amplitude for the particle to travel from the source, through slit to, then to the detector, is <f|1><1|i>. The same goes for slit two, just replace |1> with |2>.

With no way of telling the difference between the particle passing through slit one or two, the probability amplitude is <f|i>=<f|1><1|i>+<f|2><2|i>=A₁+A₂. Then the probability to go from source to detector is P(i→f)=|A₁+A₂|²=A₁²+A₂²+A₁A₂cos(Δψ), where Δψ is the relative phase between the two amplitudes. The last term, A₁A₂cos(Δψ), is the interference term.

Now, if you put some particle detection mechanism at slit one, you CAN distinguish between the two paths from intial state to final state. The means that we may no longer add probability amplitudes, but must rather add the probabilies, just like in classical mechanics. Explicitly then, P(i→f)=P(i→1→f)+P(i→2→f)=|<f|1><1|i>|²+|<f|2><2|i>|²=A₁²+A₂². No interference term. All because you can distinguish the path.

That's the formal/mathematical explanation. The physical explanation is given elsewhere in this thread.

 

[marksesl]

With no way of telling the difference between the particle passing through slit one or two, the probability amplitude is <f|i>=<f|1><1|i>+<f|2><2|i>=A₁+A₂. ..
Now, if you put some particle detection mechanism at slit one, you CAN distinguish between the two paths from intial state to final state.

That's all fine and well and very interesting, but very misleading, i.e., "With no way of telling the difference," vs. ".. you can distinguish between the two paths ... ." Surely it is the very act of placing the detector that causes decoherence and wave-function collapse. We can only know of what we caused ourselves.