Thread: How quantum is wave-particle duality of Couder's walking droplets?

There are getting popularity great Couder's experiments about classical objects having wave-particle duality: oil droplets on vertically vibrating liquid surface - constantly creating periodic waves around. interaction with these ("pilot") waves allows us to observe 'quantum effects':interference pattern in double-slit experiment (particle goes a single trajectory, but it interacts with waves it created - going through all trajectories), tunneling depending on practically random hidden parameters (highly complex state of the field) or orbit quatization condition - that particle has to 'find a resonance' with the field - after single orbit, its internal phase has to return to the initial state.
It's difficult to find good intuition about these experiments from only static pictures - the first time I had occasion to see videos was recent congress on emergent quantum mechanics where Couder had the opening lecture and most of speakers were excited about these experiments. Fortunately I've recently found a youtube video of these experiments:


Some free materials: two-slit experiment paper, Europhysicsnews general paper, slides.
The main qualitative difference with microscopic physics is that while Couder uses external clock, particles should rather have internal one - such understanding of wave-particle duality was started by de Broglie in his doctoral thesis:
that with particle's energy: E = mc^2
comes some internal periodic process: E = hf
It is reminded in very interesting Hestenes paper, in which there is also described recent experimental confirmation of this effect (called e.g. zitterbewegung): http://fqxi.org/data/essay-contest-f..._time_essa.pdf
Such internal periodic motion creates periodic wave-like perturbations of surrounding field - giving localized entity also wave nature ... localized constructions of the field are called soltions, so it suggests to search for particles solitons models, which often have such internal periodic motion, like breathers.

What do you think about these experiments? About such understanding of wave-particle duality?
Have particles both natures simultaneously, or maybe only one of them in one time?
In such case, when and how it is switched? What about Afshar experiment?

update: there has just appeared proceedings (with summarizing article) from mentioned recent Emergent Quantum Mechanics congress in Vienna in which Couder had the opening lecture: http://iopscience.iop.org/1742-6596/361/1

update: good fresh 108 pages presentation http://www.physics.utoronto.ca/~coll...der/Couder.pdf

You have left out the option I would have voted for: "it means they are neither particles nor waves but something which has some attributes we associate with those classical (macroscopic) phenomena as well as other attributes which do not relate to either".

OK. That might be a bit long for the poll...

Strange, I thought about "it's more complicated" option, but I think the classification is quite clear:
- wave - delocalized, with some phase (periodic motion) involved - expressed mainly in interference, orbit quantization,
- corpuscular - there is some localized entity involved, like most of the mass density is in a tiny ball (e.g. 10^-15m for electron), or especially the center of charge - singularity of electric field. It expresses e.g. in colliders for which electron is practically zero radius. There is also no blurring of charge observed.

So is there something delocalized, phase related associated with particles?
Do particles have some region where their mass/charge is localized?
Aren't these yes or no questions?
I know the standard answer is "it's complicated", nobody will ever understand it, just "shut up and calculate" ... but does this status quo has stronger base than socio-historical?
What's wrong with answer of these experiments that it's quite simple and intuitive?

Here is Feynman quote about interference from his QM book:
« … In this chapter we shall tackle immediately the basic element of the mysterious behavior in its most strange form. We choose to examin a phenomenon which is impossible, absolutely impossible, to explain in any classical way and which is at the heart of quantum mechanics. In reality it contains the only mystery. We cannot make the mystery go away by explaining how it works . We will just tell you how it works.… »
Does it still apply after Couder's interference?

I'm actually not saying "it's complicated." I'm just saying that the "duality" may be an artefact of a mistaken attempt to classify things incorrectly. The "wave" and "particle" (or "corpuscle" if you prefer) descriptions may just be analogies we try and apply based on our experience in the macroscopic world. But we are applying these to "things" which aren't waves or particles.

I think Couder's experiments are interesting; they may be a useful analogy of some aspects of quantum behaviour that inspire new ways of thinking. I'm not sure they can be taken too literally as meaning that electrons are like drops bouncing on a fluid (the aether?).

The Hestenes article is very interesting. I haven't come across the zitter-electron idea before (and I don't know enough to say anything other than: "interesting").

Originally Posted by Strange

I'm actually not saying "it's complicated." I'm just saying that the "duality" may be an artefact of a mistaken attempt to classify things incorrectly. The "wave" and "particle" (or "corpuscle" if you prefer) descriptions may just be analogies we try and apply based on our experience in the macroscopic world. But we are applying these to "things" which aren't waves or particles.

So you say we should search for the answer out of entities of this world we have experience about ... and it's not complicated?
So where should we search? In parallel universes? String theories in dozens of dimensions? Noncommutative geometries? ... you probably want to say you don't know, but still don't agree with simple answers ... what's wrong with them?

I think Couder's experiments are interesting; they may be a useful analogy of some aspects of quantum behaviour that inspire new ways of thinking. I'm not sure they can be taken too literally as meaning that electrons are like drops bouncing on a fluid (the aether?).

Nowadays the "aether" is Lorentz invariant and called a field - like electromagnetic.
There is no problem to expand this field a bit to additionally allow for topological solitons e.g. in the center of charge - to avoid infinities requires deforming EM field into weak/strong interaction, what requires additional energy density - gives particle mass ... Ellipsoid field solitons - particle menagerie correspondence? - Science Forums
You'd probably say that electron stops being corpuscle in orbital? So look at modern classical approximations: Free-fall atomic model - Wikipedia, the free encyclopedia
For longer times it becomes so complicated that only thermodynamical considerations become reasonable ... and doing it right (e.g. maximizing entropy) leads to that because of fluctuations, classical trajectories are stochastically shifted exactly toward densities of near quantum eigenstates: http://arxiv.org/pdf/1111.2253
But still we also need Schrodinger's picture - amplitudes describing probabilities and phases describing expected relative phase (of the internal periodic motion) while being in given point.

The Hestenes article is very interesting. I haven't come across the zitter-electron idea before (and I don't know enough to say anything other than: "interesting").

Internal periodic motion is quite natural for localized configurations of field (solitons), look for example at animations here: Breather - Wikipedia, the free encyclopedia

Originally Posted by Jarek Duda

So you say we should search for the answer out of entities of this world we have experience about ... and it's not complicated?

I'm just saying it is wrong to think of electrons (or whatever) as little billiard balls which can turn into waves (or as wavy-billiard balls). They are neither of these things. They are electrons and we have developed very accurate descriptions of them. And will, no doubt develop better ones. I don't see any reason why they should be intuitively understandable as if they were billiard balls. They are what they are.

So where should we search?

In the real world where we have already found so much.

There is no problem to expand this field a bit to additionally allow for topological solitons e.g. in the center of charge - to avoid infinities requires deforming EM field into weak/strong interaction, what requires additional energy density - gives particle mass ...

Or maybe it is deformations in the space-time defined by loop quantum gravity. Who knows.

You'd probably say that electron stops being corpuscle in orbital?

I'd say that maybe they never were "corpuscles" (1) and in an orbital they are electrons as they are everywhere else.

(1) "corpuscle" has a very old fashioned sound, almost Newtonian.

Originally Posted by Strange

I'm just saying it is wrong to think of electrons (or whatever) as little billiard balls which can turn into waves (or as wavy-billiard balls). They are neither of these things. They are electrons and we have developed very accurate descriptions of them. And will, no doubt develop better ones. I don't see any reason why they should be intuitively understandable as if they were billiard balls. They are what they are.

Nobody is saying that they are like little billiard balls - there have also simultaneously wave nature involved.
Look at Couder's droplets - they are simultaneously localized objects and conjugated wave - it is conceptually simple, but leads to very nontrivial interactions/behavior.
We cannot forget about any half of this duality.

Or maybe it is deformations in the space-time defined by loop quantum gravity. Who knows.

Different concepts can lead to the same answers ... the fact is that EM field has no longer meaning in the center of charge, so it has to be somehow deformed there ... by the way electric field has also unit topological charge around ...

I'd say that maybe they never were "corpuscles" (1) and in an orbital they are electrons as they are everywhere else.
(1) "corpuscle" has a very old fashioned sound, almost Newtonian.

Newtonian?? brrrrrrrrrr
Wait ... wasn't quantum mechanics created on classical one? Aren't there WKB semiclassical approximations starting with classical ones? Isn't standard approach to calculate Feynman path integrals considering perturbations of classical trajectory? ...
Want it or not - classical mechanics is deeply hidden in quantum - as some approximation to which we add hbar: wave nature.
And so for Couder's droplets - in some approximation they behave classically, than you add wave nature to considerations.

@Jarek
You also left out the most obvious answer with regard to Couder's quantum analogy: Particles are corpuscles and steered by a wave in phase with the motion of the particle.

materion, I think you are referring to Bohm's pilot wave?
Of course this wave has essential influence on the motion of the particle - greatly expressed in the movie.
The current state of the field store in deep way the history of the system, which mostly expresses as fluctuations, like in Couder's explanation of tunneling. Adding fluctuations to considerations is made by using thermodynamical models - an so models based on Maximal Entropy Random Walk leads to probability density being squares of coordinates of dominant eigenstate of Hamiltonian for given situation, like Schrodinger or Bose-Hubbard - going to the ground state as quantum mechanics would thermodynamically predict.

From the other side there are also results of synchronizing the phases, like in orbit quantization or interference.
Here is nice picture from paper of prof. Croca - the corpuscle/charge goes single path, but wave it created (so called theta wave) also goes the other (similarly as for Couder's droplets) - resulting in interference:

croca.jpg

Originally Posted by Jarek Duda

I think you are referring to Bohm's pilot wave?

Well, nearly, I'm referring to my opinion, which is influenced by de Broglie, Bohm, Couder, etc, but slightly different. You may check my essay on the subject at FQXi FQXi Community
My experience is that it makes quantum behaviour intuitive.

Thanks for Croca reference.

Arjen Dijksman

Originally Posted by Jarek Duda

Have particles both natures simultaneously, or maybe only one of them in one time?

Quantum objects have both wave and particle characteristics, yet cannot be fully described by either of those.

Originally Posted by Jarek Duda

So is there something delocalized, phase related associated with particles?
Do particles have some region where their mass/charge is localized?
Aren't these yes or no questions?

They're not yes or no questions, because the HUP makes it impossible to determine all properties of the quantum object simultaneously with arbitrary precision. Thus it depends on which observable you choose to measure, and how you do it.

Arjen,
thanks for the essay - there are plenty of ways for seeing the wave nature, like dBB or your needles and qualitatively they are similar.
I see Gerhard Groessing has commented your essay - he was the organizer of the conference I've mentioned - most of speakers there was talking about similar models of interference.
... around and around almost a century old de Broglie's idea ... but are we moving forward?
Ok, so probably all but defenders of orthodox mystery agree that situation looks somehow like in dBB, especially it is equivalent with Schrodinger picture ... so what's now?

To try to make a step forward, we need to start searching for models of particles ...
Extend the concept of electromagnetic field to handle with singularity in the charge, explain its quantization, add mass to this localized object ... search for soliton particle models...

Originally Posted by Markus Hanke

Originally Posted by Jarek Duda

So is there something delocalized, phase related associated with particles?
Do particles have some region where their mass/charge is localized?
Aren't these yes or no questions?

They're not yes or no questions, because the HUP makes it impossible to determine all properties of the quantum object simultaneously with arbitrary precision. Thus it depends on which observable you choose to measure, and how you do it.

HUP restricts measurement capabilities - of extremely complicated processes.
The question is about objective situation - HUP says nothing about it ... while considering wavefunction, you use muuuch better precision than measurable.

Originally Posted by Jarek Duda

HUP restricts measurement capabilities - of extremely complicated processes.

No, it's simple pairs of variables, like position and momentum for example.

From continuous wavefunction it returns a single position/momentum. Does it mean this wavefunction contained only this position/momentum?

ps. How would you measure both in a simple way???

Apropos, there is nice way to measure where was (localized?) electron before being ripped off by potential: http://physicsbuzz.physicscentral.co...-of-atoms.html

671260397.jpg

Oh, here are another interesting measurements - of average trajectories of interfering single photons in two-slit experiment:
http://www.sciencemag.org/content/33.../1170.abstract

double1.jpg

From continuous wavefunction it returns a single position/momentum. Does it mean this wavefunction contained only this position/momentum?
ps. How would you measure both in a simple way???

I see what you mean. The actual measurement is of course never simple, I agree. And you can't measure them both at the same time with arbitrary precision anyway.
What I meant to say was rather that the observables themselves are simple variables like momentum, velocity, energy etc, not complex wave functions. We do not measure wave functions, only observables.

Indeed, from the point of view of "standard quantum mechanics" everything is simple - just draw a prism, half-silvered mirror and voila - you only have to make philosophy about these few lines ...
But is it so simple? So how does half-silvered mirror works? This EM interaction of trillions of particles ... Or maybe let's start with"simpler" questions, like: what is EM field configuration of a single photon?
You might look at measurement results as simple abstract entities ... but still you should have in mind that in fact there is extremely complicated reality behind this idealization ...
But it was only post scriptum ...

My main point was that the wavefunction contains muuuuuuuch more information than measurement result.
HUP restricts only the second - it says absolutely nothing about the behavior of wavefunction.
As you have written - "HUP makes it impossible to determine all properties of the quantum object simultaneously with arbitrary precision" ... but it doesn't say that objectively they have no these properties - only that we cannot measure them.
Let's focus on the search for objective physics - focusing on subjective one would be like saying that there was no wavefunction behind observation we got.

Originally Posted by Jarek Duda

what is EM field configuration of a single photon?

The EM field does not self-couple ( unlike the gravitational field, for example ), and therefore a single photon does not carry any EM field.

My main point was that the wavefunction contains muuuuuuuch more information than measurement result.

Yes, it contains all possible measurement results, and the correlations between them.

HUP restricts only the second - it says absolutely nothing about the behavior of wavefunction.

Yes, I agree.

but it doesn't say that objectively they have no these properties - only that we cannot measure them.

Interesting thought - I am not actually sure about whether this is right or not. I totally agree about the measurement bit, but the other thing...? Mathematically you get from one picture to the other via Fourier transformations, so e.g. if you have a wave function in the momentum formulation you can get to the position formulation by performing a Fourier transform. There is no formulation of the wave function which directly relates both of them without using integral transforms. So how is this interpreted in real life ?

Originally Posted by Markus Hanke

Originally Posted by Jarek Duda

what is EM field configuration of a single photon?

The EM field does not self-couple ( unlike the gravitational field, for example ), and therefore a single photon does not carry any EM field.

You want to say that photon has nothing to do with EM field??????????? I thought even orthodoxians called photon a carrier/quant of EM interaction?

How optical photon is created? By changing spin of electron by one: e.g. from -1/2 to +1/2 ... in other words: by turning photon 180deg, not true?
Because of Noether theorem, angular momentum conservation creates then twist-like wave of (EM) field (like behind marine propeller): a photon carrying angular momentum, not true?
The difference from marine propeller is that there is no viscosity in this field - twist-like wave doesn't dissipate, but can be produced by a single atom and much later absorbed by another single atom, like while watching 'undeformed' single photons from different galaxies.

deexcitation_rs.jpg

Where vortex line is transversal intersection of Re(phi)=0 and Im(phi)=0 submanifolds - where wavefunction is zero and quantum phase makes 2pi rotation while looking at loop around such line - it means there is a single magnetic flux quant going through such loop (phase difference on path P is ).

My main point was that the wavefunction contains muuuuuuuch more information than measurement result.

Yes, it contains all possible measurement results, and the correlations between them.

Not true - it contains only probability density of possible measurement results.
However, it still contains much more information, which evolves in unique unitary way ... until wavefunction collapse like a measurement ...

Does collapse mean that QM has stopped working? Not really ...
Using simple nice pictures and simplified QM of a few entities is practical QM - neglecting enormous amount of parameters seen only as an environment.
Expanding the set of objects our quantum mechanical considerations contain, can result in that this collapse remains unitary evolution ...
Such considerations quickly becomes unpractical, but imagining quantum mechanics expanded to the whole universe - such finally fundamental QM of the wavefunction of the Universe, would no longer have an environment - there would be no longer wavefunction collapse there. Atoms of our bodies, of our measurement apparatus are a part of unitary evolution of this wavefunction.
And so, as you've agreed - HUP has nothing to do with the evolution of wavefunction of the universe - everything is objectively defined in such picture - picture unreachable by our calculations, but which we should have in mind to understand the foundations of our reality.

There is no formulation of the wave function which directly relates both of them without using integral transforms.

Fourier transform is unitary - is only rotation - only changes the point of view on the same information - there is no need for using simultaneously both of them.

Originally Posted by Jarek Duda

You want to say that photon has nothing to do with EM field?

No Jarek, what I said was that a single photon does not carry its own EM field. In other words, a single photon does not emit another photon to self-interact. Please be more careful when you read my comments.

Not true - it contains only probability density of possible measurement results.

Did you not say it contains much more than measurement results ? Of course we understand that these results are defined by probability densities.
Sorry, I think I lost you here now. What are you trying to say ?

such finally fundamental QM of the wavefunction of the Universe, would no longer have an environment - there would be no longer wavefunction collapse there.

I assume you are referring to the Wheeler deWitt equation ? The resulting wave function is only a geometrical boundary metric, there is still wave function collapse taking place ( at least so far as I understand it ).

And so, as you've agreed - HUP has nothing to do with the evolution of wavefunction of the universe

Jarek, I agreed to no such thing. We had not before spoken about the wave function of the universe. What I agreed to was only this (quote) : "HUP restricts only the second - it says absolutely nothing about the behavior of wave function."
I must urge you to be more careful in replying to posts, and not to put words into people's mouths. This is very bad form.

Originally Posted by Markus Hanke

No Jarek, what I said was that a single photon does not carry its own EM field. In other words, a single photon does not emit another photon to self-interact. Please be more careful when you read my comments.

You have written "a single photon does not carry any EM field." ... while it not only carry, but is a configuration of EM field.

Did you not say it contains much more than measurement results ? Of course we understand that these results are defined by probability densities.
Sorry, I think I lost you here now. What are you trying to say ?

No, I have written that "the wavefunction contains muuuuuuuch more information than measurement result" - continuous function contains much more information than a single value - I didn't say it also contain the measurement outcome, in such case I would probably write "contain also much more additional information".

I assume you are referring to the Wheeler deWitt equation ?

No, I'm not referring to any specific equation, but only to an idealized expansion of considered quantum mechanics to larger and larger systems up to the whole Universe - such that finally there is no longer environment oudside, so everything evolves in unitary way in such unreachable finally fundamental QM.
Interaction with environment is required for wavefunction collapse, not true?

Jarek, I agreed to no such thing. We had not before spoken about the wave function of the universe. What I agreed to was only this (quote) : "HUP restricts only the second - it says absolutely nothing about the behavior of wave function."

"the second" refers to measurement (wavefunction collapse) - can the observer be a part of measured quantum system?
From the point of view of idealized wavefunction of universe, there is no longer an external observer, wavefunction collapse - HUP doesn't apply.

Originally Posted by Jarek Duda

You have written "a single photon does not carry any EM field." ... while it not only carry, but is a configuration of EM field.

Yes, that is what I had written - and what I meant by that is that there is no EM field surrounding a single photon. It is not self-interacting, unlike gravity for example; that was also part of my sentence, but you cut that bit out.

No, I'm not referring to any specific equation, but only to an idealized expansion of considered quantum mechanics to larger and larger systems up to the whole Universe

That is in essence the Wheeler-deWitt equation.

Interaction with environment is required for wavefunction collapse, not true?

Interesting question, not sure what the answer to that is.

From the point of view of idealized wavefunction of universe, there is no longer an external observer, wavefunction collapse - HUP doesn't apply.

If there is no wave function collapse, then there is no value to the observables. The question doesn't make sense. How do you decide if the HUP applies or not if there is no one there to perform a measurement ?

Originally Posted by Markus Hanke

Yes, that is what I had written - and what I meant by that is that there is no EM field surrounding a single photon. It is not self-interacting, unlike gravity for example; that was also part of my sentence, but you cut that bit out.

I've read it once again and still would interpret as previously your answer to "what is EM field configuration of a single photon?" ... not important.
I think you focus too much on perturbative approximation - by definition this approximation rather cannot bring answer to this question - it replaces particles with abstracts, destribing their behaviour by some effective parameters.
So the question remains: what is EM field configuration of a single photon?
What does its "spin 1" means? Does it have magnetic moment?(no) Does it have angular momentum?(yes)
Why even after light years of travel it doesn't dissipate? (is soliton)

That is in essence the Wheeler-deWitt equation.

I don't think we are ready to write some concrete equiations ... you just imagine Schrodinger equation for whole atom, a molecule ... system ... universe ...

Interaction with environment is required for wavefunction collapse, not true?

Interesting question, not sure what the answer to that is.

So what is wavefunction collapse? "Instant out of QM process"? Definitely not instant - e.g. photoemission takes a few attoseconds ( Delay in Photoemission Science 2010) - it is still a continuous processes while including e.g. surrounding EM field into considerations.

From the point of view of idealized wavefunction of universe, there is no longer an external observer, wavefunction collapse - HUP doesn't apply.

If there is no wave function collapse, then there is no value to the observables. The question doesn't make sense. How do you decide if the HUP applies or not if there is no one there to perform a measurement ?

If there is no place to apply something, it doesn't apply there - not true?

Good video! It's what I have been saying for years.

There is new PRL paper about these droplets: this time they show classical analogue of Zeeman effect: imagine e.g. (ortho-)positronium or proton-antiproton pair and turn on magnetic field along the axis they rotate around. Obtained force toward/outward the axis can be simulated by Coriolis force while rotating the pool.
There is discrete family of such bounded two-droplet states and while rotating the pool they observe splitting of their distances depending on the direction and velocity (fig. 2c).

The paper can be downloaded also from here: http://stilton.tnw.utwente.nl/people...ted/Zeeman.pdf
Here is news article: Bouncing droplets simulate Zeeman effect - physicsworld.com

Very nice new youtube presentation:

There are lots of new paper on this subject, like about trajectories averaging to quantum trajectories like in the video above: http://math.mit.edu/~bush/wordpress/...rrals-2013.pdf
or some general papers: http://math.mit.edu/~bush/wordpress/...7/MB1-2013.pdf , http://windw.dk/2013Bouncing.pdf
Here are some additional materials, videos: Walking droplets

If someone disagree that behavior of these droplets is analogous to quantum mechanical, look at de Broglie-Bohm interpretation:http://en.wikipedia.org/wiki/De_Brog...ry#Derivations
We just make Madelung transformation of Schrodinger equation: take psi=R exp(iS) and write equations for this action (S) and density rho=R^2. For density we get standard continuity equation, while for S we get Hamilton-Jacobi equation - exactly like for classical mechanics, but modified by h^2 correction because of interaction with these "pilot" waves of quantum phase.

If someone is worried if we can use such pictures of sub-quantum behavior because of Bell inequalities, here is a nice lecture and paper that these inequalities are violated e.g. in classical Ising model:
http://www.perimeterinstitute.ca/vid...-no-go-theorem
http://arxiv.org/vc/arxiv/papers/1211/1211.1411v1.pdf
so the belief that these inequalities should be fulfilled by local deterministic models is not true.

Originally Posted by Jarek Duda

Nowadays the "aether" is Lorentz invariant and called a field - like electromagnetic.
There is no problem to expand this field a bit to additionally allow for topological solitons e.g. in the center of charge - to avoid infinities requires deforming EM field into weak/strong interaction, what requires additional energy density - gives particle mass

What???

Originally Posted by Jarek Duda

To try to make a step forward, we need to start searching for models of particles ...
Extend the concept of electromagnetic field to handle with singularity in the charge, explain its quantization, add mass to this localized object ... search for soliton particle models...

That would be standard QED renormalization and regularization + standard Higgs mechanism

Originally Posted by Jarek Duda

As you have written - "HUP makes it impossible to determine all properties of the quantum object simultaneously with arbitrary precision" ... but it doesn't say that objectively they have no these properties - only that we cannot measure them.

This is wrong.

Originally Posted by Jarek Duda

Originally Posted by Markus Hanke

Originally Posted by Jarek Duda

what is EM field configuration of a single photon?

The EM field does not self-couple ( unlike the gravitational field, for example ), and therefore a single photon does not carry any EM field.

You have to specify which photon you mean. Real one or monochromatic planewave. If you mean planewave it`s obviously zero. If you mean some real state of light that contains approximtely 1 photon it`s fairly easy to calculate E once you write the state explicitly.

Originally Posted by Gere

What???
That would be standard QED renormalization and regularization + standard Higgs mechanism

There are lots of soliton models in physics, also of particles - here are some sources: Soliton particle models?
Here also Higgs potential has local maximum in zero, what gives solitons mass - exactly like in nice animation of soliton-antisoliton annihilation here: Topological defect - Wikipedia, the free encyclopedia

This is wrong.

What is wrong? That HUP restricts the possibilities of very sophisticated phenomenas: measurements?

You have to specify which photon you mean. Real one or monochromatic planewave. If you mean planewave it`s obviously zero. If you mean some real state of light that contains approximtely 1 photon it`s fairly easy to calculate E once you write the state explicitly.

Ok, so you have hydrogen excited to p and l=0 (zero orbital angular momentum) - it deexcitates to s state and produces optical photon: EM field carrying energy, momentum and angular momentum ... which travels without dissipation and can finally excite e.g. another hydrogen atom ... what is EM configuration of such photon? Where it got its angular momentum from?

I would say that it is a twist-like wave because of electron changing spin by 1 here: e.g. from -1/2 to +1/2, what means twisting by 180 deg - Noether theorem says that angular momentum has to be conserved by the field, so like behind marine propeller, such twist creates wave carrying angular momentum - photon.
In contrast to water, EM does not have viscosity, so this wave doesn't dissipate.
Here is nice a picture of two kinds of angular momentum of EM waves: http://en.wikipedia.org/wiki/Angular_momentum_of_light

Originally Posted by Jarek Duda

What is wrong? That HUP restricts the possibilities of very sophisticated phenomenas: measurements?

The HUP is not about measurement.

HUP says that if we would like to measure two noncommuting observables (properties of the system), their uncertainties have to be bounded by given relation.
If we are not performing measurements, what does it say?

Originally Posted by Jarek Duda

Here also Higgs potential has local maximum in zero, what gives solitons mass - exactly like in nice animation of soliton-antisoliton annihilation here: Topological defect - Wikipedia, the free encyclopedia

Yes it has but thats not what gives particles mass. Energetical minimum (vacuum) of Goldstone potential is not at zero but at constant radial distance from zero. That means that vacuum is infinitely degenerated and loses symmetry to phase transformation. Lagrangian is however symmetric to this transformation therefore we have to gauge our vacuum in order to get rid of unphysical Goldstone boson (angular component of general complex field) which in turn gives mass to (shifts its minimum) radial component of general complex field. This is simplest example of Higgs mechanism in case of complex scalar field with quartic selfinteraction.

Originally Posted by Jarek Duda

Ok, so you have hydrogen excited to p and l=0 (zero orbital angular momentum) - it deexcitates to s state and produces optical photon: EM field carrying energy, momentum and angular momentum ... which travels without dissipation and can finally excite e.g. another hydrogen atom ... what is EM configuration of such this photon? Where it got its angular momentum from?

where



where is annihilation operator ( is polarization) and is normalized lorentzian distribution in k space. The information about deexctitation and atom is in . Therefore you need to know profile of transition spectral line and it`s mean frequency. is basicaly that. Next you compute observable dependant on time like this.



If you have nothing to do you may perform commutations and integrate explicitly I`m not sure how long it will take though Thing is you won`t get anything surprising basicaly just almost planewave helix with a bit spread amplitude.

Originally Posted by Gere

Yes it has but thats not what gives particles mass. Energetical minimum (vacuum) of Goldstone potential is not at zero but at constant radial distance from zero. That means that vacuum is infinitely degenerated and loses symmetry to phase transformation.

You have exactly the same in soliton particle models.
For example imagine 2D vector field with Higgs-like potential V(v)=(1-|v|^2)^2
So this field energetically prefer to be unit vectors |v|=1, breaking the symmetry toward some direction in every point ... but if the field makes hedgehog-like configuration around some point (e.g. v(x)=x), in the center there cannot be chosen any direction: the field has to get to symmetric v=0 ... what costs potential energy - gives this topological soliton rest energy (mass) - exactly like in the wikipedia animation.
The vacuum dynamics - where potential is zero (|v|=1) is also electromagnetism here (zero mass Goldstone bosons). For example here is field configuration for two opposite topological charges in different distances:


we can see that the closer they are, the smaller stress (energy)of the field - opposite charges attract (analogously the same repel).
Here are papers of prof. Faber showing that you can get naturally Maxwell's equations for such topological charges: Particles as stable topological solitons - Abstract - Journal of Physics: Conference Series - IOPscience [hep-th/9910221] A Model for Topological Fermions

If you have nothing to do you may perform commutations and integrate explicitly I`m not sure how long it will take though Thing is you won`t get anything surprising basicaly just almost planewave helix with a bit spread amplitude.

Indeed in quantum mechanics we usually see photons as a plane waves ... but plane waves are waves in the whole spacetime - do you really think that a single hydrogen atom creates 3+1 dimensional wave of all sizes like the Universe?

Originally Posted by Jarek Duda

HUP says that if we would like to measure two noncommuting observables (properties of the system), their uncertainties have to be bounded by given relation.
If we are not performing measurements, what does it say?

It says that the values (strictly, the uncertainty in those values) are related in that way. It is nothing to do with limits of measurement.

Ok, you are right - values of observables ... we measure.
Like for position-momentum: it is relation between widths while performing Fourier transform. E.g. plane wave has no localization (is uniform in the whole spacetime), while Dirac delta (point particle) has uniform distribution in momentum space.

So there is some objective property (like a wave), but its values of operators are not Dirac deltas - while measurenments we ask physics about these values.

OK but this is far away from established physics. Topological theories are used only in very specific cases in condensed matter. Maybe it will work but as of today this is not the case.

"First of all, most of the work on solitons is formal theory - analyses of soliton solutions in QFTs that are interesting theoretically but that are known not to describe the Universe around us. Second, when one wants models of particle physics in our world, solitons typically carry "exotic" e.g. magnetic monopole charges, so they're bound to be heavy. This application of solitons is a small fraction of the soliton literature. Third, an even smaller fraction are exceptions - e.g. magnetic monopole description of quarks and leptons via the "electromagnetically dual" gauge group." - Luboš Motl, PhD.

Originally Posted by Jarek Duda

Indeed in quantum mechanics we usually see photons as a plane waves ... but plane waves are waves in the whole spacetime - do you really think that a single hydrogen atom creates 3+1 dimensional wave of all sizes like the Universe?

If you would actualy look at the state I constructed you would find out that I constructed coherent state from localized photon pulses.

So what do you think is the difference between particles, solitons (and e.g. Couder's droplets)?
All of them have corpuscle like charge (droplet), which is conjugated with waves it creates - what leads to quantum phenomenas.
For example for topological solitons: Abrikosov vortices (fluxons), the fact that we can observe their trajectories doesn't prevent them from interference: Phys. Rev. Lett. 71, 2311 (1993): Observation of the Aharonov-Casher effect for vortices in Josephson-junction arrays

About your optical photon, still Fourier transform (momentum space) is not convenient for localized waves (ok, maybe in 1D, but not in 3D). Would you model waves behind marine propeller in momentum space?
We need to understand spatial configuration of this wave carrying angular momentum (because of twisting electron).

Originally Posted by Jarek Duda

So what do you think is the difference between particles, solitons (and e.g. Couder's droplets)?
All of them have corpuscle like charge (droplet), which is conjugated with waves it creates - what leads to quantum phenomenas.
For example for topological solitons: Abrikosov vortices (fluxons), the fact that we can observe their trajectories doesn't prevent them from interference: Phys. Rev. Lett. 71, 2311 (1993): Observation of the Aharonov-Casher effect for vortices in Josephson-junction arrays

So what? These are not fundamental particles these are basicaly macroscopic quasiparticles that behave like they behave. If something behaves like quantum object doesn`t mean that it is fundamental quantum object. Stupid string behaves like particle in QW, doesn`t mean it is quantum.

Originally Posted by Jarek Duda

About your optical photon, still Fourier transform (momentum space) is not convenient for localized waves (ok, maybe in 1D, but not in 3D). Would you model waves behind marine propeller in momentum space?
We need to understand spatial configuration of this wave carrying angular momentum (because of twisting electron).

What? Why not? I can describe whatever I want in k space. Dimension is not relevant here. I`m sorry but you seem to me like a mathematician. You are proposing models that are not established and properly tested while obviously not understanding basic elements of quantum optics/field theory. I gave you explicit way how to compute E(r,t) of REAL coherent single photon state. I even basicaly told you what you will get. The wave carries angular momentum so what?

Originally Posted by Gere

So what? These are not fundamental particles these are basicaly macroscopic quasiparticles that behave like they behave. If something behaves like quantum object doesn`t mean that it is fundamental quantum object. Stupid string behaves like particle in QW, doesn`t mean it is quantum.

So you are saying that e.g. electron is fundamental, while soliton isn't ...
But what is electron? Gauss theorem says that divergence of electric field is zero everywhere ... unless there are charges inside.
Charges like electron are singularities of electric field - the field goes to infinity in the center - making electron an extremely nontrivial configuration of the field.

Soliton is also a nontrivial configuration of the field, usually a singularity with topological charge, conserved in topological analogue of Gauss theorem (e.g. Hopf's) ... so what is the difference from "fundamental charge" like electron?

What? Why not? I can describe whatever I want in k space. Dimension is not relevant here. I`m sorry but you seem to me like a mathematician. You are proposing models that are not established and properly tested while obviously not understanding basic elements of quantum optics/field theory. I gave you explicit way how to compute E(r,t) of REAL coherent single photon state. I even basicaly told you what you will get. The wave carries angular momentum so what?

Sure we can always perform Fourier transform to get from position to momentum space ... what I am saying is that it is not always convenient.
For example when we are talking about localized configurations like solitons or photons ... especially when there is a nonlinearity - required for solitons and creating interactions in momentum space ... sure we can work on them using Feynman diagrams - with simple approximations of nonlinearities and making everything extremely complicated ...

Originally Posted by Jarek Duda

If we are not performing measurements, what does it say?

It says quite simply that these variables are Fourier transforms of one another. Whether or not actual measurements are performed is irrelevant.

Originally Posted by Jarek Duda

As you have written - "HUP makes it impossible to determine all properties of the quantum object simultaneously with arbitrary precision" ... but it doesn't say that objectively they have no these properties - only that we cannot measure them.

Actually, if you look into the underlying basis of the HUP, then a quantum object cannot possess precise values for all possible observables. This due to the nature of the observables themselves, that there exists a mathematical incompatibility between particular observables. However, a pure quantum state is a precise state. This is a point that seems to be overlooked by many people. That is, there is an observable for which a pure quantum state will produce a single value with certainty. It is when some other observable is measured that the result will be a statistical distribution of different values. In other words, it is not the quantum object itself that is indeterminate, but that the indeterminism is due to the misalignment between the quantum object and the observable being measured. Thus, one cannot dismiss the fundamental role played by measurement, for it is the choice of the observable being measured that determines how the quantum object will behave.

Indeed, as I have already responded to Strange, HUP says that there is uncertainty of values of observatbles ... which we measure.
Like for position-momentum: it is relation between widths while performing Fourier transform. E.g. plane wave has no localization (is uniform in the whole spacetime), while Dirac delta (point particle) has uniform distribution in momentum space.

So there is some objective property (like a wave), but its values of operators are not Dirac deltas - here we are not asking about values of observables, but about these objective properties below - which we cannot directly measure, but we can measure their far consequences.
Like we cannot completely measure the wavefunction of Schrodinger's hydrogen, but we can measure its consequence: energy spectrum.

Originally Posted by Jarek Duda

but about these objective properties below - which we cannot directly measure, but we can measure their far consequences.

But, in principle at least, we can measure the precise observable that a pure quantum state represents. We tend to focus on position and momentum and other similarly basic observables and ignore that we can form a wide variety of observables such a two-peaked position function as in the double-slit experiment, or the creation and annihilation operators that are a particular combination of position and momentum. The basic "problem" with quantum mechanics is that we only get one opportunity to measure a quantum state, and if we choose the "wrong" observable (the observable that is misaligned with the quantum state), then we change the quantum state as it appears to the observer.

I should remark that I am always going to interpret quantum physics in terms of the many-worlds interpretation and quantum decoherence. Thus, I am always going to see a measurement in terms of an entanglement between different versions of the observer within the mulitiverse with each eigenstate component of the quantum state being measured.

The essence of quantum measurement can be seen in Stern-Gerlach experiment:

no matter what was the spin of incoming atoms, the gradient of magnetic field aligns these spins to up or down (along the magnetic field) - we can measure which one was chosen by checking direction of displacement from straight trajectory.
So if we place a few of them in line, the order of such "measurements" affects succeeding ones.

The measurement takes some complex state of the system and projects it into eigenspace of the observable operator, choosing a single eigenfunction - "synchronizes" the system with the measuring phenomena, disturbing its internal dynamics.
If we want to understand what is really going on below quantum description, we have to forget for a moment about these complex measurements, disturbing system, and focus on objective model like dynamics of single electrons assisted by h-order dBB "pilot waves" (exactly like in Couder's picture) ... and find measurable far consequences of such models.

Fascinating stuff. This thread, has to be the best read on the forum, at this moment in time.