Do photons carry more than energy, momentum and angular momentum?

[jarekd]

Well, field theories where changes in the field at, say, Alpha Centauri have an immediate effect here on Earth are non-local, even if they are deterministic. Field theories, where the changes in the field move at some finite speed are not.

Field theories we use are based on Lagrangian/Hamiltonian, what leads to continuous evolution due to PDEs like E-L or Schrodinger's ... with finite propagation speed.

I am talking about the setup. HBT used the setup first to measure the (classical)effect named after them, but the same setup is routinely used to characterize antibunching.
(...) Single photon detections create anticorrelations at spatially separated detectors.

And he has shown that effects in his setup can be explained by a field theory: electromagnetism governed by Maxwell's equations ... why do you think that field theory is not enough to explain that these deexciting atoms are not independent (what would lead to Poisson distribution), but are somehow synchronized to get antibunching distribution?
Synchronization of atoms in a solid is quite natural ... we can look at regular crystal through "quantum" phonons ... or as a system of sticks and springs, which normal modes are these phonons.

I am not sure what you are aiming at. Why should it?

Indeed, why should field theories fulfill Bell inequalities, while at least one of them (QM) gives good prediction for their violation?
The setup of Bell theorem is naive classical mechanical - no wonder it is violated by physics.
Please show this kind of violation for a field theory setup.

I do not get your setup. Sorry.

Ok, let us pass DCQE and focus here as it seems more clear. The setup is quite clear as written in the thread:
https://dl.dropboxusercontent.com/u/12405967/freeelectron.jpg
As we know, physics is CPT symmetric - so while laser stimulates photon emission, if we would construct its CPT analogue (what seem simple for free electron laser), shouldn't we stimulate photon absorption instead of photon emission of standard laser?
Above picture shows CPT transformation of situation with laser hitting a target - while stimulating emission of laser causes excitation of target, shouldn't stimulated absorption of lasAr cause deexcitation of target?

The cat would start out in a true superposition state which is loosely interpreted as "neither dead nor alive" and would develop towards a mixed state. For the mixed state, if you repeat the experiment very often (poor cat), you get both a dead and alive cat 50% of the time, but it is objectively dead or alive in every repetition. You just have a mixed state due to lack of knowledge. The timescale over which the cat develops from a true superposition towards the mixed state is its decoherence time. This is roughly the time scale on which some interaction with the outside world or even the within the constituents of the cat occurs, which breaks the superposition. It scales exponentially with system size (which is also the problem of creating many qubits for quantum computing). As a cat is pretty large, I would assume it has a decoherence time of next to nothing. Only stuff which almost does not interact with anything has been shown to get to (moderately) long coherence times. I think nuclear spins do pretty well or NV centers in diamond.

Let us be more humanitarian and do the experiment just once: so you are saying that "the cat would start out in a true superposition state which is loosely interpreted as "neither dead nor alive" and would develop towards a mixed state".
But there are two observers:
- one sitting next to the cat and so immediately seeing its status,
- the other is separated, e.g. one light year away - and so for a year he has no chance to know the status.
Would quantum descriptions of these two observers be identical?

Ok, assuming that there is no restoring force and you somehow have mirrors freely floating in vacuum, you will get some displacement. The question is whether this displacement will be larger than the minimal displacement of the mirror you will get anyway because the initial momentum of your mirror is not precisely known, but only to within the bounds of uncertainty.

Good explanation, but using a subjective observer - I am saying that situation with photon going through one or another path objectively differs by mirror's momentums - physics would know which path was chosen by the photon.

Introducing observer (especially conscious) is what makes QM mystical.
Measurement is usually an extremely complex process, involving wavefunction collapse (unless weak).
Collapse is going out of unitary evolution, but quantum models we consider usually consist of just a few bodies - neglect everything else. And so wavefunction collapse is seen as a result of interaction with this environment we neglect.
Imagining "complete QM" - evolving wavefunction of the Universe, there is no longer external environments/observers ... there is only unitary evolution of some objective physics.
Observer built from atoms is just a part of this physics - we can forget about his measurements and think what objectively is happening there ...

Single atom? Not really. But already simple things like a plasma or bremsstrahlung can.

So you agree that quantization of spectrum from a single atom is just a result of quantization of orbitals?
So is such photon released from single excited atom just EM wave carrying the differences (due to Noether theorem): of energy, momentum and angular momentum (from orbital angular momentum or twisting spin 180 deg)?

 

[Cthugha]

Field theories we use are based on Lagrangian/Hamiltonian, what leads to continuous evolution due to PDEs like E-L or Schrodinger's ... with finite propagation speed.

We were discussing dBB here, which is an explicit case of the wave function living in configuration space and being non-local. There are of course also field theories with finite propagation speed.

And he has shown that effects in his setup can be explained by a field theory: electromagnetism governed by Maxwell's equations ... why do you think that field theory is not enough to explain that these deexciting atoms are not independent (what would lead to Poisson distribution), but are somehow synchronized to get antibunching distribution?

What should be synchronized? You typically do not get full antibunching if you have more than one atom present. You get weak antibunching for more than one atom, but this works well for independent atoms (which does not lead to a Poissonian distribution for a finite number of emitters, but approaches it as the number grows).

Synchronization of atoms in a solid is quite natural ... we can look at regular crystal through "quantum" phonons ... or as a system of sticks and springs, which normal modes are these phonons.

But that is completely unrelated to the topic at hand. Synchronization of several atoms in emission processes is rather of interest in terms of superradiance.

Indeed, why should field theories fulfill Bell inequalities, while at least one of them (QM) gives good prediction for their violation?
The setup of Bell theorem is naive classical mechanical - no wonder it is violated by physics.
Please show this kind of violation for a field theory setup.

This depends on the field theory. If it is local and realistic, it fulfills Bell's inequality. If you consider clinging to both as naive classical, then yes, it is naive.

Ok, let us pass DCQE and focus here as it seems more clear. The setup is quite clear as written in the thread:
https://dl.dropboxusercontent.com/u/12405967/freeelectron.jpg
As we know, physics is CPT symmetric - so while laser stimulates photon emission, if we would construct its CPT analogue (what seem simple for free electron laser), shouldn't we stimulate photon absorption instead of photon emission of standard laser?
Above picture shows CPT transformation of situation with laser hitting a target - while stimulating emission of laser causes excitation of target, shouldn't stimulated absorption of lasAr cause deexcitation of target?

Sorry, I still fail to see your point. Maybe I need to invest some time into that.

Let us be more humanitarian and do the experiment just once: so you are saying that "the cat would start out in a true superposition state which is loosely interpreted as "neither dead nor alive" and would develop towards a mixed state".
But there are two observers:
- one sitting next to the cat and so immediately seeing its status,
- the other is separated, e.g. one light year away - and so for a year he has no chance to know the status.
Would quantum descriptions of these two observers be identical?

First, quantum mechanics is statistical in nature Unfortunately, it is not humanitarian. It does not tell us much about a single experiment, but I suppose you are well aware of that, so there is no really meaningful quantum description of a single event. You can take Bayesian approaches trying to give some meaning to single events, but you do not get much out of it in terms of physics. Their observations would be identical, though. Whether the quantum description is the same, depends on your definition of description, really. The way of expressing the superposition state would usually involve writing its density matrix which has the standard terms on the diagonal and coherences between the two pure states on the off-diagonal. The off-diagonal elements will usually decay with time leaving only the on-diagonal elements. If the two observers each do some measurement on an ensemble which allows them to do state tomography, they will find different density matrices (corresponding to the time dependence), but governed by the same time dependence.

Good explanation, but using a subjective observer - I am saying that situation with photon going through one or another path objectively differs by mirror's momentums - physics would know which path was chosen by the photon.

Well, the facts tell us that there still is interference. I am not a friend of personalizing physics and telling it what it should and should not know. Maybe to many people doing that is the reason why it is not humanitarian. Jokes aside, you seem to assume uncertainty is not intrinsic, which leads to quite complicated models. You can still keep a view like this taking versions of the Bohmian interpretation, though.

Introducing observer (especially conscious) is what makes QM mystical.
Measurement is usually an extremely complex process, involving wavefunction collapse (unless weak).
Collapse is going out of unitary evolution, but quantum models we consider usually consist of just a few bodies - neglect everything else. And so wavefunction collapse is seen as a result of interaction with this environment we neglect.

But there are plenty of papers on decoherence which consider the environment in detail. In many papers not focusing on the foundations of qm, people do not care about the exact nature of the environment as treating it effectively works more than well enough.

Imagining "complete QM" - evolving wavefunction of the Universe, there is no longer external environments/observers ... there is only unitary evolution of some objective physics.
Observer built from atoms is just a part of this physics - we can forget about his measurements and think what objectively is happening there ...

I can imagine a lot, but at the end of the day people want models giving predictions and results that can actually be calculated. Physics is more about the art of building a working model than it is about being satisfying from the ontological point of view. While there are of course people interested in both, predictions differences you can actually measure are what usually counts.

So you agree that quantization of spectrum from a single atom is just a result of quantization of orbitals?

For the simple case of PL from a single emitter? Trivially yes. For the general case it is not that easy, though.

So is such photon released from single excited atom just EM wave carrying the differences (due to Noether theorem): of energy, momentum and angular momentum (from orbital angular momentum or twisting spin 180 deg)?

I would not look at it this way as there are to many pit traps when trying to go from this very special case to the general case. I suppose you can construct a way to look at it this way, though, for single atoms.

 

[jarekd]

We were discussing dBB here, which is an explicit case of the wave function living in configuration space and being non-local. There are of course also field theories with finite propagation speed.

dBB uses Schrödinger equation after Madelung transformation: http://en.wikipedia.org/wiki/De_Broglie–Bohm_theory#Derivations
You get continuity condition for density, and Hamilton-Jacobi with h-order potential due to wave nature (like for Couder's droplets) - where do you see nonlocality here?

What should be synchronized? You typically do not get full antibunching if you have more than one atom present. You get weak antibunching for more than one atom, but this works well for independent atoms (which does not lead to a Poissonian distribution for a finite number of emitters, but approaches it as the number grows).

There are complex EM interactions between atoms ... for example imagine two Bohr's hydrogens near each other - shouldn't they synchronize orbital movement of their electrons?
If electromagnetism was enough to explain the original HBT, why do you think it is not enough to explain dependencies changing distribution from the Poissonian?

This depends on the field theory. If it is local and realistic, it fulfills Bell's inequality. If you consider clinging to both as naive classical, then yes, it is naive.

But Schrodinger equation is local, while QM violate Bell inequalities ...
Have you seen something suggesting that e.g. Maxwell's equations fulfill Bell inequalities?
Or any Lagrangian field theory, like Klein-Gordon, which is quite close to Schrodinger?

Sorry, I still fail to see your point. Maybe I need to invest some time into that.

Do you agree that photon emission after CPT transformation becomes photon absorption?
So should CPT analogue of laser stimulate photon absorption instead of emission?
When we place not excited target in path of standard laser, it causes its excitation ... so what if we would place excited target in path of CPT analogue of laser?

First, quantum mechanics is statistical in nature Unfortunately, it is not humanitarian. It does not tell us much about a single experiment, but I suppose you are well aware of that, so there is no really meaningful quantum description of a single event. You can take Bayesian approaches trying to give some meaning to single events, but you do not get much out of it in terms of physics. Their observations would be identical, though. Whether the quantum description is the same, depends on your definition of description, really. The way of expressing the superposition state would usually involve writing its density matrix which has the standard terms on the diagonal and coherences between the two pure states on the off-diagonal. The off-diagonal elements will usually decay with time leaving only the on-diagonal elements. If the two observers each do some measurement on an ensemble which allows them to do state tomography, they will find different density matrices (corresponding to the time dependence), but governed by the same time dependence.

Ok, I see you agree that quantum mechanics of an observer is just his subjective description - QM among others is a tool to work with our incomplete knowledge (like statistical physics).
But when there was no observers, like in the beginning of the Universe, QM was still working, for example determining atomic spectra - this means that there is some objective physics/QM which doesn't need observer - instead of blurring the picture by subjectivity, let us try to focus on this physics.
Sure we cannot directly measure it, but we can predict its far outcomes and compare them to the reality - like we don't need to measure wavefunction everywhere to conclude energy spectra from Schrodinger equation.

Let us leave for later thinking how to measure its far outcomes, and earlier try to understand objective mechanisms, like complex internal dynamics of atom: producing localized twist-like EM wave: photon.

Well, the facts tell us that there still is interference. I am not a friend of personalizing physics and telling it what it should and should not know. Maybe to many people doing that is the reason why it is not humanitarian. Jokes aside, you seem to assume uncertainty is not intrinsic, which leads to quite complicated models. You can still keep a view like this taking versions of the Bohmian interpretation, though.

My point here is that objectively - e.g. just after Big Bang, when there was no conscious observers - there is a physical difference between situations when photon chooses one path or another.
Objectively energy cannot choose any trajectory between emitter and detector - for each of them there is objectively different final momentum distribution of the system.
So objectively photon in vacuum would travel by straight line - for some detection moment, in given moment in the past it should have in quite well defined position.

But there are plenty of papers on decoherence which consider the environment in detail. In many papers not focusing on the foundations of qm, people do not care about the exact nature of the environment as treating it effectively works more than well enough.

So you agree that increasing the system up to the wavefunction of the Universe, there would be no longer exterior and so it would evolve in unitary way (without collapse)?
First we should understand what is objectively going on there, then we should be able to conclude measurable far consequences ... like in cosmological models.

For the simple case of PL from a single emitter? Trivially yes. For the general case it is not that easy, though.

To go to a general case, we should start with really understanding e.g. what is objectively happening while deexcitation of single hydrogen atom ...
When there is a single electron in p orbital, with zero orbital angular momentum ... to produce wave carrying angular momentum, this electron had to twist its spin 180 deg?
This produced twist-like wave can finally hit some ground state hydrogen, giving its electron twist and energy to move to higher orbit?
Do you agree?

 

[Cthugha]

dBB uses Schrödinger equation after Madelung transformation: http://en.wikipedia.org/wiki/De_Broglie–Bohm_theory#Derivations
You get continuity condition for density, and Hamilton-Jacobi with h-order potential due to wave nature (like for Couder's droplets) - where do you see nonlocality here?

Have a look at the guiding equation for some particle. It depends on the current position of every single other particle in the whole universe. That is very non-local. Deterministic, but still absolutely non-local.

There are complex EM interactions between atoms ... for example imagine two Bohr's hydrogens near each other - shouldn't they synchronize orbital movement of their electrons?
If electromagnetism was enough to explain the original HBT, why do you think it is not enough to explain dependencies changing distribution from the Poissonian?

Because you just need a light field with more noise to explain HBT, while you need a light field with a noise level below the classical limit (below shot noise) to explain antibunching and similar non-classical states of light. There is distribution in classical em which can do that.

But Schrodinger equation is local, while QM violate Bell inequalities ...
Have you seen something suggesting that e.g. Maxwell's equations fulfill Bell inequalities?
Or any Lagrangian field theory, like Klein-Gordon, which is quite close to Schrodinger?

Yes, it is local, but does not satisfy realism. Using just plain Maxwell equations, you will not be able to get violations of Bell Inequalities.

Do you agree that photon emission after CPT transformation becomes photon absorption?
So should CPT analogue of laser stimulate photon absorption instead of emission?
When we place not excited target in path of standard laser, it causes its excitation ... so what if we would place excited target in path of CPT analogue of laser?

I do not know.

Ok, I see you agree that quantum mechanics of an observer is just his subjective description - QM among others is a tool to work with our incomplete knowledge (like statistical physics).

No, I never said that. Those two will of course not find the time dependence of the density matrix by just checking at a single time.

But when there was no observers, like in the beginning of the Universe, QM was still working, for example determining atomic spectra - this means that there is some objective physics/QM which doesn't need observer - instead of blurring the picture by subjectivity, let us try to focus on this physics.

QM is not about conscious observers. Any irreversible interaction is a measurement. The universe does not need someone to watch that.

My point here is that objectively - e.g. just after Big Bang, when there was no conscious observers - there is a physical difference between situations when photon chooses one path or another.
Objectively energy cannot choose any trajectory between emitter and detector - for each of them there is objectively different final momentum distribution of the system.
So objectively photon in vacuum would travel by straight line - for some detection moment, in given moment in the past it should have in quite well defined position.

Maybe. Maybe not. As already said, I am not a friend of telling the universe what it must have done. I am quite sure it does not care. You can try to define what you think has happened as objective, but I do not see any reason why your version of what happens should be preferred over any other interpretation predicting exactly the same events. At the moment there is no experimental evidence indicating what exactly happens between photon emission and detection.

So you agree that increasing the system up to the wavefunction of the Universe, there would be no longer exterior and so it would evolve in unitary way (without collapse)?
First we should understand what is objectively going on there, then we should be able to conclude measurable far consequences ... like in cosmological models.

Well, it would be hard to collapse the wave function of "everything there is". In the information theory approaches to qm, collapse corresponds to the arrival of new information which might become impossible at some point in some interpretations. Other interpretations like consistent histories do not have any collapse at all. But I doubt going these ways makes things more objective.

To go to a general case, we should start with really understanding e.g. what is objectively happening while deexcitation of single hydrogen atom ...
When there is a single electron in p orbital, with zero orbital angular momentum ... to produce wave carrying angular momentum, this electron had to twist its spin 180 deg?
This produced twist-like wave can finally hit some ground state hydrogen, giving its electron twist and energy to move to higher orbit?
Do you agree?

Maybe. Maybe not. This is one model out of many. It does not do to well when trying to reproduce tricky effects, like the HBT mentioned above, by the way.

 

[jarekd]

Have a look at the guiding equation for some particle. It depends on the current position of every single other particle in the whole universe. That is very non-local. Deterministic, but still absolutely non-local.

Sure if we would like to treat particle like in classical mechanics (like Bell did), there would be always something missing - some "nonlocality".
But we are not talking about classical mechanics here!
All the time I am talking about field theories - that like in Couder's picture, beside corpuscles/solitons there are fields "piloting" behavior of these particles (like quantum phase, EM field) ... indeed these fields depend on the whole history of the system, but evolve in continuous, deterministic - local way.

Because you just need a light field with more noise to explain HBT, while you need a light field with a noise level below the classical limit (below shot noise) to explain antibunching and similar non-classical states of light. There is distribution in classical em which can do that.

I think you have missed "no" in the last sentence? If so, could you refer to some source?
But generally synchronization can be made through extremely weak conjugation of oscillators (like atoms) - even classically electrons of atoms should synchronize Bohr's orbits, making their deexcitations no longer independent.

Yes, it is local, but does not satisfy realism. Using just plain Maxwell equations, you will not be able to get violations of Bell Inequalities.

So you are claiming that Maxwell's equations fulfill bell inequalities - could you support it somehow?
For example imagine there is a process creating pair of EM twist-like waves: in random way, but still fulfilling angular momentum conservation.
Would such purely EM version of EPR fulfill Bell inequalities?
What is its difference from the real EPR?

I do not know.

Here is a hint: http://en.wikipedia.org/wiki/Antiparticle#Feynman.E2.80.93Stueckelberg_interpretation

No, I never said that. Those two will of course not find the time dependence of the density matrix by just checking at a single time.

Those two observers have just different density matrix: one immediately sees the status of the cat, the other has to wait at least one year for any information...
Do you claim that their quantum descriptions have the same density matrix?
If no, doesn't it mean that density matrix in this case only represents their incomplete knowledge?

QM is not about conscious observers. Any irreversible interaction is a measurement. The universe does not need someone to watch that.

I thought you have agreed that wavefunction collapses - "irreversible interaction" is an effect of interacting with environment?
So what if we would include the particles/fields of this environment in the quantum description? Or further expanded it to the whole Universe?
Sure we cannot practically do it, but the question is about objective behavior, like when there was no yet conscious observers.

Maybe. Maybe not. As already said, I am not a friend of telling the universe what it must have done. I am quite sure it does not care. You can try to define what you think has happened as objective, but I do not see any reason why your version of what happens should be preferred over any other interpretation predicting exactly the same events. At the moment there is no experimental evidence indicating what exactly happens between photon emission and detection.

I am not asking about my subjective version ... just oppositely - you are talking only about subjective (conscious?) observers ...
I am asking about objective physics - distant from subjective observers like me ... being part of this objective physics.

Maybe. Maybe not. This is one model out of many. It does not do to well when trying to reproduce tricky effects, like the HBT mentioned above, by the way.

Ok, so please tell something about these many alternatives: for electron deexcitating without change of orbital angular momentum?
Do you want to say that photon it produces have zero angular momentum?
Or maybe that angular momentum does not have to be conserved?

 

[Cthugha]

Sure if we would like to treat particle like in classical mechanics (like Bell did), there would be always something missing - some "nonlocality".
But we are not talking about classical mechanics here!
All the time I am talking about field theories - that like in Couder's picture, beside corpuscles/solitons there are fields "piloting" behavior of these particles (like quantum phase, EM field) ... indeed these fields depend on the whole history of the system, but evolve in continuous, deterministic - local way.

Well, you can avoid the non-locality issue in terms of a model which is not realistic, which some field theories do.

I think you have missed "no" in the last sentence? If so, could you refer to some source?

Oh, sorry. My sentence had a "sign error". It is complicated to find a good reference without knowing your level of expertise in quantum optics, but the following paper has some information for experts and novices alike:
P. Grangier et al, "Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences", 1986 Europhys. Lett. 1 173.

So you are claiming that Maxwell's equations fulfill bell inequalities - could you support it somehow?
For example imagine there is a process creating pair of EM twist-like waves: in random way, but still fulfilling angular momentum conservation.
Would such purely EM version of EPR fulfill Bell inequalities?
What is its difference from the real EPR?

Ehm, I do not get your point. The point of entanglement is more than just angular momentum conservation. When checking the correlations at different polarizer settings, one would expect to see results governed by Malus' law, while in experiments you see that his is not the case. This is the fundamental point of many publications on entanglement. For a moderately easy summary, see J. H. Eberly, "Bell inequalities and quantum mechanics", Am. J. Phys. 70, 276 (2002)

Those two observers have just different density matrix: one immediately sees the status of the cat, the other has to wait at least one year for any information...
Do you claim that their quantum descriptions have the same density matrix?
If no, doesn't it mean that density matrix in this case only represents their incomplete knowledge?

The density matrix evolves with time. Both will just find the density matrix for the time they measure it, isn't that trivial?

I thought you have agreed that wavefunction collapses - "irreversible interaction" is an effect of interacting with environment?
So what if we would include the particles/fields of this environment in the quantum description? Or further expanded it to the whole Universe?
Sure we cannot practically do it, but the question is about objective behavior, like when there was no yet conscious observers.

I have agreed that wave function collapse is an effect of interacting with the environment in certain interpretations. I still do not see where conscious observers come into play. Sure, you can try to formulate a wave function for the whole universe, which probably would not even collapse from the early Copenhagen point of view.

I am not asking about my subjective version ... just oppositely - you are talking only about subjective (conscious?) observers ...
I am asking about objective physics - distant from subjective observers like me ... being part of this objective physics.

If objective physics exists. You can formulate a lot, but what is it worth if we cannot find out whether it is right or wrong? This is very interesting from the philosophical point of view and there are ontological arguments that make objective physics seem attractive. Still, we cannot draw any safe conclusion beyond what we can actually tell apart via our own little subjective experience via measurements.

Ok, so please tell something about these many alternatives: for electron deexcitating without change of orbital angular momentum?
Do you want to say that photon it produces have zero angular momentum?
Or maybe that angular momentum does not have to be conserved?

The energy and momentum can go to some kind of particle with well defined properties. It can go to a field. If so, the field can be local or delocalized. The atom and the particle field may go into a superposition state which really collapses to some well defined state as soon as there is some interaction with something else. Just read about all the interpretations of QM from dBB over consistent histories to MWI which are not ruled out and you will find many alternative versions of what might happen "objectively".

 

[jarekd]

Well, you can avoid the non-locality issue in terms of a model which is not realistic, which some field theories do.

Field is defined in every point of spacetime, fulfill e.g. E-L equations, evolves in deterministic way - usually with finite propagation speed (is local) ... what do you mean by "not realistic"?

Oh, sorry. My sentence had a "sign error". It is complicated to find a good reference without knowing your level of expertise in quantum optics, but the following paper has some information for experts and novices alike:
P. Grangier et al, "Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences", 1986 Europhys. Lett. 1 173.

Ok, http://www.haverford.edu/physics/love/teaching/Physics302PJL2009Recitation/03%20Hanbury%20Brown%20Twiss/PhotonAntiCorrelation-Grangier-Roger-Aspect.pdf , but I don't think I understand the problem.
Calcium atom produces v1 photon and a moment later v2. Detection of v1 turns on photomultipliers to detect v2, such that only single photon should pass.
So why is the coincidence counter if only one of Nc, Nr detectors can detect it?

And generally there is lots of effects called "non-classical" as a synonym of "we don't understand it".
Like interference called by Feynman the essence of quantum mechanics, absolutely impossible to understand classically ... while now Couder's do analogous experiment with macroscopic droplets ...
Or while stochastic models predicted semiconductor to conduct well, surprisingly it didn't because e.g. of Anderson's "quantum" localization ... while it turns out that standard stochastic models usually don't fulfill the requirement for thermodynamical models: to maximizing uncertainty - if we do them right, we get exactly the same stationary probability distribution as quantum ground state - with its localization properties ( https://www.physicsforums.com/showthread.php?t=710790 ).

Ehm, I do not get your point. The point of entanglement is more than just angular momentum conservation. When checking the correlations at different polarizer settings, one would expect to see results governed by Malus' law, while in experiments you see that his is not the case. This is the fundamental point of many publications on entanglement. For a moderately easy summary, see J. H. Eberly, "Bell inequalities and quantum mechanics", Am. J. Phys. 70, 276 (2002)

I am saying that if photons are EM waves carrying angular momentum, you don't longer need quantum mechanics: assume just some random "whirl - antiwhirl" pair and simulate Maxwell's equations.
Why should it give different correlations than QM?
How QM "changes" this purely electromagnetic situation?

The density matrix evolves with time. Both will just find the density matrix for the time they measure it, isn't that trivial?

I am asking about the moment just after cat's death - first observers sees it, the second have to wait one year.
How their density matrces look in this moment?

I have agreed that wave function collapse is an effect of interacting with the environment in certain interpretations. I still do not see where conscious observers come into play. Sure, you can try to formulate a wave function for the whole universe, which probably would not even collapse from the early Copenhagen point of view.(...)
If objective physics exists. You can formulate a lot, but what is it worth if we cannot find out whether it is right or wrong? This is very interesting from the philosophical point of view and there are ontological arguments that make objective physics seem attractive. Still, we cannot draw any safe conclusion beyond what we can actually tell apart via our own little subjective experience via measurements.

From perspective of such wavefunction of universe, there is objective physics, evolves in unitary (nearly time-symmetric) way ... and observers are just interacting sets of atoms.
My point here is only that even if we cannot directly measure something, we can ask what is objectively happening there - and compare far consequences with observations.

Like Schrodinger's model of atom - we rather cannot directly measure the whole wavefunction, but we can assume that it behaves accordingly to his equation - getting far consequences, like objective hydrogen energy spectrum.
It makes the wavefunction (ok, up to gauge equivalence relation) some objective (not necessarily fundamental) property of physics - being/interacting there, it does no mater if someone looks at it ...

And so we should try to find the configuration of photon's EM wave e.g. from p l=0 hydrogen electron deexcitating to s ... we should also try to find EM configuration of different particles, like electron being both charge and tiny magnet ...
Then calculate far consequences of these models, compare with reality ... get deeper understanding, find new effects ...
... but such questions are currently practically unanswered - we know much more e.g. about nonexistent strings than about EM structure of photon or electron ...

The energy and momentum can go to some kind of particle with well defined properties. It can go to a field. If so, the field can be local or delocalized. The atom and the particle field may go into a superposition state which really collapses to some well defined state as soon as there is some interaction with something else. Just read about all the interpretations of QM from dBB over consistent histories to MWI which are not ruled out and you will find many alternative versions of what might happen "objectively".

But objectively what is the EM structure of single optical photon from concrete type of deexcitation?
Is it just EM wave carrying energy, momentum and angular momentum or something more?

 

[Cthugha]

Field is defined in every point of spacetime, fulfill e.g. E-L equations, evolves in deterministic way - usually with finite propagation speed (is local) ... what do you mean by "not realistic"?

For simplicity consider Copenhagen and variants. Take the wavefunction and consider its meaning. It can be considered as a real physical entity with the physical properties of the system well defined and existing all the time. In this case collapse necessarily introduces non-locality as upon collapse, the wavefunction of the system changes everywhere at once.
You can also consider the wavefunction as some entity which has no physical reality with the physical properties of the system not existing in a well defined manner prior to measurement. Collapse is now not a problem as there is no physically real entity which changes non-locally, but there are no well defined physical properties of the system prior to measurement, giving us a theory without realism.
You can also consider the third way, where you have both locality and a system with well defined properties prior to measurement, but CHSH tests and Bell tests show that such local and realistic models are not tenable.

And generally there is lots of effects called "non-classical" as a synonym of "we don't understand it".

That is plain wrong. From a classical point of view, measurements which do not disturb the system are possible. There is no way to get ideal antibunching (which requires zero variance of the photon number) in such a setting.

Like interference called by Feynman the essence of quantum mechanics, absolutely impossible to understand classically ... while now Couder's do analogous experiment with macroscopic droplets ...

I do not see the relevance of Couder's experiments here. They provide some nice pictures, but the underlying physics of his experiments and what happens in qm is very different.

I am saying that if photons are EM waves carrying angular momentum, you don't longer need quantum mechanics: assume just some random "whirl - antiwhirl" pair and simulate Maxwell's equations.
Why should it give different correlations than QM?
How QM "changes" this purely electromagnetic situation?

Consider polarization-entangled light. With a "whirl-antiwhirl" pair with random, but well-defined polarizations for each repetition, you can place polarizers in the two beam paths and check coincidences after the polarizers. For standard em, you now expect that you can calculate the transmission through the polarizers using Malus' law. For each photon, the transmission probability will be given by the squared cosine of the difference between the polarization axis of the photon and the polarizer setting. So for correlation count experiments, you have to calculate the projection of the preexisting polarization axis on the polarizer axis for each photon individually and then calculate the correlation. So even for a fixed difference between the polarizer axes in the two detection arms, the correlation depends on the preexisting values of the photon polarization. For qm, you do not have these predefined values and the coincidence count rate will depend only on the relative setting of the two polarizer axes. When comparing the coincidence count rates for three different relative polarizer settings and get the average, you get different predictions for the highest coincidence count rates you can get for theories with preexisting values and no nonlocal stuff and other theories. Experiment do not agree with the prediction for local theories with preexisting values. Any basic publication on Bell's inequalities should be able to explain this much better than I can do it on a forum.

 

[jarekd]

For simplicity consider Copenhagen and variants. Take the wavefunction and consider its meaning. It can be considered as a real physical entity with the physical properties of the system well defined and existing all the time. In this case collapse necessarily introduces non-locality as upon collapse, the wavefunction of the system changes everywhere at once.
You can also consider the wavefunction as some entity which has no physical reality with the physical properties of the system not existing in a well defined manner prior to measurement. Collapse is now not a problem as there is no physically real entity which changes non-locally, but there are no well defined physical properties of the system prior to measurement, giving us a theory without realism.
You can also consider the third way, where you have both locality and a system with well defined properties prior to measurement, but CHSH tests and Bell tests show that such local and realistic models are not tenable.

Ok, now you are no longer referring to "not realistic" theories, but to wavefunction collapse - breaking the unitary evolution.
I was already referring to this problem and you have agreed that collapse is an effect of interacting with the environment - so it is just a matter of (subjective observer) considering larger system - objectively there don't have to be any collapse - there can be just a continuous evolution.

And so where do you need discontinuous "collapse" in dBB, which is practically extension of classical mechanics, or in Couder's picture?
Definitely not in interference as it is usually needed in orthodox interpretation ...

That is plain wrong. From a classical point of view, measurements which do not disturb the system are possible. There is no way to get ideal antibunching (which requires zero variance of the photon number) in such a setting.

Interesting - so imagine there is a classical Bohr's atom of natural size - how would you measure it without disturbing?

I was asking you to help me understand the problem you see with http://www.haverford.edu/physics/love/teaching/Physics302PJL2009Recitation/03%20Hanbury%20Brown%20Twiss/PhotonAntiCorrelation-Grangier-Roger-Aspect.pdf ?
If it just that "classical mechanics" doesn't predict double deexcitation of calcium atom, I completely agree - but it doesn't mean that classical field theory cannot.

First of all, as classical atom model everybody refer to Bohr's ... but even classically this model is just wrong as electron has strong magnetic dipole moment, what results in Lorentz force perpendicular to its velocity - circular orbits cannot be stable. Here it is corrected: http://en.wikipedia.org/wiki/Free-fall_atomic_model
Secondly, electron has wave nature, which causes h-order corrections to classical models and orbit quantization ... we need also field carrying these "pilot waves", depending on the whole history ... but evolving in deterministic and continuous way.

So I wouldn't say that we cannot explain deexcitation using classical field theory, but that this route is very complex and poorly explored.

I do not see the relevance of Couder's experiments here. They provide some nice pictures, but the underlying physics of his experiments and what happens in qm is very different.

Sure, there are differences, but they provide clear mechanism for basic "quantum phenomenas", like interference, tunneling and orbit quantization - please explain the difference from their quantum analogues?

Consider polarization-entangled light. With a "whirl-antiwhirl" pair with random, but well-defined polarizations for each repetition, you can place polarizers in the two beam paths and check coincidences after the polarizers. For standard em, you now expect that you can calculate the transmission through the polarizers using Malus' law. For each photon, the transmission probability will be given by the squared cosine of the difference between the polarization axis of the photon and the polarizer setting. So for correlation count experiments, you have to calculate the projection of the preexisting polarization axis on the polarizer axis for each photon individually and then calculate the correlation. So even for a fixed difference between the polarizer axes in the two detection arms, the correlation depends on the preexisting values of the photon polarization. For qm, you do not have these predefined values and the coincidence count rate will depend only on the relative setting of the two polarizer axes. When comparing the coincidence count rates for three different relative polarizer settings and get the average, you get different predictions for the highest coincidence count rates you can get for theories with preexisting values and no nonlocal stuff and other theories. Experiment do not agree with the prediction for local theories with preexisting values. Any basic publication on Bell's inequalities should be able to explain this much better than I can do it on a forum.

Both QM and Malus law say that probability drops with square of cosinus of angle - so what is the difference between them?

 

[Cthugha]

Ok, now you are no longer referring to "not realistic" theories, but to wavefunction collapse - breaking the unitary evolution.
I was already referring to this problem and you have agreed that collapse is an effect of interacting with the environment - so it is just a matter of (subjective observer) considering larger system - objectively there don't have to be any collapse - there can be just a continuous evolution.

Ok, back to the basics... "Non-realistic" theories are those, where there are no elements of reality assigned to whatever is going to be measured before measurement. This includes many theories involving collapse, but also others, where the wavefunction is not considered a real entity. I agreed that you can see collapse as an effect of interacting with the environment in terms of a suuch a non-realistic theory. The general problem shown by Bell's inequalities or CHSH schemes is pretty simple. Any theory does (at keast) one of the following things:

1) It is non-realistic in the sense given above.
2) It has non-local elements.
3) It does not reproduce the predictions of qm and thus is at odds with experiment.

This is well known and accepted and if you find any fault with that, please write rebuttals to every paper on Bell inequalities/CHSH and so on.

And so where do you need discontinuous "collapse" in dBB, which is practically extension of classical mechanics, or in Couder's picture?
Definitely not in interference as it is usually needed in orthodox interpretation ...

We already have discussed that several times now. In the point above we were discussing non-realistic interpretations. dBB is instead realistic, but non-local.

Interesting - so imagine there is a classical Bohr's atom of natural size - how would you measure it without disturbing?

I was asking you to help me understand the problem you see with http://www.haverford.edu/physics/love/teaching/Physics302PJL2009Recitation/03%20Hanbury%20Brown%20Twiss/PhotonAntiCorrelation-Grangier-Roger-Aspect.pdf ?
If it just that "classical mechanics" doesn't predict double deexcitation of calcium atom, I completely agree - but it doesn't mean that classical field theory cannot.

It is not double deexcitation. It is about double excitation of the detectors. In a purely classical theory, you do not get this probability to 0. If you can, please show me.

Sure, there are differences, but they provide clear mechanism for basic "quantum phenomenas", like interference, tunneling and orbit quantization - please explain the difference from their quantum analogues?

For starters you need permanent energy input and the effects scale differently. I am not saying that these experiments are not nice visualizations. They are. But it is very tempting to take the analogies too far. Couder himself is very careful about pointing out that they are just analogies.

Both QM and Malus law say that probability drops with square of cosinus of angle - so what is the difference between them?

Take entangled photons with, say, orthogonal polarization. Take two polarizers set to transmit orthogonal polarizations. Check the simultaneous transmission of the photons through the polarizers. For a local and realistic theory, the coincidence count rate you get will depend on the relative angles. Say you have photons with polarizations at 0 and 90 degrees. If the polarizers are set to 45 and 135 degrees, you get a 50 % chance for the transmission of each. So when you get a detection event after the first polarizer, the odds of getting a detection at the second detector, too, is 50%.

In non-realistic settings, the polarization of photons is undefined prior to measurement. However, transmission through the 45 degree polarizer automatically collapses the two photons to the 45 degree/145 degree state. If you detect a photon after polarizer one, you now have a 100% probability of detecting a photon at the other detector, too. Non-local settings like dBB are obviously able to achieve the same result.

If you do all the phase averaging needed for a random source and compare three different polarizer settings, you can finally arrive at some variant of Bell's inequality and test whether the coincidence count rate of the first or second scenario matches reality. It is the second scenario.