What are the implications of this experiment?

[Demystifier]

I wonder if the following is the case.

1. The experiment satisfies Standard Quantum Mechanics.
2. But the experiment doesn't satisfy Copenhagen (which in its purest form is about
having no trajectory of any kind even for ensembles)
3. But Modern Standard QM already embedded Copenhagen and Bohmian in the Trajectory
4. Hence the experiment satisfies Standard Quantum Mechanics but not Copenhagen.

Which part do you agree and don't.
I wonder which part IllyaKuryakin agrees and doesn't.
It's possible we are all having some semantic mismatch in the agreements.

Have you ever heard about Ehrenfest theorem?
http://en.wikipedia.org/wiki/Ehrenfest_theorem
This is one way how the old-fashioned Copenhagen QM introduces SOME trajectories. If you understand that, then it may help you to say that weak trajectories are something similar.

 

[DevilsAvocado]

To say it friendly, the Wikipedia article on "wave-particle duality" is somewhat misleading.

So why don’t you make it right? I’m especially interested in your rewriting on this:

http://en.wikipedia.org/wiki/Wave–particle_duality#Treatment_in_modern_quantum_mechanics

Treatment in modern quantum mechanics

Wave–particle duality is deeply embedded into the foundations of quantum mechanics, so well that modern practitioners rarely discuss it as such. In the formalism of the theory, all the information about a particle is encoded in its wave function, a complex valued function roughly analogous to the amplitude of a wave at each point in space. This function evolves according to a differential equation (generically called the Schrödinger equation), and this equation gives rise to wave-like phenomena such as interference and diffraction.

The particle-like behavior is most evident due to phenomena associated with measurement in quantum mechanics. Upon measuring the location of the particle, the wave-function will randomly "collapse," or rather, "decoheres" to a sharply peaked function at some location, with the likelihood of any particular location equal to the squared amplitude of the wave-function there. The measurement will return a well-defined position, (subject to uncertainty), a property traditionally associated with particles.

Although this picture is somewhat simplified (to the non-relativistic case), it is adequate to capture the essence of current thinking on the phenomena historically called "wave–particle duality".

Look, I think you are reading too much into this. My use of "wave-particle duality" is not because I’m a CI fundamentalist; I’m not married to any interpretation (yet). I used it in a more general term. AFAIK you do have both a Pilot Wave and Particles in dBB, for example.

"Wave-particle duality" was a notion of the socalled "old quantum mechanics", which is full of such paradoxes and leads in almost all cases to wrong predictions. E.g., the Bohr-Sommerfeld model of the hydrogen atom by chance predicts the correct energy levels (using an ad hoc hypothesis on how to select the "allowed trajectories of the electron in phase space") but it totally fails to predict the shape of hydrogen atoms, which are in their ground state spheres, not little circular disks. Old quantum theory cannot explain atoms with one than more electrons without introducing new "rules". That's not what physicists call a fundamental theory.

Yeah I know; that’s why Niels Bohr got the 1922 Nobel Prize in physics "for his services in the investigation of the structure of atoms and of the radiation emanating from them".

This is Bohr’s own words on QM formalism from 1948:

"The entire formalism is to be considered as a tool for deriving predictions, of definite or statistical character, as regards information obtainable under experimental conditions described in classical terms and specified by means of parameters entering into the algebraic or differential equations of which the matrices or the wave-functions, respectively, are solutions. These symbols themselves, as is indicated already by the use of imaginary numbers, are not susceptible to pictorial interpretation; and even derived real functions like densities and currents are only to be regarded as expressing the probabilities for the occurrence of individual events observable under well-defined experimental conditions. (Bohr, 1948, p. 314)"​

If you are trying to erase Niels Bohr from the history of QM, you’ve failed.

For this reason, they were looking all the time since 1900 (when Planck discovered the law describing the black-body spectrum) for a fully selfconsistent theory, and this has been found by Heisenberg in 1925 and then worked out by Born, Jordan, Heisenberg, Pauli and many others. A bit later the same theory has been discovered independently by Schrödinger ("wave mechanics") and by Dirac (the most general form). This is what is today called "quantum theory", and there you don't need any "wave-particle dualism", but you have a general framework to describe the behavior of particles and fields. In a sense particles and fields are unified to one fundamental principle, called quantum fields.

And I’m sure you know that Richard Feynman – one of the founding fathers of QED and the creator of Feynman diagrams used in QFT – once said about the double-slit experiment, that:

"All of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment."​

But please be my guest; describe what’s going on here, using only QFT and no "wave-particle dualism":

https://www.youtube.com/watch?v=FCoiyhC30bc

And while you’re at it, could you please explain how electron microscopy works without any reference to wave-particle duality?

This new hype about "trajectories of photons" measured in socalled weak measurements is a bit unjustified since the findings, while quite interesting, do not contradict quantum theory at all.

Who said it contradicts QM??

As massless particles with spin 1 there's not even a well-defined position observable at all! Thus, one can not find a limit where to interpret a photon as a quasiclassical particle.

Where’s the limit for calling it a field?

 

[Cthugha]

And while you’re at it, could you please explain how electron microscopy works without any reference to wave-particle duality?

This duality questions comes up so often on these forums that there even is a FAQ entry on why there is no real duality in qm and it should not be regarded as such. See the following link:
https://www.physicsforums.com/showpost.php?p=867751&postcount=3"

 

[Ken G]

I wonder if the following is the case.

1. The experiment satisfies Standard Quantum Mechanics.
2. But the experiment doesn't satisfy Copenhagen (which in its purest form is about
having no trajectory of any kind even for ensembles)
3. But Modern Standard QM already embedded Copenhagen and Bohmian in the Trajectory
4. Hence the experiment satisfies Standard Quantum Mechanics but not Copenhagen.

Which part do you agree and don't.

The problem is in interpreting what CI says. There is nothing in this experiment that does not satisfy the CI just fine, because the CI has a correspondence principle (it is a lynchpin of the CI, they invented it, http://en.wikipedia.org/wiki/Correspondence_principle), and this experiment is a mundane example of the correspondence principle. CI does not say you get no concept of "average trajectory" at the macro level, it says you get no concept of a particular trajectory at the quantum level. Which you don't. (This is also related to Demystifier's excellent point about Ehrenfest's theorem, which dovetails nicely with the correspondence principle.)

 

[Ken G]

If they indeed performed measurements on photons and it is between emitter and detector. Then it is already Bohmian in spirit! Because in Copenhagen.. what happens between emission and detection is close door or invalid. So if a photon is indeed detected. Then it's no longer Copenhagen even if position is not well defined like full blood Bohmian pilot wave and particle ontology!

I'm afraid the problem here is entirely in a misunderstanding of the CI. People apparently think Bohr and Heisenberg were buffoons who weren't aware of Einstein's Nobel prize for the photon nature of light! In actuality, the CI is fine with the photon concept. The CI is an interpretation of quantum mechanics (read it like this: quantum mechanics). What you are referring to is the fact that the CI makes assertions about photons only after the experiment is done on them. So what the photon did is just what it was detected to do, and nothing more. So to do CI, all you have to do is assert nothing except what was actually measured, it's very easy.

 

[Ken G]

My use of "wave-particle duality" is not because I’m a CI fundamentalist; I’m not married to any interpretation (yet).

Actually, I think your Wiki is just fine, and the FAQ at https://www.physicsforums.com/showpos...51&postcount=3 also makes good points but reaches a bizarre conclusion in my opinion. It basically says waves and particles are unified in QM, which I completely agree with, but then says that means there's no duality, which in my mind gives a pretty strange interpretation of the meaning of the word "duality". Duality is all about taking seemingly different things, like waves and particles, and showing how they can be unified into a single thing. Look at how "duality" is used in string theory, or the mathematical concept of a "dual space." There's no connotation of unresolved paradox in the term duality, and quantum mechanics is a beautiful example of the duality concept, as applied to the particle and wave concepts. Indeed, one could easily argue that the crowning achievement of quantum mechanics is explaining, to whatever extent physics theories can explain, the duality of particles and waves.

So what I'm saying is, the real culprit here, and this is the real motivator of that FAQ entry, is not the phrase "wave-particle duality", which is fully appropriate. The real culprit is in the kind of wishy-washy "this is a paradox" way that wave-particle duality gets talked about. Like so many other things in physics, they are only paradoxes when one applies a kind of naive realism born from everyday experience. The whole point of a physics theory is to get past the naive impression of paradox and into an understanding of why there is no paradox, and that's just exactly what "duality" means.

 

[AntonL]

Another group of scientist are using "weak measurement" to bypass Heisenberg uncertainty principle and measure the wave-function of a single photon

http://physicsworld.com/cws/article/news/46284

 

[Ken G]

As soon as I clicked on your link, I was thinking, "so when are they going to add together lots of measurements and pretend they all somehow apply to a single wavefunction." It's just another classical limit, what's the big mystery here. I just really want one of these authors to say "when we add up the results of all these weak measurements, we get information not contained in the classical limit because..." , because I just don't see any additional information there. What outcomes are they gaining predictive power over?

 

[unusualname]

As soon as I clicked on your link, I was thinking, "so when are they going to add together lots of measurements and pretend they all somehow apply to a single wavefunction." It's just another classical limit, what's the big mystery here. I just really want one of these authors to say "when we add up the results of all these weak measurements, we get information not contained in the classical limit because..." , because I just don't see any additional information there. What outcomes are they gaining predictive power over?

The classical limit is a wavefunction? I'd love to see the classical derivation of that!

 

[Ken G]

The classical limit is a wavefunction? I'd love to see the classical derivation of that!

The classical limit is wave function, not a wavefunction. But yes, it certainly is, have you ever seen a classical wave calculation? The classical wave function is a real function in practice, but in calculations it is almost always easier to treat it as a complex function, and then restrict to real answers only when you actually fit to the measured boundary conditions. Since you never fit a quantum wavefunction to boundary conditions, since you can't measure them, it's not suprising this step doesn't come up. But in both cases, fluxes are controlled by the squared amplitudes of the wave functions, and the measured quantities are real. Look at classical radio astronomy, for example.

This "classical limit" business is really very simple. Just tell me something that these people can measure with "weak measurements", and then add up a whole bunch of them, and come up with a bit of information that I cannot tell you how to get that same information classically. I already covered the "average trajectory" diagram, and no information has been offered to even suggest it is not the same as a classical flux streamline diagram.

 

[unusualname]

The classical limit is wave function, not a wavefunction. But yes, it certainly is, have you ever seen a classical wave calculation? The classical wave function is a real function in practice, but in calculations it is almost always easier to treat it as a complex function, and then restrict to real answers only when you actually fit to the measured boundary conditions. Since you never fit a quantum wavefunction to boundary conditions, since you can't measure them, it's not suprising this step doesn't come up. But in both cases, fluxes are controlled by the squared amplitudes of the wave functions, and the measured quantities are real. Look at classical radio astronomy, for example.

so another experiment, this one published in Nature: http://www.nature.com/nature/journal/v474/n7350/full/nature10120.html, misleading everybody you think?

 

[Ken G]

Well, that is certainly a very different experimental claim than the one this thread is based on. And I could also point out that of course they are not measuring the wave function, because any wave function has an arbitrary uniform complex phase. They claim to get both the real and imaginary parts, which would mean they know that arbitrary phase, which would violate some pretty deeply held symmetries of physics. So yes, they are definitely misleading people by not mentioning that their "measurements" must only be unique up to an arbitrary overall phase, so cannot really be a measurement of the real and imaginary parts of the wave function. But that may be a bit of a nitpick-- what actual significance they have achieved is a matter for another thread, one that does not deal with trajectories or the deBB, since this experiment you cite has nothing to do with those.

 

[unusualname]

Well, that is certainly a very different experimental claim than the one this thread is based on. And I could also point out that of course they are not measuring the wave function, because any wave function has an arbitrary uniform complex phase. They claim to get both the real and imaginary parts, which would mean they know that arbitrary phase, which would violate some pretty deeply held symmetries of physics. So yes, they are definitely misleading people by not mentioning that their "measurements" must only be unique up to an arbitrary overall phase, so cannot really be a measurement of the real and imaginary parts of the wave function. But that may be a bit of a nitpick-- what actual significance they have achieved is a matter for another thread, one that does not deal with trajectories or the deBB, since this experiment you cite has nothing to do with those.

Yes but I was only responding to your post about http://www.nature.com/nature/journal/v474/n7350/full/nature10120.html where you suggest this supports your idea that only buffoons are doing weak measurements experiments, and any results can be reproduced classically. I thought this one was not supporting your case really (pun intended)

 

[Ken G]

To be accurate, I never said the first thing about weak measurements. Everything I said referred to adding up a huge aggregate of weak measurements, and thinking that the correspondence principle will somehow be momentarily abrogated just because weak measurements were involved. That's what I'm talking about. Just exactly what a weak measurement, by itself, is is probably worthy of a different thread, because this thread is about a particular way of using them, that I claim is drawing conclusions that are pretty clearly unsubstantiated until someone can answer my question:
what information is reflected in the "average trajectory" plot of this experiment that is not obtainable classically, and what evidence is there that the average trajectory plot is not the same as a classical flux streamline diagram? I still await the answer to this simple question, that the referee of that paper should have also asked.

 

[unusualname]

To be accurate, I never said the first thing about weak measurements. Everything I said referred to adding up a huge aggregate of weak measurements, and thinking that the correspondence principle will somehow be momentarily abrogated just because weak measurements were involved. That's what I'm talking about. Just exactly what a weak measurement, by itself, is is probably worthy of a different thread, because this thread is about a particular way of using them, that I claim is drawing conclusions that are pretty clearly unsubstantiated until someone can answer my question:
what information is reflected in the "average trajectory" plot of this experiment that is not obtainable classically, and what evidence is there that the average trajectory plot is not the same as a classical flux streamline diagram? I still await the answer to this simple question, that the referee of that paper should have also asked.

I agree, but you didn't find the classical derivation yourself, I pointed out the 1976 paper by Prosser which does derive this (pdf download) (Already referenced by the bohmians in Bohmian trajectories for photons )

So you were kinda guessing, and in the single photon case it turns out you were correct.

But now it seems there are results obtained by this method which you can't reduce to a "classical explanation", and in fact suppose the hypothetical experiment for the two-photon system may be done soon. If it matches the "trajectories" derived by Ghose et al will you withdraw your assertion that these experiments are not showing anything interesting, even if the Bohmian analysis is the simplest prediction of the results?

 

[Ken G]

I agree, but you didn't find the classical derivation yourself, I pointed out the 1976 paper by Prosser which does derive this (pdf download) (Already referenced by the bohmians in Bohmian trajectories for photons )

So you were kinda guessing, and in the single photon case it turns out you were correct.

Actually, I feel I gave a solid plausibility argument, I wouldn't call it a guess. But I do appreciate your more authoritative reference, not that it seemed to make any difference to those who already had different opinions.

But now it seems there are results obtained by this method which you can't reduce to a "classical explanation", and in fact suppose the hypothetical experiment for the two-photon system may be done soon.

My comments were about this thread, and the implications of that one experiment. In particular, if there was any problem with the Copenhagen interpretation of the "average trajectory" concept. By arguing the concept is classical, I refuted any claims that there were. That was all I was trying to do.

If it matches the "trajectories" derived by Ghose et al will you withdraw your assertion that these experiments are not showing anything interesting, even if the Bohmian analysis is the simplest prediction of the results?

If anyone can show that averaging lots of weak measurements give trajectories that somehow mean something more about what the individual photons are doing than what you can get from classical flux streamlines, then yes, I will agree that there is something more to it. If, on the other hand, if there is not such a difference, you will admit the claims of the authors is overblown.

 

[unusualname]

If anyone can show that averaging lots of weak measurements give trajectories that somehow mean something more about what the individual photons are doing than what you can get from classical flux streamlines, then yes, I will agree that there is something more to it. If, on the other hand, if there is not such a difference, you will admit the claims of the authors is overblown.

You won't get any "classical flux streams" for a two-photon experiment.

personally, I think dBB is wrong, but it is (temporally) interesting if they can calculate the outcomes of such experiments (which admittedly haven't been done yet)

(ie I think it will be shown to be more to do with how we are measuring things than how nature actually is)

 

[Ken G]

You won't get any "classical flux streams" for a two-photon experiment.

OK, but this thread is about an experiment of single photons. If you want to start a two-photon thread and talk about that, go ahead, but what I'm saying here is quite focused on the question in the OP of this thread.

personally, I think dBB is wrong, but it is (temporally) interesting if they can calculate the outcomes of such experiments (which admittedly haven't been done yet)

I agree there might be something interesting there, or there might not be, but it's a different issue.

(ie I think it will be shown to be more to do with how we are measuring things than how nature actually is)

I think that too.

 

[Demystifier]

Here is the explicit verification that the measured trajectories are indeed the Bohmian ones:
http://xxx.lanl.gov/abs/1109.4436

 

[Ken G]

Excellent, the paper makes my point perfectly, as in the main conclusion: " In this way, one concludes again that they Bohm trajectories are simply hydrodynamical and kinematically portraying the evolution of the probability density. The average photon trajectories can be viewed likewise."
You see, I never said the Bohm trajectories didn't work, I said there was no evidence they were any different from a classical interpretation of an ensemble, like a garden variety sound wave. I believe this paper shows I was right. The paper flat out says : "Many adherents to Bohm’s version of quantum mechanics assert that the trajectories are what particles actually do in nature. From the experimental results above no one would claim that photons actually traversed these trajectories, since the momentum was only measured on average and the pixel size of the CCD is still quite large. Other views of Bohm’s trajectories do not go as far as to claim that they are what particles actually do in nature. "

 

[vijayan_t]

See this

 

[Demystifier]

So now someone needs to weakly measure the average trajectories for the two-photon case!

Back to the labs guys.

Now we have a concrete proposal:
http://lanl.arxiv.org/abs/1207.2794

 

[unusualname]

Now we have a concrete proposal:
http://lanl.arxiv.org/abs/1207.2794

Yes, but non-locality is obvious in QM, what Bohmian Mechanics needs to show is determinism.

(By non-locality being obvious, I mean it's obvious according to the numerous EPR Bell-type experiments.)

I doubt the results of the experiment proposed in this paper will be at all interesting unless it becomes necessary to calculate trajectories in such a setup on industrial scales - then the Bohm method might be useful. :-)

 

[Demystifier]

The weakly measured trajectories ARE deterministic, so I don't understand what do you mean that "BM needs to show determinism".

 

[unusualname]

The weakly measured trajectories ARE deterministic, so I don't understand what do you mean that "BM needs to show determinism".

I mean that all QM models would predict the trajectories if the correct calculations are carried out (maybe the Bohm calculation is more efficient, but doesn't mean zilch regarding Nature)
and so BM adherents need something much more convincing, like a (anti) Bell type argument to show determinism is possible. ie construct an experiment where pre-existing properties can be proved to have existed.

And of course you have the HUGE problem of explaining the Standard Model from BM, which will be difficult since BM doesn't even have concept of quantum spin degree of freedom.

 

[Demystifier]

I mean that all QM models would predict the trajectories if the correct calculations are carried out (maybe the Bohm calculation is more efficient, but doesn't mean zilch regarding Nature)
and so BM adherents need something much more convincing, like a (anti) Bell type argument to show determinism is possible. ie construct an experiment where pre-existing properties can be proved to have existed.

If you are pointing out that these weakly measured trajectories do not prove that Bohmian interpretation is correct, then I agree.

And of course you have the HUGE problem of explaining the Standard Model from BM, which will be difficult since BM doesn't even have concept of quantum spin degree of freedom.

There is no such problem for BM. First, BM contains wave functions which DO have spin degrees of freedom. Second, when spin is measured, e.g., by Stern-Gerlach apparatus, then what is really measured is not spin as such, but a position of a particle.

For more details see also
http://xxx.lanl.gov/abs/1205.1992 (a chapter in a published book)