Who is puzzled by the delayed choice?

[Demystifier]

Many physicists (especially experimentalists) seem puzzled by the delayed choice experiments (DCE), because, as they argue, such experiments seem to change the past.
Here I discuss DCE from the point of view of (not 1, not 2, not 3, but) 7 major interpretations of quantum mechanics: 4 variants of the Copenhagen interpretation (see https://www.physicsforums.com/showthread.php?t=332269 ), statistical ensemble interpretation, many-world interpretation and Bohmian interpretation. None of these interpretations suggests that (DCE) change the past. So why so many people are puzzled by DCE? Obviously, because none of these 7 major interpretations seems acceptable to them. Or more generally, because NONE of the existing consistent interpretations of QM seems acceptable to them.

1. Shut up and calculate: You can consistently calculate the probabilities for different measurement outcomes without asking anything about deeper meaning of the numbers you obtain. Clearly, without asking such questions there is no reason to suspect that experiments might change the past.

2. Positivistic interpretation: There is no reality (or it does not make sense to talk about reality) except the measured reality. So, if you don't measure the past (which you don't in DCE), there is no reason to say that experiments may change the past.

3. Collapse interpretation: The collapse of the wave function takes place at the instant of time at which you make the measurement. Thus, in DCE, the wave ALLWAYS goes through both slits, no matter what you do after that. But, depending on your actions after the wave passing through the slits, at the instant of measurement the wave may collapse to a new wave function which differs significantly from the the wave function before the collapse. It is a radical change of the wave function, but it does not affect the past of it.

4. Information interpretation: Wave function represents your knowledge about the system. This is knowledge that allows you to predict (with non-perfect certainty) the outcomes of FUTURE experiments. At the instant of measurement your knowledge of course changes (updates), which serves to predict the outcomes of new future experiments. This knowledge is never used to predict the outcomes of the PAST experiments, unless the past experiments have actually been done and their results are recorded. In this case, these predictions on past experiments are allways compatible with the recorded data, so there is no reason to say that experiments change the past.

5. Statistical ensemble interpretation: Quantum mechanics says nothing about individual particles, but only about statistical properties of large ensembles of particles of equally prepared systems. More precisely, it says something about statistical properties for the case when they are MEASURED. So, if you don't measure the properties in the past, then QM says nothing about them. Since it says nothing about them, then, in particular, it does not say that the past properties have changed.

6. Many-world interpretation: The wave allways goes through both slits. However, due to decoherence, at the instant of measurement (and at the position of the measurement apparatus) the wave splits into many non-communicating branches, which makes the illusion of collapse as in 3. This branching does not modify the wave function in the past.

7. Bohmian interpretation: The (pilot) wave splits as in 6. The particle takes one definite trajectory ending-up in one of the branches. During its motion, the particle does not change its past.

To conclude, I claim that anyone who argues that DCE affects the past must first explain why neither of the existing consistent interpretations of QM is not acceptable to him/her.

 

[DrChinese]

What, you didn't want to mention Relational Blockworld? That handles this case nicely too. I guess we could let RUTA give it in his words.

 

[GeorgCantor]

Many physicists (especially experimentalists) seem puzzled by the delayed choice experiments (DCE), because, as they argue, such experiments seem to change the past.
Here I discuss DCE from the point of view of (not 1, not 2, not 3, but) 7 major interpretations of quantum mechanics: 4 variants of the Copenhagen interpretation (see https://www.physicsforums.com/showthread.php?t=332269 ), statistical ensemble interpretation, many-world interpretation and Bohmian interpretation. None of these interpretations suggests that (DCE) change the past. So why so many people are puzzled by DCE? Obviously, because none of these 7 major interpretations seems acceptable to them. Or more generally, because NONE of the existing consistent interpretations of QM seems acceptable to them.

1. Shut up and calculate: You can consistently calculate the probabilities for different measurement outcomes without asking anything about deeper meaning of the numbers you obtain. Clearly, without asking such questions there is no reason to suspect that experiments might change the past.

2. Positivistic interpretation: There is no reality (or it does not make sense to talk about reality) except the measured reality. So, if you don't measure the past (which you don't in DCE), there is no reason to say that experiments may change the past.

3. Collapse interpretation: The collapse of the wave function takes place at the instant of time at which you make the measurement. Thus, in DCE, the wave ALLWAYS goes through both slits, no matter what you do after that. But, depending on your actions after the wave passing through the slits, at the instant of measurement the wave may collapse to a new wave function which differs significantly from the the wave function before the collapse. It is a radical change of the wave function, but it does not affect the past of it.

4. Information interpretation: Wave function represents your knowledge about the system. This is knowledge that allows you to predict (with non-perfect certainty) the outcomes of FUTURE experiments. At the instant of measurement your knowledge of course changes (updates), which serves to predict the outcomes of new future experiments. This knowledge is never used to predict the outcomes of the PAST experiments, unless the past experiments have actually been done and their results are recorded. In this case, these predictions on past experiments are allways compatible with the recorded data, so there is no reason to say that experiments change the past.

5. Statistical ensemble interpretation: Quantum mechanics says nothing about individual particles, but only about statistical properties of large ensembles of particles of equally prepared systems. More precisely, it says something about statistical properties for the case when they are MEASURED. So, if you don't measure the properties in the past, then QM says nothing about them. Since it says nothing about them, then, in particular, it does not say that the past properties have changed.

6. Many-world interpretation: The wave allways goes through both slits. However, due to decoherence, at the instant of measurement (and at the position of the measurement apparatus) the wave splits into many non-communicating branches, which makes the illusion of collapse as in 3. This branching does not modify the wave function in the past.

7. Bohmian interpretation: The (pilot) wave splits as in 6. The particle takes one definite trajectory ending-up in one of the branches. During its motion, the particle does not change its past.

To conclude, I claim that anyone who argues that DCE affects the past must first explain why neither of the existing consistent interpretations of QM is not acceptable to him/her.

Aren't these types of questions the very reason why time is thought to be not fundamental, but emergent in M-Theory?

http://discovermagazine.com/2007/jun/in-no-time



"The purpose of this talk is to review the case for the idea that space and
time will end up being emergent concepts; i.e. they will not be present in
the fundamental formulation of the theory and will appear as approximate
semiclassical notions in the macroscopic world. This point of view is widely
held in the string community and many of the points which we will stress
are well known.
Before we motivate the idea that spacetime should be emergent, we should
discuss the nature of space in string theory."


http://arxiv.org/PS_cache/hep-th/pdf/0601/0601234v1.pdf

Emergent Spacetime
Nathan Seiberg, Institute for Advanced Study, Princeton, NJ 08540 USA



Is anyone convinced that a reasonable conclusion on the DCE can be reached within the framework of the existing interpretations?

 

[Cthugha]

So why so many people are puzzled by DCE?

In my opinion most of these people are puzzled because they do not understand the difference between single-photon interference and two-photon interference. Mixing up the properties of these processes will produce strange interpretations of DCQE experiments - regardless of which interpretation of QM you prefer.

 

[Frame Dragger]

Whatever happened to "shut up and calculate"? When did this turn into "everyone gets their own ontology?"

 

[zonde]

5. Statistical ensemble interpretation: Quantum mechanics says nothing about individual particles, but only about statistical properties of large ensembles of particles of equally prepared systems. More precisely, it says something about statistical properties for the case when they are MEASURED. So, if you don't measure the properties in the past, then QM says nothing about them. Since it says nothing about them, then, in particular, it does not say that the past properties have changed.

I would like to add something to this explanation.
First, ensemble is really traveling all the paths in experimental setup. There can be no doubt about that even from classical perspective as long as we remember that result of experiment still depends from all subensembles of whole ensemble if we try to do some splitting.
Second, from perspective of ensemble there is hardly any past because what is past for some part of ensemble is present for other part and future for yet another part.

 

[Demystifier]

What, you didn't want to mention Relational Blockworld? That handles this case nicely too. I guess we could let RUTA give it in his words.

Well, I have mentioned 7 MAJOR interpretations, where "major" means "supported by the largest number of physicists" (and does not imply that they are better than other interpretations).

 

[Demystifier]

Aren't these types of questions the very reason why time is thought to be not fundamental, but emergent in M-Theory?

Not at all. The motivation for M-theory is entirely different.

 

[RUTA]

Is anyone convinced that a reasonable conclusion on the DCE can be reached within the framework of the existing interpretations?

The Relational Blockworld interpretation dispatches QM "mysteries," such as DCE and QLE, very simply. Essentially, RBW is a form of ontic structural realism that says QM provides a rule for the acausal, adynamical, 4D description of an experiment. For example, the wave function is neither dynamic nor "real" (has no ontic status), so the measurement problem is a non-starter.

Once you get past the belief that "explanation" has to entail a "dynamical story" about objects moving in (some) space as a function of time, i.e., accept the blockworld view per relativity, then you open the possibility for spacetime laws, e.g., Einstein's eqns of GR, that aren't even spatiotemporally local (nonseparable). Explanatory power is greatly improved once you decide not to constrain your explanations to "story telling."

"There is no dynamics within space-time itself: nothing ever moves therein; nothing happens; nothing changes. In particular, one does not think of particles as moving through space-time, or as following along their world-lines. Rather, particles are just in space-time, once and for all, and the world-line represents, all at once, the complete life history of the particle." Geroch, R., General Relativity from A to B, University of Chicago Press, Chicago, 1978, pp. 20-21.

 

[Demystifier]

Is anyone convinced that a reasonable conclusion on the DCE can be reached within the framework of the existing interpretations?

Yes. Me, for example.

 

[Demystifier]

For example, the wave function is neither dynamic nor "real" (has no ontic status), so the measurement problem is a non-starter.

What IS real (ontic) in RBW?

 

[RUTA]

What IS real (ontic) in RBW?

Any'thing' that can be modeled classically (X and P commute). No size restriction. However, 'things' are not made ultimately of ever smaller 'things', they're made of relations. And, when you model a phenomenon, you must do so in its 4D entirety. That's why the wave function models the experiment as a whole in both space and time (to include outcomes).

 

[Demystifier]

Any'thing' that can be modeled classically (X and P commute). No size restriction. However, 'things' are not made ultimately of ever smaller 'things', they're made of relations. And, when you model a phenomenon, you must do so in its 4D entirety. That's why the wave function models the experiment as a whole in both space and time (to include outcomes).

So it is essentially the Rovelli relational interpretation (which is a variant of the information interpretation, number 4. on my list). Is there any important difference between this interpretation and Rovelli interpretation?

 

[GeorgCantor]

Once you get past the belief that "explanation" has to entail a "dynamical story" about objects moving in (some) space as a function of time, i.e., accept the blockworld view per relativity, then you open the possibility for spacetime laws, e.g., Einstein's eqns of GR, that aren't even spatiotemporally local (nonseparable). Explanatory power is greatly improved once you decide not to constrain your explanations to "story telling."

"There is no dynamics within space-time itself: nothing ever moves therein; nothing happens; nothing changes. In particular, one does not think of particles as moving through space-time, or as following along their world-lines. Rather, particles are just in space-time, once and for all, and the world-line represents, all at once, the complete life history of the particle." Geroch, R., General Relativity from A to B, University of Chicago Press, Chicago, 1978, pp. 20-21.

A virtual world agrees with all the evidence but it seems to imply that all of our assumptions are wrong at the same time - realism, locality, causality, free-will, randomness. Or maybe you're not willing to go that far yet?

 

[RUTA]

So it is essentially the Rovelli relational interpretation (which is a variant of the information interpretation, number 4. on my list). Is there any important difference between this interpretation and Rovelli interpretation?

We agree with Rovelli (see van Fraassen's characterization of RQM: http://www.princeton.edu/~fraassen/abstract/Rovelli_sWorld-FIN.pdf) that there is no view from nowhere, i.e., there can't be an "external view" since any observer is always defined in the context of everything else. It's hard to say exactly where we differ with RQM because we can't find his axioms whence QM (he admits he doesn't have them in quant-ph/9609002 and I don't find them in van Fraassen). I have the distinct impression, however, that his "real quantum system" exists in addition to the pieces of equipment in the experiment, while there is no additional ontic structure in RBW. Certainly RBW is farther along since we have a way to recover quantum physics relationally (arXiv 0908.4348, we received word today that it is accepted for presentation at PSA 2010).

As regards quantum information theory, RBW provides an answer to the question "information about what?" When Fuchs says: "The quantum system represents something real and independent of us; the quantum state represents a collection of subjective degrees of belief about something to do with that system (even if only in connection with our experimental kicks to it). The structure called quantum mechanics is about the interplay of these two things -- the subjective and the objective." ( quant-ph/0205039, p. 5.) We would simply say the "quantum system" is the composition of the experimental equipment depicted in Figures 1-4 of the arXiv paper above.

 

[Demystifier]

Thanks, RUTA!

 

[RUTA]

A virtual world agrees with all the evidence but it seems to imply that all of our assumptions are wrong at the same time - realism, locality, causality, free-will, randomness. Or maybe you're not willing to go that far yet?

It's semantics I guess, but in RBW I would say "reality" is composed of classical objects, which are spatiotemporal geometric distributions over graphs (which aren't "real"), so "reality" isn't (ultimately) composed of "real" things. Maybe that's along the lines of your "virtual world?" RBW's philosopher of science would probably complain about my posting this, he would have a much better response :-)

 

[Demystifier]

Niels Bohr said:
"If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet."

To answer the question posed in the title of this thread, I would add:
"If delayed choice quantum eraser shocked you more than the rest of quantum mechanics, you haven't understood the rest of quantum mechanics yet."

 

[San K]

Yes. Me, for example.

Ok, what would the conclusion be?...:)

 

[Demystifier]

Ok, what would the conclusion be?...:)

See the first post on this thread.

 

[Demystifier]

I believe now I finally understood the reason why so many physicists are puzzled by the delayed choice. Let me share it with you.

The origin is in the fact that such experiments are closely related to the so-called "WHICH WAY" experiments. The name of such experiments suggests that they really measure the way along which the particle travels. So, naive physicists are inclined to think that the particle chooses only one path (through only one of the slits) in these experiments, and therefore that there cannot be any interference effect. From that, it is easy to get a paradox and conclude that there must be a change-of-the-past involved.

But this, of course, is wrong. The so-called "which way" experiments do NOT really measure the way along which the particle travels. Indeed, these experiments only measure the FINAL particle position at the detector, from which the rest of the particle's "path" is RECONSTRUCTED, rather then really measured. Moreover, this reconstruction is based on a naive classical reasoning about motion of particles, so validity of this reconstruction is very dubious. Actually, it is more than dubious - it is completely unjustified. Indeed, neither of the 7 major interpretations analyzed in post #1 justifies the assertion that these "measured paths" represent the actual paths and that there is nothing traveling along the other paths. Just the opposite, all these interpretations agree that there is a wave function traveling through BOTH slits (even though they disagree on what this wave function actually is), which is ultimately why the interference is possible.

To conclude, the "which way" experiments are not really which way experiments. Those who understand it should not be puzzled by the delayed choice experiments. And those who are puzzled by the delayed choice experiments must be thinking (incorrectly, of course) that the "which way" experiments really ARE which way experiments. But they are not. They are just misleadingly called so.

 

[StandardsGuy]

Number 1 is clearly nonsense. Number 2 has an opinon (is biased). None of them clearly disproves Fred Alan Wolf in his book "Star Wave - Mind, Consciousness, and Quantum Physics" where he talks about the quasar light being bent by gravity, and given two paths. It seems we have three opinions of physicists: (1) the past does not get changed, (2) it does get changed, and (3) there is no past to change, so forget what you saw [you idiot]. Do any of you have any data showing the number of physicists who prescribe to each of the 7 interpretations?

 

[DylanLou]

Just the opposite, all these interpretations agree that there is a wave function traveling through BOTH slits (even though they disagree on what this wave function actually is), which is ultimately why the interference is possible.

Hi,

but, as you said, if we have a wavefunction passing through two slits we should have an interference pattern. Therefore, how is that possible that when we put a measuring device (wheter it is possible or not to effectively measure the which way information) this interference will not show up?

 

[Demystifier]

Hi,

but, as you said, if we have a wavefunction passing through two slits we should have an interference pattern. Therefore, how is that possible that when we put a measuring device (wheter it is possible or not to effectively measure the which way information) this interference will not show up?

The presence of the measuring device changes the wave function, including its interference properties.

More technically, the system traveling through the slits becomes entangled with the device, so the traveling system cannot longer be described by a coherent wave function. Instead, it is described by a mixed density matrix, which lacks information about relative phases and hence does not exhibit interference.

 

[StandardsGuy]

The presence of the measuring device changes the wave function, including its interference properties.

You seem to be talking about the original double slit experiment. A later one put the detectors farther 'down stream' where they couldn't possibly do that (that's why it's called delayed choice) and the result was the same. I see no way of separating this from human consciousness of expectation.

 

[Demystifier]

You seem to be talking about the original double slit experiment. A later one put the detectors farther 'down stream' where they couldn't possibly do that

Why not? The wave function is present even there.

(that's why it's called delayed choice)

It is called delayed because it happens after the wave traveled through the slits. But wave can be influenced at any place where wave is present, not only at the slits.

I see no way of separating this from human consciousness of expectation.

Then my post #18 refers to you as well.

 

[StandardsGuy]

Why not? The wave function is present even there.

This requires that some function goes back in time to change the photons at the slits. Going back in time is fully allowed by the mathematics of quantum theory. Richard Feynman even suggested it. Why do you and so many others find it so shocking?

 

[Ken G]

What I don't understand is why anyone sees anything that involves changing the past in DCQE. Exactly what is supposed to be getting "changed"? All I see is an experiment where if you correlate outputs using a different apparatus, you get different types of correlations. What has that got to do with the past?

To me, what DCQE tells us is that we were wrong to imagine that a pattern that was not a two-slit interference pattern does not contain anywhere in it two-slit interference. The DCQE shows us that even in a pattern that we don't see the two-slit interference still has two-slit interference in it, but the two-slit interference is not apparent because it has been offset, losing coherence, by whatever details of the apparatus are allowing "which way" information. Change the apparatus, change the information you have available. What else is new?

To see that the two-slit interference is actually there, but not apparent, we simply need to erase the which-way information and do the appropriate correlations. Poof-- a non-interference pattern is seen to actually be two two-slit patterns that are offset to cover the tracks of the two-slit interferences.

So we have two completely different ways of interpreting a non-two-slit-interference pattern-- we can say there was no interference there because "which way" information exists, or we can say that there was two-slit interference there but the presence of which-way information requires that the multiple sources of two-slit interferences must destructively interfere to be consistent with the which-way information. When we can take two equivalent approaches, we must recognize that nature leaves the issue indeterminate. There is no such thing as the "actual" interference that occurs, it all depends on how we conceptualize the interference. This is routine in all kinds of physics, not just quantum mechanics-- when there are many ways to skin a cat, we should not imagine the cat is "actually" skinned in anyone particular way.

So this all seems to me much like standard complementarity in quantum mechanics-- there is only so much information available, so to know one thing forces us to lose track of something else. Here, to know "which way" forces us to lose the information in the two-slit interferences, or we can erase the "which way" and recover the two-slit interference information. It's the same if we erase knowledge of position and thereby recover knowledge of momentum.

Moreove, the "delayed" aspect, and the "changing the past", seem like complete red herrings to me-- all we are doing with respect to time is making different measurements that we are going to correlate, what difference does it make when those measurements were made? The information appears at the moment when the correlations are made, and no information about the correlations even exists prior to comparing the data, regardless of when the data was taken. And the idea that this somehow violates relativity seems to me to be the worst error of all-- it's just the opposite, relativity tells us above all that physics is not global, it is local, and so we should never imagine that a correlation between two datasets exists anywhere except in places where both those datasets are present.

 

[Demystifier]

This requires that some function goes back in time to change the photons at the slits.

What do you mean by "photons", if not the wave function itself? The only consistent way (I am aware of) of talking about photons different from waves is in terms of Bohmian interpretation. But I have explained in the first post that this interpretation (number 7) does not involve any change back in time.

 

[Demystifier]

What I don't understand is why anyone sees anything that involves changing the past in DCQE. Exactly what is supposed to be getting "changed"? All I see is an experiment where if you correlate outputs using a different apparatus, you get different types of correlations. What has that got to do with the past?

To me, what DCQE tells us is that we were wrong to imagine that a pattern that was not a two-slit interference pattern does not contain anywhere in it two-slit interference. The DCQE shows us that even in a pattern that we don't see the two-slit interference still has two-slit interference in it, but the two-slit interference is not apparent because it has been offset, losing coherence, by whatever details of the apparatus are allowing "which way" information. Change the apparatus, change the information you have available. What else is new?

To see that the two-slit interference is actually there, but not apparent, we simply need to erase the which-way information and do the appropriate correlations. Poof-- a non-interference pattern is seen to actually be two two-slit patterns that are offset to cover the tracks of the two-slit interferences.

So we have two completely different ways of interpreting a non-two-slit-interference pattern-- we can say there was no interference there because "which way" information exists, or we can say that there was two-slit interference there but the presence of which-way information requires that the multiple sources of two-slit interferences must destructively interfere to be consistent with the which-way information. When we can take two equivalent approaches, we must recognize that nature leaves the issue indeterminate. There is no such thing as the "actual" interference that occurs, it all depends on how we conceptualize the interference. This is routine in all kinds of physics, not just quantum mechanics-- when there are many ways to skin a cat, we should not imagine the cat is "actually" skinned in anyone particular way.

So this all seems to me much like standard complementarity in quantum mechanics-- there is only so much information available, so to know one thing forces us to lose track of something else. Here, to know "which way" forces us to lose the information in the two-slit interferences, or we can erase the "which way" and recover the two-slit interference information. It's the same if we erase knowledge of position and thereby recover knowledge of momentum.

Moreove, the "delayed" aspect, and the "changing the past", seem like complete red herrings to me-- all we are doing with respect to time is making different measurements that we are going to correlate, what difference does it make when those measurements were made? The information appears at the moment when the correlations are made, and no information about the correlations even exists prior to comparing the data, regardless of when the data was taken. And the idea that this somehow violates relativity seems to me to be the worst error of all-- it's just the opposite, relativity tells us above all that physics is not global, it is local, and so we should never imagine that a correlation between two datasets exists anywhere except in places where both those datasets are present.

This, more or less, is what I am saying too, especially in the first post of this thread.

 

[Ken G]

Yes, I think we very much agree, our ways of describing it are merely affected by our various perspectives and perhaps different ways of saying it might resonate with different readers, or stimulate different objections to our stance. I'm sure you cringe just as much as I do when you read a lot of what is said about DCQE (like photons that were originally determined to go through only one slit being told by some choice in a later experiment to go back in time and split and go through both slits instead, or some other such highly forced and awkward interpretation), so I think this was a good thread for you to start!

I also think you made a good point in the OP in regard to the interpretations. It seems like people go to great lengths to settle on one or other self-consistent interpretation, but all of a sudden when DCQE comes up, they toss out their favored interpretation and immediately resort to pseudo-classical kinds of language that would never even stand up to their own favored interpretation! Or, we get popularized articles that feel no need to adopt any standard interpretation, because those "weren't meant for DCQE" or some such thing. This abandoning of interpretations will always lead to paradoxical sounding results, the same thing happens with that darned cat!

 

[StandardsGuy]

...what is said about DCQE (like photons that were originally determined to go through only one slit being told by some choice in a later experiment to go back in time and split and go through both slits instead, or some other such highly forced and awkward interpretation),

You just answered your own question of post 28. As I see it, any interpretation is as awkward as any other. You may have made a good point in #28, though. Are you saying that the observation of the interference pattern (the wave) or the scatter pattern (the particle) is just the Heisenberg Uncertainty principle at work?

 

[StandardsGuy]

What do you mean by "photons", if not the wave function itself? The only consistent way (I am aware of) of talking about photons different from waves is in terms of Bohmian interpretation. But I have explained in the first post that this interpretation (number 7) does not involve any change back in time.

I mean, by my understanding of this interpretation, that the wave (of the past) taking two paths, has changed into particles taking one path. You seem to not understand that a delay means that time has passed in which the wave has already traveled some distance. Or do you think the wave is everywhere at once?

I know nothing about the Bohmian interpretation except what you posted. So it seems there is still a wave through each slit which both have to collapse, but only one particle materializes. Can you explain why that happens only when people are looking for particles?

 

[Ken G]

You just answered your own question of post 28. As I see it, any interpretation is as awkward as any other. You may have made a good point in #28, though. Are you saying that the observation of the interference pattern (the wave) or the scatter pattern (the particle) is just the Heisenberg Uncertainty principle at work?

I believe the analogy has merit, yes. But mostly what I'm saying is that the presence of interference, or what kind of interference is present, is not a physically demonstrable fact. The same pattern, or absence of pattern, can be interpreted in many ways, some involving various types of interference between the slits, others not involving any interference between the slits. Let me give you a clear example-- put a linear polarizer in each slit, with a 90 degree relative rotation. You don't get a two-slit pattern on the wall, because you have which-way information. You can say that the reason you don't get a two-slit pattern is that the orthogonal polarizations don't interfere, but is it an objective fact that no interference is occurring? No, it isn't-- each linear polarization can be thought of as a superposition of opposite circular polarizations. But each of those circular polarizations, by themselves, certainly do interfere with the same circular polarization coming from the other slit! Analyzed this way, the linear polarizers do indeed undergo two-slit interference, but it isn't apparent in the final pattern because the different interferences end up being incoherent with each other and don't result in a pattern (sound like the two correlated DCQE signals?).

And, to complete the analogy, we can recover the two-slit pattern by "erasing" the which-way information, by inserting a polarizer at 45 degrees to both of the polarizers in the slits, before the photons reach the detecting wall. Now some of the interference that was always there but wasn't showing up on the wall is allowed to show up on the wall, and the two-slit pattern appears, even though there are polarizers in the slits that, with a different setup, would provide "which way" information. This is true even if the 45 degree polarizers are a light year from the slits, and were put in place long after the light passed through the slits. The morals of the story:
1) the apparatus as a whole determines the outcome, not pieces of the apparatus, and it makes no difference at what time the elements of the apparatus were placed there, and
2) what interference does or does not happen is a function of our analysis, not the apparatuses. Any description that gets the answer right is just as valid a way to talk about what "really happened" as any other.

 

[Demystifier]

I mean, by my understanding of this interpretation, that the wave (of the past) taking two paths, has changed into particles taking one path.

I think that such interpretation of QM does not make sense.

I know nothing about the Bohmian interpretation except what you posted. So it seems there is still a wave through each slit ...

Correct.

... which both have to collapse,

Not correct. In Bohmian interpretation wave function never really collapses. It only splits into separate branches that do not know about each other.

but only one particle materializes.

Not correct. There is only one particle which takes only one path, but the particle does not "materialize". Instead, it exists all the time, irrespective of the wave function. The purpose of the wave is only to guide the MOTION of the particle, not to create the particle.

Can you explain why that happens only when people are looking for particles?

People are irrelevant. What is relevant is the measuring apparatus. The wave function that guides the particle interacts with the wave function that guides the apparatus-particles. This interaction changes the particle-guiding wave function, which affects the particle trajectory AFTER the interaction.

For more details about the Bohmian interpretation, see e.g.
http://xxx.lanl.gov/abs/quant-ph/0611032