In-principle existence of which-way info

[Swamp Thing]

It seems to me that, although QM involves many mathematical constructs that are a bit daunting and may take a long time to master, this is not necessarily an insuperable barrier to the learner's progress.

What is perhaps more potentially confusing is, identifying all the subtle ways that "which-way" information may lurk in the system, unbenknownst to us.

How do the experts learn to identify all the ways in which "which-way" information may, in principle, be recorded in some corner of the apparatus, or encoded in some subtle property of the measurement results?

How could a rigorous algorithm be developed that would do this job automatically -- something that one could call a "which-way wizard" or a "distinguishability wizard?

 

[Simon Bridge]

It seems to me that, although QM involves many mathematical constructs that are a bit daunting and may take a long time to master, this is not necessarily an insuperable barrier to the learner's progress.

That is correct - otherwise nobody would ever learn quantum mechanics.

What is perhaps more potentially confusing is, identifying all the subtle ways that "which-way" information may lurk in the system, unbenknownst to us.

Not really - by the time it is important, you'll get taught the correct concepts.

How do the experts learn to identify all the ways in which "which-way" information may, in principle, be recorded in some corner of the apparatus, or encoded in some subtle property of the measurement results?

Practice. You can verify different possible ways information of any kind may be hidden from you by constructing a model assuming the hidden information exists and comparing the results with experiment.

How could a rigorous algorithm be developed that would do this job automatically -- something that one could call a "which-way wizard" or a "distinguishability wizard?

I have a feeling Godel's theorem rules that out.
Basically we use "scientific method" to develop and discard models.
For the specific information you are talking about - the models are pretty well established.

See:
http://arxiv.org/abs/1404.6065

 

[atyy]

I suspect that none of the which-way arguments are really correct, because until a measurement is made, if the system is known, then the evolution is in principle reversible, so there cannot be any which way information extracted. Feynman's lectures do present quantum mechanics in this way, and I doubt it is truly correct.

 

[atyy]

As an example, a complicated experiment in which it is difficult to figure out what is happening by asking whether "which way" information has been obtained is found in http://arxiv.org/abs/1304.7469, Asking photons where have they been by Ariel Danan, Demitry Farfurnik, Shimshon Bar-Ad, Lev Vaidman. However, there should be a way to calculate the results in the standard formalism, and one proposal for such a standard calculation is http://arxiv.org/abs/1410.8454, Knowing "where the photons have been" by Karol Bartkiewicz, Antonín Černoch, Dalibor Javůrek, Karel Lemr, Jan Soubusta, Jiří Svozilík.

 

[Swamp Thing]

Thanks for the replies! I shall look up the referred docs.
ST

 

[Simon Bridge]

I had to look up "which way information" to get an idea of what people seem to mean, jic ... I think we will end up needing to know what Swamp Thing is calling "which way information" to properly answer the question. What I could find relates it to the "strength" of the interference pattern (in 2-slit experiments) when some form of weak detection is imposed... and then you try to describe it in terms of information theory.

I did see that some people take this to mean that Nature knows "which way" and the pattern is related to how well we know "which way"... which implies that quantum interference is an artifact of the observer and we should look for a hidden-variables model (i.e. pilot waves) to explain it.
I would take this as incorrect, but it does seem persistent.

I suspect this sort of thing is more due to the minds insistence on understanding things in terms of classical trajectories.

 

[Swamp Thing]

I have a feeling Godel's theorem rules that out.

Do you mean, the art of classifying an experiment (or parts of it) in terms of distinguishability, lies outside the formalism of QM?

 

[atyy]

I suspect this sort of thing is more due to the minds insistence on understanding things in terms of classical trajectories.

Yes, but even serious scientists use this sort of language. So I think one must accept it as at least informally ok. However, as far as I understand, it isn't really formally correct, or at least I usually confuse myself completely if I try to use "which way" thinking.

Feynman:http://www.feynmanlectures.caltech.edu/III_01.html#Ch1-S7
http://www.feynmanlectures.caltech.edu/III_01.html#Ch1-S7

Aspect:
(51:17)

 

[Swamp Thing]

Yes, but even serious scientists use this sort of language. So I think one must accept it as at least informally ok. However, as far as I understand, it isn't really formally correct,

If "which way" is just a heuristic aid in thinking about experiment / set up, what is the rigorous way? Finally, the answer we want is something like, "should we add first and then square, or should we square first and then add" -- and there should be a way to decide this without any hand-waving.

 

[atyy]

If "which way" is just a heuristic aid in thinking about experiment / set up, what is the rigorous way? Finally, the answer we want is something like, "should we add first and then square, or should we square first and then add" -- and there should be a way to decide this without any hand-waving.

In addition to the treatment given by Bartkiewicz et al, you can also look at http://arxiv.org/abs/1007.3977, Demystifying the Delayed Choice Experiments by Bram Gaasbeek.

 

[bhobba]

If "which way" is just a heuristic aid in thinking about experiment / set up, what is the rigorous way?

Th full mathematical theory as found in books like Ballentine.

Thanks
Bill