Exploring Photon Trajectories in Double Slit Experiments

[DevilsAvocado]

I have no idea what are you trying to say here.

Neither do I!

1) Mathematically, weak trajectories and Bohmian trajectories are identical.
2) Ontologically, weak trajectories and Bohmian trajectories are totally unrelated.​

It’s probably that (dreadful ) 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...

 

[SpectraCat]

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.

 

[zenith8]

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.

 

[Ken G]

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.

 

[zenith8]

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?

 

[Ken G]

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.

 

[SpectraCat]

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.

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)?

 

[DevilsAvocado]

... 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?

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!

 

[Demystifier]

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.

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.

 

[zenith8]

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.

 

[Ken G]

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.

 

[DevilsAvocado]

... 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! ()

 

[Ken G]

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.

 

[SpectraCat]

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.

 

[Demystifier]

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.

 

[Ken G]

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.

 

[Ken G]

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.

 

[SpectraCat]

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.

 

[Demystifier]

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.

 

[zenith8]

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.).

 

[zenith8]

... 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!

That's very funny, well done. Especially the vomiting smiley. Cute.

Look, the OP asks a question about deBB. I answer it. Seems like he agrees with my answer. That ain't propaganda. Why don't you try the same trick on Copenhagenists or many-worlders occasionally, just for a bit of variety?

 

[Ken G]

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.

I guess that meant something, but what, I have no idea. Do you, or do you not, think that the average trajectory figure could be made with experiments on sound waves going through two slits? Because I'm saying not a single person here has given any argument, nor did the authors of the paper, that their figure would be any different from that. And I gave a very simple argument that it should be the same: it involves the classically averaged limit. This is called the correspondence principle.

 

[Ken G]

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 think I have a pretty good feel for the CI, it's really a very simple approach. These are its two main tenets:
1) the reality that physics is trying to explain is only what can be measured.
2) everything else is a theory whose goal is to use mathematical objects to successfully predict what can be measured.
So the CI is all about dichotomy, about keeping track of what we actually know by measurement, and what we are just using as a device to think about and predict measurements. All other interpretations involve conflating these two elements that CI keeps separate. That the two are different is demonstrably true, so if anyone would conflate them, they are adding something to CI, not removing anything from CI. All they are doing is something that CI thinks they should not do, but they do not remove or contradict any conclusions that CI reaches. CI is a subset of all other interpretations.

I simply plugged in "wavefunction" for <representation of the quantum system> above.

The key word is "reprsentation." The mantra of CI is the map is not the territory.

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.

Nothing in this experiment contradicts the behind-the-scenes wavefunction that CI would use to correctly predict everything that happened in this experiment.

This whole thread is about the comparison of predictions from interpretations of QM and how they are reflected (or not) in experimental measurements.

And there's your problem right there-- "interpretations" of QM are called interpretations because they do not predict, they simply help do the math of the predictions, and they are a matter of personal taste. If they made any different predictions, they would be alternate theories, not interpretations. That's quite straightforward-- different theories make different predictions, different interpretations just put something different in your head while you make the same predictions. If at some future point, there are actually different theories, it's likely that one interpretation will seem the closest to the new theory, but at present, there is not any such new theory, and certainly nothing in this experiment calls for it. It doesn't even call for anything beyond classical wave mechanics, in fact.

 

[zenith8]

And there's your problem right there-- "interpretations" of QM are called interpretations because they do not predict, they simply help do the math of the predictions, and they are a matter of personal taste. If they made any different predictions, they would be alternate theories, not interpretations. That's quite straightforward-- different theories make different predictions, different interpretations just put something different in your head while you make the same predictions. If at some future point, there are actually different theories, it's likely that one interpretation will seem the closest to the new theory, but at present, there is not any such new theory..

And there's your problem, right there. This thread is about deBB, and because deBB does make different predictions - since it in principle allows particles to be not distributed according to the Born rule - it is a different theory. Such predictions are difficult, but not impossible to test experimentally. In the unlikely event of such predictions being confirmed, it would bring about a revolution of the way we see physics. It would probably bring about developments in the mathematics as the full weight of the world's physicists turned only to theories which allow such anomalies to happen. It's a long shot, certainly - but such things should be looked at.

But because - despite what you say being perfectly correct - you retain the usual tendency to stamp on anyone who doesn't work according to the principles laid down by Bohr, you do damage. You think you are being rigorous and intellectually honest, but by doing this, you and people like you in effect make it very difficult for people to work on theories like deBB which are different to the mainstream. It's actually perfectly OK to do informed speculation on what might exist and work out the testable consequences. And furthermore, it's not illegal, OK?

 

[Ken G]

And there's your problem, right there. This thread is about deBB, and because deBB does make different predictions - since it in principle allows particles to be not distributed according to the Born rule - it is a different theory.

Predictions that cannot be tested don't count, I don't care if Bohm says exactly 24 angels fit on a pin. What matters to this thread is that nothing in that experiment doesn't obey the Born rule. Do you see some result from this experiment that doesn't obey the Born rule? Then why bring it up?

In the unlikely event of such predictions being confirmed, it would bring about a revolution of the way we see physics.

That is both true and irrelevant to this experiment.

You think you are being rigorous and intellectually honest, but by doing this, you and people like you in effect make it very difficult for people to work on theories like deBB which are different to the mainstream.

That is not at all true. All I'm doing is requiring a certain standard of result, a standard that is simply not being lived up to. The damage to deBB is not from people like me, who only say "prove it", it is from people like the authors of this paper, who claim that deBB is doing something in regard to this experiment that it is not doing at all. What we are seeing, and see so often, is people who have a personal taste for deBB trying to see it in experiments where in fact it is simply not being exhibited-- it is just as "behind the scenes" as it always is. It's a smokescreen, pure and simple, and I do no damage by pointing that out. If you think my argument is too forceful, it is so easily refuted: just tell me why, when you average lots and lots of quantum measurements in a two-slit experiment with as many calcite bells and whistles as you want, you do not get the result of a classical wave. Simple!

 

[Demystifier]

I guess that meant something, but what, I have no idea.

Yes, that's exactly the problem. You have no idea what do I mean when I say "equation", and cannot understand that "equation" is not an equation. Since you do not understand me (which may very well be my fault), it's pointless to continue that discussion with you.

 

[Ken G]

I see, so because I said "the divergence of the energy flux vector field is zero", and you don't see a "=", you don't see that as an equation, and so you don't have to deal with my argument. For those who do think that is an equation, let me just summarize with these questions:
1) What evidence do we have that the "average trajectory" diagram is any different from an energy flux streamline diagram for a classical wave passing this apparatus (by which I mean, crank up the intensity until you can measure the field amplitudes)?
2) Does anyone see it as a teeny problem that we have no evidence of #1?

 

[unusualname]

After determining the energy flow for a double slit from Maxwell's equations ( abs , pdf ) the same author published another paper claiming he had a model where the photons from each slit do go to just one side of the pattern. He suggested an experiment to test this by simply measuring the flight time of the photons (this will destroy the interference pattern but he just wants to test whether any photons from the right slit go to the lhs and vice-versa)

I don't know if such an experiment was ever carried out.

Quantum Theory and the Nature of Interference - Prosser 1976 ( pdf download )

 

[Ken G]

Excellent, thank you for finding that reference. So at least we have a specific comparison to a Maxwell-type classical calculation! Why weren't such comparisons in the paper we are discussing, seems like an obvious question. What I find significant is that Prosser wanted to draw the same conclusions from the classical Maxwell approach that we are now hearing touted as some special result of the ensemble-averaged "weak measurement" approach! See my point?

It is sounding like a pretty clear case of a preconceived notion that is being shoehorned into every outcome. I would argue that it is perfectly obvious from basic symmetry requirements that any outcome that results in something that looks like streamlines (which cannot cross) is going to produce a picture that looks like all the photons from one slit go to one side. Far more interesting would be an outcome that found a mixture via an analysis more sophisticated than an ensemble-averaged streamline approach, but of course you'll never get that with these classically-equivalent approaches.

Demystifier: now you have the equations I was talking about, maybe I should have said "Maxwell's equations" and "Poynting flux" instead of "LaPlace's equation" and "classical waves". I thought it was all obvious, but I could have been clearer. The only question that remains is, do you see any significance in a flux streamline picture drawn using Maxwell's equations being used in essentially the same way the new "average trajectory" figure is being used, and do you understand what I have been saying now? I was at a loss why my relatively trivial argument was being so disparaged.

 

[Demystifier]

Demystifier: now you have the equations I was talking about,

Yes, that makes me happy for two reasons. First, because now we have something concrete to talk about. Second, because now I see that you only pretended that you didn't see what I meant by "equations".

Now a few comments on the paper.

Poynting vector is indeed a natural way to associate trajectories with solutions of Maxwell equations. But can such trajectories be measured? Or more precisely, can the Poynting vector be measured by "ordinary" (i.e. not weak) measurements?

Here is my answer. Quantum interference is the most interesting (i.e. most incompatible with classical waves) when photons are sent through the slits one by one. So let us discuss only that case. To reproduce the trajectories EXPERIMENTALLY, one should measure BOTH the photon positions and the Poynting vector on these positions. However, without weak measurements, one cannot measure both (this is like measuring both position and momentum of a single quantum particle). Therefore, the trajectories cannot be measured without weak measurements.

To avoid confusion, one can measure both for a classical electromagnetic field, which corresponds to the case when many photons travel through the slits at once. This corresponds to a simultaneous measurement of a classical position and momentum of a piece of "fluid" made up of many particles, which can be done. But as I already explained above, this is not what the goal is. It's "too classical" to be really interesting.