Exploring Photon Trajectories in Double Slit Experiments

SpectraCat
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In the aftermath of the recent Steinberg paper where they reconstruct average photon trajectories in the double-slit experiment, it has been pointed out several times that the reconstructed average trajectories strongly resemble the single-photon trajectories predicted by Bohmina mechanics. Indeed, the authors themselves mention this point explicitly in the paper, but are careful to say that the reconstructions in their work are interpretation-independent.

Having looked again at the 2001 paper where the Bohmian trajectories for photons in the double slit experiment are calculated (http://arxiv.org/abs/quant-ph/0102071), I found the most striking thing to be that the trajectories appear to never cross the dividing line between the slits. That would seem to mean that the left hand side of the interference pattern arises ONLY from photons passing through the left hand slit, and vice versa for the right hand side of the pattern. But then how can we reconcile this with the usual explanation of the double slit, which says that having "which-path" information about the photons should destroy the interference pattern?

Sorry if this question has been asked before (I guess I am not the first to be confused by this), but it didn't come up in a quick search through the threads, and it seemed relevant in light of the discussion of the latest double-slit experiment with weak-measurements.
 
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SpectraCat said:
the trajectories appear to never cross the dividing line between the slits. That would seem to mean that the left hand side of the interference pattern arises ONLY from photons passing through the left hand slit,
No, it doesn't mean that. You seem to be forgeting that, in Bohmian mechanics, particles are not the only entities that pass through the slits.
 
Demystifier said:
No, it doesn't mean that. You seem to be forgeting that, in Bohmian mechanics, particles are not the only entities that pass through the slits.

No, I wasn't forgetting ... I just wasn't aware that the pilot wave had equivalent "reality" to the particles in BM. So it's ok for us to know that if a particle hits a particular spot on the screen, we can map it back to having come through a particular spot in one of the slits, because the pilot wave went through both slits? I thought there was a "random quantum potential" in BM which was responsible for the observed probabilistic results in experiments ... how does that factor into this experiment? Does it just give the particles a "kick" as they pass through the slits, so you cannot predict the trajectories ahead of time?

Perhaps my question is clearer in the context of the quantum eraser experiment. In the standard interpretation, the particles are "polarization tagged" so that you can tell which one went through each slit, but then the "eraser" removes the "which path" information, restoring the interference pattern. However if you always know "which path" the particles traveled through in BM, how does the "polarization tagging" destroy the interference pattern, and how does the "eraser" restore it?

@Demystifyer .. I completely understand if you don't want to type up full answers to this .. lord knows you've probably done it 20 times already. If you can just give me a link to one of your previous explanations, or to a web resource, that would be fine. I have searched myself without success. Also, I hope it is clear that the tone of this thread is intended to be "I don't understand yet", rather than "I don't think BM is correct".
 
SpectraCat said:
So it's ok for us to know that if a particle hits a particular spot on the screen, we can map it back to having come through a particular spot in one of the slits, because the pilot wave went through both slits?
Yes.

SpectraCat said:
I thought there was a "random quantum potential" in BM which was responsible for the observed probabilistic results in experiments ...
No. There is nothing random in BM. Randomness is an illusion, resulting from our ignorance of the initial particle position.

SpectraCat said:
Does it just give the particles a "kick" as they pass through the slits, so you cannot predict the trajectories ahead of time?
No. The slit has a finite width, so particles may have different positions when they pass through the slit. If you don't know what that position is, you can only tell what is a probability for a given position.

SpectraCat said:
However if you always know "which path" the particles traveled through in BM ...
But you don't know that, because you don't know the initial position.

SpectraCat said:
Also, I hope it is clear that the tone of this thread is intended to be "I don't understand yet", rather than "I don't think BM is correct".
Is it anything clearer now?
 
Demystifier said:
Yes.


No. There is nothing random in BM. Randomness is an illusion, resulting from our ignorance of the initial particle position.

Fair enough .. I guess should have said "unknowable initial conditions" that give the illusion of randomness ... that is what I was trying to get across.

No. The slit has a finite width, so particles may have different positions when they pass through the slit. If you don't know what that position is, you can only tell what is a probability for a given position.

But you don't know that, because you don't know the initial position.

But I am not talking about *before* the experiment .. I am talking about after it. Above you seemed to agree that once you know a particle has hit the screen at a particular spot, you could follow exactly one trajectory back to the place on exactly one of the slits where that particle "originated" (treating the slit as the source). What I still don't understand is why that doesn't constitute "which path" information in the context of the double slit, where having such information makes observing the interference pattern impossible. Is the importance of such "which path" information somehow just an artifact of the CI?

It seems that in the Bohmian picture, we end up with a lot more information than in the CI picture ... we know which slit a particle passed through, and we know that the pilot wave passed through both slits. In the CI picture, we know that the wavefunction passed through both slits, but we cannot say anything about the particle-like properties of that event. What I don't understand is why it is not possible to use the extra information from BM to design an experiment to distinguish between the two interpretations.

Is it anything clearer now?

Not yet .. but perhaps starting to converge ... :wink:
 
SpectraCat said:
No, I wasn't forgetting ... I just wasn't aware that the pilot wave had equivalent "reality" to the particles in BM. So it's ok for us to know that if a particle hits a particular spot on the screen, we can map it back to having come through a particular spot in one of the slits, because the pilot wave went through both slits? I thought there was a "random quantum potential" in BM which was responsible for the observed probabilistic results in experiments ... how does that factor into this experiment? Does it just give the particles a "kick" as they pass through the slits, so you cannot predict the trajectories ahead of time?

Perhaps my question is clearer in the context of the quantum eraser experiment. In the standard interpretation, the particles are "polarization tagged" so that you can tell which one went through each slit, but then the "eraser" removes the "which path" information, restoring the interference pattern. However if you always know "which path" the particles traveled through in BM, how does the "polarization tagging" destroy the interference pattern, and how does the "eraser" restore it?

@Demystifyer .. I completely understand if you don't want to type up full answers to this .. lord knows you've probably done it 20 times already. If you can just give me a link to one of your previous explanations, or to a web resource, that would be fine. I have searched myself without success. Also, I hope it is clear that the tone of this thread is intended to be "I don't understand yet", rather than "I don't think BM is correct".

Bohmian interpretation is a set of assumptions. One might agree with some and disagree with others and you could have an new interpretation that still works/explains.For example:

1. particle and wave both happen (particle goes through one of the slits and wave through both)

2. the process is deterministic - there is no connect with 1, it's simply an assumption. one might as well assume that the process is random. The interpretation would still work.

3. there is a pilot wave. even if you assume it's not there, experiments (such as DCQE) are still explainable by sub-samples/coherence.

The wave equations would still (probabilistic) predict the position of the photon/electron, while allowing for the randomness.
 
SpectraCat said:
Above you seemed to agree that once you know a particle has hit the screen at a particular spot, you could follow exactly one trajectory back to the place on exactly one of the slits where that particle "originated" (treating the slit as the source).
You could do that if you also knew the wave function of the system. But the interaction with the screen modified the wave function in a complicated way which in practice you cannot know exactly (this effect is better known under the name of decoherence), so you cannot really follow the trajectory back.

SpectraCat said:
Is the importance of such "which path" information somehow just an artifact of the CI?
It is an artifact of a weird interpretation, but not really of the Copenhagen one.
SpectraCat said:
What I don't understand is why it is not possible to use the extra information from BM to design an experiment to distinguish between the two interpretations.
Because any experiment involves decoherence, which for all practical purposes destroys information as I explained above.

More generally, decoherence seems to wash out measurable differences between all interpretations.
 
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Could this experiment be done using entangled particles? If so, would decoherence still occur?
 
What gets me about those trajectories is I think they are being completely oversold. It's not at all clear what an "average trajectory" really is, when you put together all those subtle "weak measurements", but it seems to me that the output they publish in their figure could be obtained much more easily, and it would be much clearer what they are actually seeing.

So let me ask this. Can anyone argue that I would not get the exact same figure the following way: I set up their exact apparatus, but I put my detecting wall at various different distances, repeating over and over until I map out not just a 1D detection-rate function, but a full 2D detection-rate field. The field is of course normalized to represent a divergence-free photon flux. Then I simply draw the divergence-free lines of flux of that 2D field. Why am I not getting their exact same figure, using no "weak measurement" at all? Why is their figure nothing but the 2D divergence-free lines of flux of a completely classical wave?

(ETA: I see this is being discussed on a much longer thread, so I present the question there too, it might be more appropriate to answer it there.)
 
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  • #10
Lost in Space said:
Could this experiment be done using entangled particles?
Yes.

Lost in Space said:
If so, would decoherence still occur?
Yes.
 
  • #11
Ken G said:
So let me ask this. Can anyone argue that I would not get the exact same figure the following way: I set up their exact apparatus, but I put my detecting wall at various different distances, repeating over and over until I map out not just a 1D detection-rate function, but a full 2D detection-rate field. The field is of course normalized to represent a divergence-free photon flux. Then I simply draw the divergence-free lines of flux of that 2D field. Why am I not getting their exact same figure, using no "weak measurement" at all? Why is their figure nothing but the 2D divergence-free lines of flux of a completely classical wave?
If I understood you correctly, you measure only the particle positions, not the velocities or momenta. By repeating it many times, you obtain the probability density scalar rho(x) everywhere. What I don't see is how you can use rho(x) to determine the (divergence-free) photon flux?
 
  • #12
The photons are essentially all the same wavelength, or could be for all the difference it would make. So there's no difficulty converting between rho(x) and an energy flux. We already do this all the time, every time we interpret a classical energy flux as a quantized photon flux. What I'm saying is equivalent to a completely classical experiment, where we simply measure the wave energy flux everywhere, and convert it into lines of flux, something we know we can do if the energy flux is divergence free (i.e., if the classical wave suffers little dissipation). The only reason I suggested it the way I did is because if one does a completely classical experiment, one is not sending the photons through one at a time, and someone might wonder if that makes a difference somehow. So the way I suggested it is (I claim) going to give the exact same figure as the completely classical way, but the process is carried out one quantum at a time.
 
  • #13
Lost in Space said:
Could this experiment be done using entangled particles? If so, would decoherence still occur?

Demystifier has already answered, but here is more info; it has been done in the http://en.wikipedia.org/wiki/Quantum_eraser_experiment" :
550px-2SlitApparatus_w3_pol.svg.png

But nature is a "tricky b**ch" :smile:, you can’t do any real measurements without breaking the wave-particle duality... see:

http://www.sciencemag.org/content/307/5711/875.abstract"
 
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  • #14
Demystifier said:
You could do that if you also knew the wave function of the system. But the interaction with the screen modified the wave function in a complicated way which in practice you cannot know exactly (this effect is better known under the name of decoherence), so you cannot really follow the trajectory back.

Ok, then what is the significance of the trajectories computed in figures like this:

Doppelspalt.jpg


I guess those are "perfect" trajectories .. i.e. predictions for what would happen in the absence of decoherence? Otherwise, I don't see why I wouldn't be able to connect a point on the detection screen with a point on a particular slit. Also, the fact that the trajectories don't cross the dividing line between the slits seems like a much more qualitative feature of the prediction ... does decoherence destroy that as well, so we can no longer be sure that particles contributing to the left-hand side of the interference pattern arise from the left-hand slit, and vice versa?

Has anyone simulated how those predictions are affected by the decoherence experienced in a "real" experiment?
 
  • #15
I don't think decoherence is really the issue here, because no matter how much docoherence you have, you still never know the trajectory that a photon will follow, you only can ever reconstruct a trajectory it followed after the fact. So the concept of "trajectory" in QM is always a purely after-the-fact notion, which means it is never something you can actually test because testing requires prediction. Someone else could always ask "how do you know it followed that trajectory" and the answer would be "it had to given my assumptions, but they're just assumptions." That's inherently true, it doesn't matter about the amount of coherence, it's just the inherent limitation of the "trajectory" concept that makes it not work as well as it does classically. Classically, trajectories are predictable.
 
  • #16
Ken G said:
I don't think decoherence is really the issue here, because no matter how much docoherence you have, you still never know the trajectory that a photon will follow, you only can ever reconstruct a trajectory it followed after the fact. So the concept of "trajectory" in QM is always a purely after-the-fact notion, which means it is never something you can actually test because testing requires prediction. Someone else could always ask "how do you know it followed that trajectory" and the answer would be "it had to given my assumptions, but they're just assumptions." That's inherently true, it doesn't matter about the amount of coherence, it's just the inherent limitation of the "trajectory" concept that makes it not work as well as it does classically. Classically, trajectories are predictable.

got an experiment for u
"consider the same interference experiment,the interference pattern produced is used to illuminate the next source in series,which then produces a new interference pattern,this gets cascaded say 10 times and the final interference pattern is obtained on the wall.
now ,the observer, observing the final interference pattern is not known of the fact that there's another observer measuring the particle position in the first stage of interference,and viceversa

"will ur answer b the same(no interference pattern) or something else?
and if u think that the experiment is not possible,state the reason along
 
  • #17
Ken G said:
The photons are essentially all the same wavelength, or could be for all the difference it would make. So there's no difficulty converting between rho(x) and an energy flux.
I still have no idea what you are talking about. Please write an EQUATION that gives the relation between rho(x) and flux.
 
  • #18
SpectraCat said:
Ok, then what is the significance of the trajectories computed in figures like this:

Doppelspalt.jpg


I guess those are "perfect" trajectories .. i.e. predictions for what would happen in the absence of decoherence?
Yes. (By the way, a weak measurement does not involve decoherence, which is exactly why weak measurements are so interesting.)

SpectraCat said:
Also, the fact that the trajectories don't cross the dividing line between the slits seems like a much more qualitative feature of the prediction ... does decoherence destroy that as well, so we can no longer be sure that particles contributing to the left-hand side of the interference pattern arise from the left-hand slit, and vice versa?
Yes.

SpectraCat said:
Has anyone simulated how those predictions are affected by the decoherence experienced in a "real" experiment?
Of course. The effect of decoherence can, for most practical purposes, be modeled by the old good collapse postulate. So if you are familiar with textbook QM, you don't really need to see the result.
 
  • #19
Demystifier said:
Yes. (By the way, a weak measurement does not involve decoherence, which is exactly why weak measurements are so interesting.)


Yes.


Of course. The effect of decoherence can, for most practical purposes, be modeled by the old good collapse postulate. So if you are familiar with textbook QM, you don't really need to see the result.

Well .. I think I *do* need to see the result in this case, although I am quite familiar with textbook QM, because I still don't understand the answer to this question:

"What (if any) is the physical significance of trajectories like the ones in the image I posted?"

If such trajectories are only meaningful in the absence of decoherence, and *complete* experiments necessarily involve decoherence (I understand about weak measurements, but you need a strong measurement to finish the experiment), then who cares about those predictions? Furthermore, doesn't that mean that the trajectories reconstructed by Steinberg et al. can't really be related to the Bohmian trajectories, since they were generated from the combination of weak and strong measurements? In that paper, they really do reconstruct the trajectories by correlating average momenta with individual points on the pattern, and tracing them back to the slits. The interference pattern in this experiment is just as "fully decohered" as any other pattern, since it is a strong measurement, so I guess I must still be missing some significant point somewhere.
 
  • #20
SpectraCat said:
Furthermore, doesn't that mean that the trajectories reconstructed by Steinberg et al. can't really be related to the Bohmian trajectories, since they were generated from the combination of weak and strong measurements?
I think it is the crucial question. My answer consists of 2 points:
1) Mathematically, weak trajectories and Bohmian trajectories are identical.
2) Ontologically, weak trajectories and Bohmian trajectories are totally unrelated.
 
  • #21
Demystifier said:
I still have no idea what you are talking about. Please write an EQUATION that gives the relation between rho(x) and flux.
Sorry, I thought it would be clear that flow vectors could be found from knowing the flux field. Let's say you had a compressible gas flowing through a 2D pipe. We then have the concept of a "flow vector," whose direction is along the streamline and whose magnitude is proportional to the mass flux along that direction. By conservation of mass, the flow vectors are divergence-free. Now imagine drawing parallel slices across the pipe, and plot along those slices a 1D "flux function", which gives the local mass flux density across the slice at each point. The question you are asking is tantamount to solving for the flow vectors given the flux functions, because once I have the flow vectors, I can draw "flow trajectories" along them. Note that these flow trajectories, also called streamlines, could equally be called "average trajectories" of the flow particles, once we recognize the flow is made of quanta.

The problem of finding the divergence-free flux vectors from the flux functions is called the "Neumann boundary problem", see for example http://en.wikipedia.org/wiki/Neumann_boundary_condition
and note that if we define y by saying that the flow vector field is the gradient of y (possible for a divergence-free flow), we have exactly the Laplace problem used as an example in that Wiki.

I claim that we have no evidence that the "average trajectories" are anything different from what I would certainly expect them to be: the streamlines of the flux vectors determined from the flux functions found by moving the detecting wall around and doing the experiment over and over.

What this also means is, we can get the same results entirely classically. We simply turn up the intensity of the light so high that we can do local flux measurements, and map out the flux functions that way.

Or, we can even look at the polarizations, classically, and form the same ratios that tell us an "average direction" for the local "average trajectories."

Or, we can solve the Bohm pilot-wave equations, which have to give the same results if they are to mean anything.

All of these roads lead to the same place: the concept of an "average trajectory" is a statistically aggregated concept, and hence is purely classical. If this is not true, I would find it quite surprising, and certainly no one has given any argument that it is not true.

Thus, I conclude what this experiment is actually saying is, "we can recover the boring classical result using a much more complicated weak measurement approach", which may tell us something about weak measurement but nothing surprising about the behavior of this system. What the experiment is not telling us is anything about the "trajectory" concept as it applies to single quanta, other than that when you aggregate the weak measurements, you do in fact get the classical answer.
 
  • #22
Ken G said:
Sorry, I thought it would be clear that flow vectors could be found from knowing the flux field.
But how can you know the flux field? (An equation might help.)

Ken G said:
We then have the concept of a "flow vector," whose direction is along the streamline
But what is the "direction of streamline" for given rho(x)?
 
  • #23
Demystifier said:
But how can you know the flux field? (An equation might help.)
It's the LaPlace equation, applied to a scalar function whose gradient is the divergence-free flow vectors. The entire problem consists in solving for that scalar function, given flow functions across the various locations of the detector walls. This is basic LaPlace, done to death in many fields of physics, it is merely a different boundary condition from what is normally seen. Let's say you were a sound engineer and you had measurements of how loud a particular speaker sounded at various places in an auditorium. Do you think you'd have any trouble calculating the sound energy flux pattern in that auditorium? Would it be a big stretch to call your results the "average trajectories" of the phonons?
 
  • #24
SpectraCat said:
... does decoherence destroy that as well, so we can no longer be sure that particles contributing to the left-hand side of the interference pattern arise from the left-hand slit, and vice versa?
Demystifier said:
Yes.

¿Qué?

Are there different dBB 'schools'...

According to http://www.bohmian-mechanics.net/", it’s the other way around??
http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/gallery/double/slide4.html

The double slit experiment, Picture 4
[URL]http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/gallery/double/double4.gif[/URL]
These are the paths, one of which the actual particle follows, according to Bohmian mechanics. Each path passes through one of the slits (left hand side); and hits the screen (right hand side) at a random position that appears |psi|2 distributed, displaying the famous diffraction fringes. Although one cannot know in advance through which slit the particle will pass, one can decide afterwards: it passes through the upper slit if and only if it hits the screen on the upper half, that is, *above the symmetry axis*.
 
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  • #25
Ken G said:
It's the LaPlace equation, applied to a scalar function whose gradient is the divergence-free flow vectors. The entire problem consists in solving for that scalar function, given flow functions across the various locations of the detector walls. This is basic LaPlace, done to death in many fields of physics, it is merely a different boundary condition from what is normally seen. Let's say you were a sound engineer and you had measurements of how loud a particular speaker sounded at various places in an auditorium. Do you think you'd have any trouble calculating the sound energy flux pattern in that auditorium? Would it be a big stretch to call your results the "average trajectories" of the phonons?
OK, now I understand your idea. However, there are at least two problems with it:

1) The solution is not unique. Namely, if you have found a solution corresponding to the velocity field v(x), then any other velocity field v'(x) of the form
v'(x)=v(x)+u(x)/rho(x)
where u(x) is an arbitrary divergence-free vector field, is also a possible solution. Indeed, such alternative solutions correspond to alternative trajectory interpretations of QM. Weak measurement, by contrast, leads to a single velocity field equal to the Bohmian one.

2) There are complications when two or more particles are involved. For simplicity, consider 2 particles. A naive extension of your idea would require two functions rho1(x1) and rho(x2). However, instead of this you must deal with a single function in a double-dimensional space rho(x1,x2). The resulting waves can hardly be thought of as "classical".
 
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  • #26
DevilsAvocado said:
¿Qué?

Are there different dBB 'schools'...

According to http://www.bohmian-mechanics.net/", it’s the other way around??
In the case you quote above, there is no measurement (and therefore no decoherence) before the screen. I was talking about the case with a strong measurement (and consequent decoherence) before the screen.

So, there are no different dBB schools on that issue. Instead, as usual, you find "inconsistencies" by comparing different things.
 
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  • #27
Demystifier said:
In the case you quote above, there is no measurement (and therefore no decoherence) before the screen. I was talking about the case with a strong measurement (and consequent decoherence) before the screen.

Ah! Thanks!
 
  • #28
Demystifier said:
I think it is the crucial question. My answer consists of 2 points:
1) Mathematically, weak trajectories and Bohmian trajectories are identical.
2) Ontologically, weak trajectories and Bohmian trajectories are totally unrelated.

But Demystifier your username... de-mystifier seems a little 'incompatible' with this...? :wink:

It works like a dream mathematically, but there is no way to relate this to the "everyday world"... :rolleyes:

How can we then get rid of the mysteries?

Is possible to use a (deterministic) "casual explanation"?

If you can't explain it simply, you don't understand it well enough -- Albert Einstein
 
  • #29
DevilsAvocado said:
But Demystifier your username... de-mystifier seems a little 'incompatible' with this...? :wink:

It works like a dream mathematically, but there is no way to relate this to the "everyday world"... :rolleyes:

How can we then get rid of the mysteries?

Is possible to use a (deterministic) "casual explanation"?

If you can't explain it simply, you don't understand it well enough -- Albert Einstein
I have no idea what are you trying to say here. :confused:
 
  • #30
Demystifier said:
OK, now I understand your idea. However, there are at least two problems with it:

1) The solution is not unique. Namely, if you have found a solution corresponding to the velocity field v(x), then any other velocity field v'(x) of the form
v'(x)=v(x)+u(x)/rho(x)
where u(x) is an arbitrary divergence-free vector field, is also a possible solution. Indeed, such alternative solutions correspond to alternative trajectory interpretations of QM. Weak measurement, by contrast, leads to a single velocity field equal to the Bohmian one.
No, those are not possible solutions, and frankly I have no idea why you think they would be. They would not produce the same flux measurements.
2) There are complications when two or more particles are involved. For simplicity, consider 2 particles. A naive extension of your idea would require two functions rho1(x1) and rho(x2). However, instead of this you must deal with a single function in a double-dimensional space rho(x1,x2). The resulting waves can hardly be thought of as "classical".
That has nothing to do with this thread. Everything going on in a two-slit experiment obeys the superposition principle. Why can you not simply accept the truth in what I'm saying?
 
  • #31
Demystifier said:
I have no idea what are you trying to say here. :confused:

Neither do I! :smile:
1) Mathematically, weak trajectories and Bohmian trajectories are identical.
2) Ontologically, weak trajectories and Bohmian trajectories are totally unrelated.​

It’s probably that (dreadful :smile:) philosophical word Ontology that messes up things for me. I interpreted this as; mathematically these trajectories are the same, but if you want to describe (and understand) this strong relation in words – it doesn’t work because then they are totally unrelated...

:rolleyes:
 
  • #32
Demystifier said:
In the case you quote above, there is no measurement (and therefore no decoherence) before the screen. I was talking about the case with a strong measurement (and consequent decoherence) before the screen.

So, there are no different dBB schools on that issue. Instead, as usual, you find "inconsistencies" by comparing different things.

But there was no strong measurement before the screen in the case I was asking about either ... the screen is the only strong measurement in a standard double-slit experiment, or in the Steinberg experiment for that matter.

So, once again from the top ... how does knowing which slit a particle went through *in an experiment* not constitute the kind of "which path" information that is shown *experimentally* (i.e. "sans interpretational mumbo jumbo") to destroy the appearance of an interference pattern?

As I suggested earlier, it might be helpful to read through a BM-based explanation of the quantum eraser experiment, since that deals with the issues I am asking about. I am assuming one exists, although I wasn't able to turn it up with a quick google search .. at least not one that I have journal access to remotely (I am traveling ATM). A reference would be most appreciated.
 
  • #33
SpectraCat said:
As I suggested earlier, it might be helpful to read through a BM-based explanation of the quantum eraser experiment, since that deals with the issues I am asking about. I am assuming one exists, although I wasn't able to turn it up with a quick google search .. at least not one that I have journal access to remotely (I am traveling ATM). A reference would be most appreciated.
Try Basil Hiley's "http://www.bbk.ac.uk/tpru/BasilHiley/QuantEraserLight.pdf" ". That should do the trick.
 
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  • #34
SpectraCat said:
So, once again from the top ... how does knowing which slit a particle went through *in an experiment* not constitute the kind of "which path" information that is shown *experimentally* (i.e. "sans interpretational mumbo jumbo") to destroy the appearance of an interference pattern?
You can be sure that if you know which slit each photon went through, then those photons are not participating in a two-slit pattern. That is what you may take to the bank here. Since they do get a two-slit pattern, we know that they are not determining which slit the photons went through. If anyone thinks they are, there are many ways of fooling oneself on that score.
 
  • #35
Ken G said:
You can be sure that if you know which slit each photon went through, then those photons are not participating in a two-slit pattern. That is what you may take to the bank here. Since they do get a two-slit pattern, we know that they are not determining which slit the photons went through. If anyone thinks they are, there are many ways of fooling oneself on that score.

You're deluding yourself mate. Remember that unless you deliberately graft on measurement apparatus then de Broglie-Bohm is a theory of what actually happens in a single system, irrespective of who happens to observe it.

Thus, as the trajectories (the streamlines of the probability current, if you must) don't cross, there is a plane of symmetry along the centreline between the two slits (see the various trajectory diagrams that have been shown). The trajectories cannot cross this plane. If we assume this plane divides the detector into left and right halves, then any particle hitting the left half of the screen must have gone through the left slit. Any particle hitting the right half of the screen must have gone through the right slit. The objectively-existing pilot wave, represented mathematically by the Schroedinger wave function, passes through both slits.

Thus, assuming that the deBB assumptions about what exists (particle and wave) are correct, then your statement is simply wrong, so I don't know why you're adopting such an attitude. Did you actually look at the trajectory diagram?
 
  • #36
zenith8 said:
You're deluding yourself mate. Remember that unless you deliberately graft on measurement apparatus then de Broglie-Bohm is a theory of what actually happens in a single system, irrespective of who happens to observe it.
That's not relevant to anything I said-- I was talking about what you can know, not what you can pretend you think you know using Bohm. That is what Bohmian mechanics is, after all-- the pretense of knowing.
Thus, as the trajectories (the streamlines of the probability current, if you must) don't cross, there is a plane of symmetry along the centreline between the two slits (see the various trajectory diagrams that have been shown). The trajectories cannot cross this plane. If we assume this plane divides the detector into left and right halves, then any particle hitting the left half of the screen must have gone through the left slit. Any particle hitting the right half of the screen must have gone through the right slit. The objectively-existing pilot wave, represented mathematically by the Schroedinger wave function, passes through both slits.
Basically what I hear there is blah, blah, pretense of knowing, blah blah. (Not trying to offend, I'm just being humorous-- yet serious about the physics.) You can't show any of it. Symmetry alone tells you the nice figure is not going to cross the center, I don't care how you make the figure, and it certainly doesn't tell you anything about what the photons "can't do."

Thus, assuming that the deBB assumptions about what exists (particle and wave) are correct, then your statement is simply wrong, so I don't know why you're adopting such an attitude.
Actually, my statement is still correct, because I was talking about what you could demonstrate you know, and you are talking about what you can pretend you know. I have no problem with people who like Bohm because it fits their prejudices about how a universe ought to work, my issue is when they claim they have shown the universe actually works that way. Until you can show the Bohm trajectories agree with this experiment, and the classical trajectories I've talked about don't, you have not actually shown any of your claims.
 
  • #37
zenith8 said:
Try Basil Hiley's "http://www.bbk.ac.uk/tpru/BasilHiley/QuantEraserLight.pdf" ". That should do the trick.

Thank you. I will read it carefully as soon as I have a little more time.

zenith8 said:
Thus, as the trajectories (the streamlines of the probability current, if you must) don't cross, there is a plane of symmetry along the centreline between the two slits (see the various trajectory diagrams that have been shown). The trajectories cannot cross this plane. If we assume this plane divides the detector into left and right halves, then any particle hitting the left half of the screen must have gone through the left slit. Any particle hitting the right half of the screen must have gone through the right slit. The objectively-existing pilot wave, represented mathematically by the Schroedinger wave function, passes through both slits.

So then, what is your answer to the question I asked in the title of this thread (I also gave some further remarks about what I find confusing in my subsequent posts)?
 
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  • #38
SpectraCat said:
... So, once again from the top ... how does knowing which slit a particle went through *in an experiment* not constitute the kind of "which path" information that is shown *experimentally* (i.e. "sans interpretational mumbo jumbo") to destroy the appearance of an interference pattern?

That’s a very good question.

But gentlemen, please excuse a layman – aren’t we 'deluding' ourselves just a little bit here?

All this information about trajectories, whether it’s standard QM, dBB or experimental, is all about statistics, right? Statistics on ensembles of particles – on average, right?

Thus AFAIK, no one can say: – Hey! I can prove that this *single* photon went thru the left slit and then was a part in creating the interference pattern on the screen!

That won’t work, huh? :rolleyes:

It’s all about statistics...

I found http://www.cbc.ca/m/rich/technology/story/2011/06/02/science-heisenberg-uncertainty-steinberg.html" from Aephraim Steinberg (emphasis mine):
"We are all just thrilled to be able to see, in some sense, what a photon does as it goes through an interferometer, something all of our textbooks and professors had always told us was impossible,"

"While it doesn't go against the rigorous theorem that Heisenberg proved, it goes against the way most of us were brought up and educated to think about the meaning of the theorem,"

"What the conclusion is for us is that although the principle when you read it really carefully is correct, many people have been interpreting it a bit too strongly."

This must mean that HUP still holds – on average! :rolleyes:
 
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  • #39
Ken G said:
No, those are not possible solutions, and frankly I have no idea why you think they would be. They would not produce the same flux measurements.
Since you do not want to present any equation to support your claims, any further discussion on it is pointless.

Ken G said:
That has nothing to do with this thread. Everything going on in a two-slit experiment obeys the superposition principle. Why can you not simply accept the truth in what I'm saying?
I think you have not understood what I am saying at all.
 
  • #40
SpectraCat said:
Thank you. I will read it carefully as soon as I have a little more time.

Great - I'd love to hear if it answers your question.

So then, what is your answer to the question I asked in the title of this thread (I also gave some further remarks about what I find confusing in my subsequent posts)?

As I said, under the assumption that the deBB assumptions about the nature of reality are true, then you certainly 'know' immediately which slit the particle passed through, once you observe where it hits the screen. However, of course, you do not 'know' whether deBB is in fact a correct description of our universe. So, as with most things, it all depends on what assumptions you allow yourself to make.

Now, people who talk about 'which way' information who subscribe to, say, the Copenhagen interpretation use the word 'know' in the sense "did I bash the particle with a great big test probe" somewhere in the vicinity of slit A and observe it to be there. That is, 'know' in the sense of 'measurement' which generally - and quite understandably - destroys the interference pattern. However, this is not the sense in which *you* are asking the question, because you're asking about deBB theory.

Note that the whole 'which way' argument couched in the Copenhagen sense is completely disingenuous, since the very phrase implies some assumption about the nature of reality - i.e. that there is some localized objectively-existing thing that passes through just one of the slits. And yet those that subscribe to the 'wavefunction as information' viewpoint routinely deny that anything passes through the two-slit system, an assumption much more ludicrous than the deBB assumption that localized objects follow the streamlines of the probability current. Something real definitely passes through the slits - to refuse to call it 'real' is merely to play with words.

The deBB assumptions about what is real are clearly the most sensible ones (why should electrons disappear when you don't look at them?) and have potentially experimentally testable consequences. So why not test them?

Oh no, K-k-k-Ken is coming to k-k-k-kill me.
 
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  • #41
Demystifier said:
Since you do not want to present any equation to support your claims, any further discussion on it is pointless.
I did give you the equation. It is called LaPlace's equation. It says the divergence of the flux vector field is zero. I also told you the boundary condition used-- we find the flux across parallel cuts of the apparatus by moving the detecting wall (as they actually do, they just think they need polarizations, which they don't). The "flux functions" are the dot product of the flux vectors with the normal to the wall. This gives us the "x component" of the flux vectors everywhere, which gives us the gradient of the x component also. Since the divergence of the flux is zero, we then locally infer the gradient of the y component everywhere. Then we reconstruct the y component from knowing its gradient everywhere, since we know it is essentially zero at the slit. I did not think the details mattered-- seemed straightforward enough to infer a flux vector distribution given the flux crossing every boundary.

I think you have not understood what I am saying at all.
I'm afraid you're not saying anything relevant to my points, so let me summarize:
1) the "trajectory" figure they give can be obtained purely classically
2) this can be done in a variety of ways-- one can do the whole thing in the classical limit and measure fluxes, one can send one photon at a time, move the detector around and repeat many times and add up the results, one can even use polarizations just as they do. All that matters is if you add up the results of many instances, you are doing a classical limit, period.
3) the conclusions of this paper are completely unjustified and overblown-- all they have really done is show that "weak measurements" can recover a classical limit, which would be pretty surprising if not true.
 
  • #42
zenith8 said:
... As I said, under the assumption that the deBB assumptions about the nature of reality are true, then you certainly 'know' immediately which slit the particle passed through, once you observe where it hits the screen. However, of course, you do not 'know' whether deBB is in fact a correct description of our universe. So, as with most things, it all depends on what assumptions you allow yourself to make.

What’s that smell...

AHHHHHH dddddddBBBBBBBB PROPAGANDA! (:smile:)
 
  • #43
zenith8 said:
As I said, under the assumption that the deBB assumptions about the nature of reality are true, then you certainly 'know' immediately which slit the particle passed through, once you observe where it hits the screen. However, of course, you do not 'know' whether deBB is in fact a correct description of our universe. So, as with most things, it all depends on what assumptions you allow yourself to make.
No, this is like arguing "what I know depends on what assumptions I make." That is not science, that is what people who believe in ghosts and ESP say. "If we assume ghosts are real, then these are ghosts." Does that sound like science? In science, to "know" something is to be able to demonstrate it against skeptical objection, not to be able to assume it.

Note that the whole 'which way' argument couched in the Copenhagen sense is completely disingenuous, since the very phrase implies some assumption about the nature of reality - i.e. that there is some localized objectively-existing thing that passes through just one of the slits.
Actually you have it quite backwards. The whole point of CI is to be able to know things without making any assumptions about the nature of reality! You know what your instrument tells you you know, very simple, very scientific. This experiment does not tell us which slit any photons went through.
 
  • #44
zenith8 said:
Great - I'd love to hear if it answers your question.



As I said, under the assumption that the deBB assumptions about the nature of reality are true, then you certainly 'know' immediately which slit the particle passed through, once you observe where it hits the screen. However, of course, you do not 'know' whether deBB is in fact a correct description of our universe. So, as with most things, it all depends on what assumptions you allow yourself to make.

Now, people who talk about 'which way' information who subscribe to, say, the Copenhagen interpretation use the word 'know' in the sense "did I bash the particle with a great big test probe" somewhere in the vicinity of slit A and observe it to be there. That is, 'know' in the sense of 'measurement' which generally - and quite understandably - destroys the interference pattern. However, this is not the sense in which *you* are asking the question, because you're asking about deBB theory.

Note that the whole 'which way' argument couched in the Copenhagen sense is completely disingenuous, since the very phrase implies some assumption about the nature of reality - i.e. that there is some localized objectively-existing thing that passes through just one of the slits. And yet those that subscribe to the 'wavefunction as information' viewpoint routinely deny that anything passes through the two-slit system, an assumption much more ludicrous than the deBB assumption that localized objects follow the streamlines of the probability current. Something real definitely passes through the slits - to refuse to call it 'real' is merely to play with words.

The deBB assumptions about what is real are clearly the most sensible ones (why should electrons disappear when you don't look at them?) and have potentially experimentally testable consequences. So why not test them?

Oh no, K-k-k-Ken is coming to k-k-k-kill me.

Ok .. I think I've got it. Basically you are saying that you can't mix and match features of interpretations ... and it seems obvious that's what I was trying to do now that you point it out. In other words:

1) in Bohmian interpretation, the interference pattern is a feature of the wavefunction passing through both slits, while the "dots on the screen" from individual measurements are a feature of the particle trajectories. Thus knowing definitively that a particle went through a particle went through a given slit is "no big deal".

2) in CI, the interference pattern is a feature of "unperturbed" wavefunctions interacting with the double-slit apparatus. The more we know about the relative probability density at a given slit (trying to avoid using the word particle ...), for example from weak measurements, the more we disrupt the interference pattern. In the limit that we can know with certainty that the probability density is concentrated at a single slit (i.e. by polarization tagging), there is no interference pattern at all.

Does that about sum it up? I expect the Bohmian side of things will become clearer when I have read that paper you linked about the quantum eraser.
 
  • #45
Ken G said:
I did give you the equation. It is called LaPlace's equation. ...
The words like "Laplace equation" are not an equation.
An expression like "x+y=z" is.
There is a reason why scientists prefer to really write the equations themselves instead of words that attempt to describe them.

If you REALLY want me understand what are you saying, please write the equations themselves, not their verbal descriptions. Only then we can really discuss it.
 
  • #46
Demystifier said:
The words like "Laplace equation" are not an equation.
Yes, that's kinda why I went on in that last post to say exactly what the equation is and how we would solve it here.
If you REALLY want me understand what are you saying, please write the equations themselves, not their verbal descriptions. Only then we can really discuss it.
You want me to translate "divergence of the flux vectors" and "equals" into mathematical notation?

If you don't like flux vectors, we can do this another way, which shows even more clearly why their result is classical. Let's do the classical experiment exactly like they do-- we measure the polarization of the classical wave field, as well as its energy flux rate at the wall (that's what they end up doing when they average). Then we apply all the same reasoning as they do (you can use their equations now), except they are applied to the classical wave field, rather than the individual photon measurements. By the correspondence principle, these are identical results. This makes it perfectly clear that all they have done is show that you can do measurements on individual photons, and average them, and recover the classical limit. None of that justifies the rather absurd "they taught us QM wrong" or "this proves Bohm was right" language we are hearing.
 
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  • #47
SpectraCat said:
2) in CI, the interference pattern is a feature of "unperturbed" wavefunctions interacting with the double-slit apparatus.
I can't let that go, because we don't want to give a false idea of what CI is. In CI, the interference pattern is an observed pattern, it comes from the instruments. Thus it is not a "feature" of any wavefunctions! The wavefunctions are predictive tools that give us the measured interference patterns. Note this is exactly what they are-- to say they are anything else is to enter into a belief system. Not that there's anything wrong with believing, "ya got to believe", but we should at least recognize it.
 
  • #48
Ken G said:
I can't let that go, because we don't want to give a false idea of what CI is. In CI, the interference pattern is an observed pattern, it comes from the instruments. Thus it is not a "feature" of any wavefunctions! The wavefunctions are predictive tools that give us the measured interference patterns. Note this is exactly what they are-- to say they are anything else is to enter into a belief system. Not that there's anything wrong with believing, "ya got to believe", but we should at least recognize it.

No, I think I phrased it correctly. I think you are conflating "shut up and calculate" with the CI. The CI certainly says the interference pattern comes from somewhere ... how else can you phrase it other than an interaction of the <representation of the quantum system> with the experimental apparatus? I simply plugged in "wavefunction" for <representation of the quantum system> above. Anyway, my point was about the *interpretation* of the experiment, so it is perfectly valid to talk about the "behind the scenes" wavefunction picture in CI in that context. This whole thread is about the comparison of predictions from interpretations of QM and how they are reflected (or not) in experimental measurements.
 
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  • #49
Ken G said:
Yes, that's kinda why I went on in that last post to say exactly what the equation is and how we would solve it here.
You want me to translate "divergence of the flux vectors" and "equals" into mathematical notation?

If you don't like flux vectors, we can do this another way, which shows even more clearly why their result is classical. Let's do the classical experiment exactly like they do-- we measure the polarization of the classical wave field, as well as its energy flux rate at the wall (that's what they end up doing when they average). Then we apply all the same reasoning as they do (you can use their equations now), except they are applied to the classical wave field, rather than the individual photon measurements. By the correspondence principle, these are identical results. This makes it perfectly clear that all they have done is show that you can do measurements on individual photons, and average them, and recover the classical limit. None of that justifies the rather absurd "they taught us QM wrong" or "this proves Bohm was right" language we are hearing.
I can imagine how you solve mathematical exercises in a high-school:
Exercise: write Pi to six decimals
Expected answer: Pi = 3.141593
Your answer: Pi is equal to three point one four one five nine three.
:smile:
 
  • #50
SpectraCat said:
Ok .. I think I've got it. Basically you are saying that you can't mix and match features of interpretations ... and it seems obvious that's what I was trying to do now that you point it out. In other words:

1) in Bohmian interpretation, the interference pattern is a feature of the wavefunction passing through both slits, while the "dots on the screen" from individual measurements are a feature of the particle trajectories. Thus knowing definitively that a particle went through a particle went through a given slit is "no big deal".

2) in CI, the interference pattern is a feature of "unperturbed" wavefunctions interacting with the double-slit apparatus. The more we know about the relative probability density at a given slit (trying to avoid using the word particle ...), for example from weak measurements, the more we disrupt the interference pattern. In the limit that we can know with certainty that the probability density is concentrated at a single slit (i.e. by polarization tagging), there is no interference pattern at all.

Does that about sum it up? I expect the Bohmian side of things will become clearer when I have read that paper you linked about the quantum eraser.
Exactly! Couldn't have put it better myself.

(except the "particle went through a particle went through a" bit, which by the time anyone reads this, you might have edited.).
 
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