It is said that there is interference in Mach–Zehnder interferometer (http://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer), because scenarios of both trajectories are physically indistinguishable ... but while reflecting by mirror, photon's momentum is changed, so momentum conservation says that mirror's momentum is also changed - doesn't it mean that there is some physical difference between the final state of these two scenarios: the first or the second mirror increased its momentum?
So imagine a perfect (gedanken)experiment - there is a floating 0K Mach-Zehnder configuration with zero initial velocities in completely empty vacuum and we send a single photon through it ... now after some chosen time (e.g. a year), we put a light on this scene to check if one(/both?) of mirrors is misplaced?
Which part of such gedankenexperiment is 'fundamentally impossible'?

More practical way to use photon momentum to find out which trajectory was chosen in interference type of experiment is watching two slits using a kind of telescope (Wheeler's experiment (http://en.wikipedia.org/wiki/Wheeler%27s_delayed_choice_experiment)) - photons coming from different slit, excitate different pixel on its matrix ...

Based on what happens with electrons, if you use single photons and if your mirrors are sensitive enough to measure the recoil from individual photons, then you don't get an interference pattern but a simple ballistic trajectory.

But momentum conservation says that there is always some small, but nonzero recoil - so there is always a physical difference between the final states of both scenarios.
The other question is if we can observe this difference - in the setup in which mirrors are floating in vacuum, time is great amplifier of the velocity: it's enough to wait and finally compare positions.

So do you think that if mirrors are floating in vacuum, there is classical behavior?
The requirement for interference is not that both scenarios are indistinguishable for physics, but for us only? (who exactly?) ...

My understanding of interference is a bit different ... first of all we cannot work only on plane waves - it was well checked that if there is a delay on one path, the interference of single photons don't longer occurs - photons are localized entities (solitons).
There was observed interference of macroscopic (topological) solitons: fluxons in supercoductor ( http://prl.aps.org/abstract/PRL/v71/i14/p2311_1 ), so it should be enough to understand interference of solitons (which are much more complicated than classical particles!).
Can single soliton interfere with itself? Let's use Fourier transform to decompose it into plane waves ... and plane waves interfere - thanks of going simultaneously through both paths.
From the other side, solitons usually have kind of singularity which cannot be split - it (particle) goes a single way, but some part of this decomposition goes the second path - this low energy wave carrying information is called theta wave in some derivative of Bohm's interpretation, like in this paper (http://redshift.vif.com/JournalFiles/V16NO2PDF/V16N2CRO.pdf).
So I would say that even in vacuum, there would be interference ...

Not so. If the rig is rigid, then there is no relative recoil. If the rig is elastic, then the recoil might be smaller than the phonon of the elastic material and the rig is effectively rigid., recoiling as a whole. And if a phonon is excited, there may not be enough spatial resolution to identify which mirror was hit. This is especially the case when the rig is bolted to the Earth.

So far you have not picked a particular mechanism to determine which mirror was hit with a single photon of light. If you pick a concrete mechanism and explain with math why you think it would give you simultaneously an interference patterns and clear information on which mirror was hit by a single photon, then I may be able to offer a concrete reason why you can't get both. If you can't do such a calculation, then further calculations by me would likely just go over your head.

http://en.wikipedia.org/wiki/Quantum_eraser_experiment


The quantum eraser experiment is a variation of Young's double slit experiment. It establishes that when a photon is acted upon in a fashion that allows which slit it has passed through to be calculated, the photon cannot interfere with itself.

http://en.wikipedia.org/wiki/Wheeler%27s_delayed_choice_experiment


Wheeler's delayed choice experiment is a thought experiment proposed by John Archibald Wheeler in 1978[1]. Wheeler proposed a variation of the famous double-slit experiment of quantum physics, one in which the method of detection can be changed after the photon passes the double slit, so as to delay the choice of whether to detect the path of the particle, or detect its interference with itself. ... An implementation of the experiment in 2007 showed that the act of observation ultimately decides whether the photon will behave as a particle or wave, verifying the unintuitive results of the thought experiment.

http://arxiv.org/abs/quant-ph/0610241

I know well Wheeler's experiment and related to it twice in this thread - so you want to say that the result will depend on if we (who again?) will decide after all to do something to determine which mirror was hit?

I have also written twice example of mechanism to determine which mirror has reflected the photon - not use a rigid optic table, but place this configuration with zero initial velocity in vacuum - mirrors are not connected to anything, but just floating separately with zero initial momentum.
So if one of mirrors has obtained some momentum, if we look at this scene after e.g. a year, it will be misplaced ...

But with only one photon, how do you propose to test if you have interference fringes or not? You still don't have an experimental design to get both fringes and certainty of photon path.

Interference in MZ means that photons always hit given detector (parallel to photon source).
So my question if there appears interference is asking if photon will always get to this detector ...

It is said that there is interference in Mach–Zehnder interferometer (http://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer), because scenarios of both trajectories are physically indistinguishable ... but while reflecting by mirror, photon's momentum is changed, so momentum conservation says that mirror's momentum is also changed - doesn't it mean that there is some physical difference between the final state of these two scenarios: the first or the second mirror increased its momentum?

Momentum has direction and magnitude making it a vector quantity. But what I don't understand fully is can an object go from totally non-inertial states to having momentum? because that is what I interpret according to what you wrote down.


So imagine a perfect (gedanken)experiment - there is a floating 0K Mach-Zehnder configuration with zero initial velocities in completely empty vacuum and we send a single photon through it ... now after some chosen time (e.g. a year), we put a light on this scene to check if one(/both?) of mirrors is misplaced?
Which part of such gedankenexperiment is 'fundamentally impossible'?

Fundamentally impossible to have occurred you mean?


More practical way to use photon momentum to find out which trajectory was chosen in interference type of experiment is watching two slits using a kind of telescope (Wheeler's experiment (http://en.wikipedia.org/wiki/Wheeler%27s_delayed_choice_experiment)) - photons coming from different slit, excitate different pixel on its matrix ...

I don't really get what this has to do with sending a photon through two-slips such as in the famous double slit experiment.

The first question seems to be kind of philosophical, but I don't think I get it - zero (momentum) vector plus nonzero equals nonzero ...
About 'fundamentally impossible' - I've meant some deep reason that a part of experiment is in principle impossible in essential way, like while explaining Maxwell's demon ...
About the third comment, in this second basic interference setups, photon's momentum also allows to determine path - specialized detectors like telescopes are able to distinguish photons having different direction of momentum vector ...

...after some chosen time (e.g. a year), we put a light on this scene to check if one(/both?) of mirrors is misplaced?This is the problem, you will disturb the mirror if you try to determine the displacement from a single photon.

There isn't any way to measure the mirror's motion without changing it. Certainly the mirror recoils from the photon momentum but the recoil can't be measured without making the mirror move again.

While the final check, we indeed destroy a lot of information ... but in that moment we are interested only at mirror's velocities after sending the photon - displacement is this velocity multiplied by time we waited (like a year), so analyzing e.g. a photo with flash of such final state, we can as precisely as we need calculate the velocities which allow to determine photon's path.

so analyzing e.g. a photo with flash of such final state, we can as precisely as we need calculate the velocities which allow to determine photon's path. If you use a camera with a flash the light will change the mirror's position before you can take a photo--any kind of photo.

If any light from anywhere at all strikes the mirror it will also change its position.

This flash affects mirror's velocity, so it will result in change of its position in the future ... but the only thing we now care about is the misplacement it achieved in the past: while the delay.
If one year is not enough, because e.g. mirror travel only 1nm, we can wait million years instead to increase it to 1mm ... anyway: such that the final interaction (of the flash) will still allow us to determine which mirror reflected the photon.

This is the least problematic point in this experiment (until someone propose discreteness of space), muuuuch worse is e.g. the possibility of preparing the set with practically zero initial relative velocities - such condition even after weakening, I think I wouldn't be able to defend ... (there appears another interesting situation: when velocities aren't as precise - there still would be a difference between our observations for both scenarios ... )
Anyway - from physics point of view, there is a difference in mirror's momentum between these two situations ... so let's return to the real question - the eye of beholder - is the role of observer really so special for results of physics? How is he even defined?
I would say that he is made of the same atoms and governed by the same physics ...
The question is: is there objective physics?

Jarek, just glancing over the thread here are my thoughts. Your proposal is valid; given enough time we could certainly turn on the lights and determine which mirror was struck, but what does that get you? An interference pattern cannot be defined by a single photon's plot. You might as well use a photon receptor/re-emitter to determine its path. Continue the experiment to the point that a pattern would emerge and, when you turn on the lights, you will find that the mirror is moving with a velocity that implies equal path traversal of the photons*.

*Actually if this was carried out in the real world, if the photon source was not in a fixed distance from the interferometer the interference pattern would quickly degrade anyway.

RJBerry, as I've already answer to rpenner, in MZ equivalent of interference pattern is that all photons hit given (parallel to the source) detector - you can imagine it that this detector is on the bright fringe, while the second one on completely dark fringe of interference pattern.
If you agree that in theory we could determine which path photon used, accordingly to understanding of interference requiring indistinguishable scenarios (paths), in such case there should be no interference - meaning that photons can get to both detectors... ?

If you agree that in theory we could determine which path photon used, accordingly to understanding of interference requiring indistinguishable scenarios (paths), in such case there should be no interference - meaning that photons can get to both detectors... ?
It's difficult for me to understand what you mean here. The main point is that anything that is done to successfully detect the photon's path necessarily destroys the interference pattern. I only agreed that, in theory, we could do this for a SINGLE photon, which is worthless. After that, the distance between the emitter and interferometer has been altered and the interference pattern will never appear anyway.

If you agree that in theory we could determine which path photon used, accordingly to understanding of interference requiring indistinguishable scenarios (paths), in such case there should be no interference - meaning that photons can get to both detectors... ?
That's correct: if the photons interact with the apparatus in such a way that the paths become distinguishable (even in principle - there doesn't need to be an observer physically present), that destroys any possibility of the photons exhibiting an interference pattern. I'm pretty sure the only reason we see interference patterns in quantum optics experiments is because there is always necessarily some Heisenberg uncertainty in the state of the apparatus to begin with, which can mask some of the impact the photons have on it. I haven't really followed the thread, so I don't know if that answers your question.

RJBerry, yes in given moment we are focusing on a single photon and we would like to know if it is able to get to the forbidden while interference detector.
Alternatively you can imagine that we run large amount of setups of the same experiment e.g. parallelly and we are interested of statistics among them.

przyk, the problem is that in principle they are always distinguishable - for physics there is mirror's momentum difference between such two scenarios (paths).
My point is that such idealized 'classification' is only approximation and so we shouldn't be satisfied with it, but search for a deeper understanding ...
I've seen a lot of explanations and it's a month or two I can finally say that I'm satisfied with my understanding of why single soliton should interfere with itself - it's briefly written in my second post and I would also gladly discuss it (3rd page of this presentation (http://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B7ppK4I%20yMhisYmI3YTAzNzYtMDkyNy00ZDAxLTg1 NGEtOTg4NWNkYzU3M%20jQ1&hl=en))

Jarek, I think your question may have been answered some time ago, by these two gentlemen:

http://upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Niels_Bohr_Albert_Einstein_by_Ehrenfest.jpg/220px-Niels_Bohr_Albert_Einstein_by_Ehrenfest.jpg

... http://en.wikipedia.org/wiki/Einstein-Bohr_debates

przyk, the problem is that in principle they are always distinguishable - for physics there is mirror's momentum difference between such two scenarios (paths).
No they're not. If the momentum transfer from a photon to the mirror is smaller than the uncertainty in the mirror's initial momentum, they're fundamentally (i.e. "for physics") not clearly distinguishable.


My point is that such idealized 'classification' is only approximation and so we shouldn't be satisfied with it
What classification? If you mean that "completely indistinguishable" and "perfectly distinguishable" are just two extremes in a spectrum, then I never said otherwise.

przyk, do you want to say that Heisenberg uncertainty allows for violation of momentum conservation??
Effect of reflection of single photon is extremely small, but when we add large number of such momentum transfers we get noticeable effect in e.g. solar winds - could it cumulate if uncertainty principle would neglect effects from single photons?
And generally uncertainty principle is extremely subjective one - it doesn't say that physics knows what is happening in it with finite precision, but only restricts our measurement capabilities, for which we use very complicated processes, usually destroying systems. If we are looking for objective physics, we can for a moment forget about this principle.
About classification of types of distinguishability, on water we have interference without such conditions - I don't think they are necessary - see 3rd page of this presentation (http://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B7ppK4I%20yMhisYmI3YTAzNzYtMDkyNy00ZDAxLTg1 NGEtOTg4NWNkYzU3M%20jQ1&hl=en). I would gladly also discuss it.

przyk, do you want to say that Heisenberg uncertainty allows for violation of momentum conservation??
No, I never said that.


Effect of reflection of single photon is extremely small, but when we add large number of such momentum transfers we get noticeable effect in e.g. solar winds - could it cumulate if uncertainty principle would neglect effects from single photons?
You could, but that won't tell you which photon took which path.


And generally uncertainty principle is extremely subjective one
What's subjective about it? The same uncertainty principle is always in effect no matter who is observing what or even if an observer is present at all.


it doesn't say that physics knows what is happening in it with finite precision, but only restricts our measurement capabilities, for which we use very complicated processes, usually destroying systems.
Are we talking about quantum mechanics or your own pet theory here? In quantum mechanics, position and momentum are Fourier conjugate variables. They're not independent quantities like they are in classical mechanics. The uncertainty principle follows from that fact. It's got nothing to do with our measurement processes. Quantum mechanics is literally incapable of consistently describing a particle with both a specific position and momentum. There is simply no such entity in the theory.


About classification of types of distinguishability, on water we have interference without such conditions
Photons aren't water. We can get photons to interfere in polarization as well as in frequency states, and we can create entangled pairs of photons or other particles and cause them to interfere non-locally. The latter is done in Bell experiments (http://en.wikipedia.org/wiki/Bell%27s_theorem): you can think of Bell inequalities as testing for the presence of non-local interference patterns. Interference terms also appear in particle scattering cross sections. For example, the production of a muon-antimuon pair from the collision of an electron-positron pair is a process that can be mediated either by a virtual photon or a Z boson. In QED, the contributions from these pathways interfere.

Quantum interference is a very general phenomenon. It's not restricted to photons or even what you'd normally call "waves".

Accordingly to path photon has chosen, given mirror will have larger momentum - it's objective fact: no measurement involved (to which uncertainty principle could be applied).

Ok, let's talk about fundamental theories ...
Let say there is some really fundamental quantum mechanics (FQM) - wave function of the universe, which e.g. (linearized) has unitary evolution - there is no longer wavefunction collapse in it ...
... but practical quantum mechanics (PQM) we are able to use, describes relatively small systems like atoms - there is always some environment it neglects - this environment interacts with our system and so evolution we are interested at depends on some parameters this model doesn't have access to - in PQM there just have to be built in (hidden) some statistical ensemble among e.g. possible states of environment - it's not fundamental theory, but effective/thermodynamical one: representing subjective knowledge of observer and so sometimes returning only probabilities.

Models representing our knowledge doesn't longer have to be local - we have for example classical analogue of EPR: we know that there is red and blue ball, which in some deterministic but unknown way are send in opposite directions - now in model representing our knowledge, getting know one color means we immediately (faster than light) get know the second color.
Another example is Maximal Entropy Random Walk, in which assuming uniform probability distribution among possible paths our walker could choose, leads to similar nonlocalities like in QM.
Another natural property of models representing our knowledge is retrocausality (like in Wheeler's experiment) - it just means that some event gave us missing information about some earlier events.

In really fundamental quantum mechanics, our system, the measuring apparatus and the observer are parts of one greater system, made of the same atoms and governed by the same physics.
If you for example are 1 light year from this experimenting observer, for a year after he made the measurement of e.g. spin of photon, in your PQM they will be still in superposition:
1/sqtr(2) (|spin up, measurement up> + |spin down, measurement down>)
while in his PQM there will be no longer such superposition.
The lesson is that to make measurement of some system, you have to be outside this system - Schroedinger's cat as the observer knows if is alive ... so increasing it up to the universe would lead to FQM with no longer environment and so wavefunction collapse(see e.g. Zurek's einselection (http://en.wikipedia.org/wiki/Einselection)).

If we want to talk about objective - fundamental quantum mechanics, there is no longer environment and so there is no longer measurements Heisenberg principle applies to - we can forget about this principle for a moment.


In quantum mechanics, position and momentum are Fourier conjugate variables.
It's a property of this effective description, saying that after measuring momentum, photon is a plane wave - is smeared over the whole universe ...
It's one of its nonsenses we have to be careful about - in fact if there is small delay on one path of MZ interferometer, there is no longer interference - in real physics (FQM) particles, photons are quite well localized.

Photons aren't water.
Classical electromagnetism is governed by quite similar wave equations (hyperbolic) as water.
And classical electromagnetism gives Malus law, similar to 'squares' in quantum mechanics leading to Bell inequality violation ...
But I agree that there is qualitative difference - photons are localized - are solitons - there is needed some nonlinearity.

Quantum interference is a very general phenomenon. It's not restricted to photons or even what you'd normally call "waves".
I would say the same, but without 'quantum' word :)

Accordingly to path photon has chosen, given mirror will have larger momentum - it's objective fact: no measurement involved (to which uncertainty principle could be applied).
I'm not sure you understood what I was saying. Suppose the mirror starts off with a perfectly defined momentum, say p. Suppose a photon travelling along one path might knock the mirror and change its momentum to p + \Delta, and suppose if it travelled along the other path, it would knock the mirror the other way and change its momentum to p - \Delta (this may not be exactly what happens in a Mach-Zehnder interferometer, but its enough to illustrate the point I'm making). In that case, the two possible final states are p + \Delta and p - \Delta. These are distinct for any \Delta (except obviously \Delta = 0), and you get no interference.

What I'm saying is that the mirror doesn't start with a definite momentum. In the simplest case*, it starts with a momentum distribution described by some wavefunction \psi(p). In that case, the two possible final states are \psi(p-\Delta) and \psi(p+\Delta). Depending on the form of \psi and the magnitude of \Delta, these two final states could be anything from clearly different to almost identical. A measure of their overlap is given by the correlation function


\int \mathrm{d}p \, \psi^{*}(p-\Delta) \psi(p+\Delta) \;,

where \psi^{*} is the complex conjugate of \psi. If you account for the fact that for instance photons can interact with the experimental apparatus, you'll typically find that the visibility of interference terms depends on such a correlation function. If \Delta is much smaller than the width of \psi then \psi(p-\Delta) \approx \psi(p+\Delta), the correlation function above is nearly 1, and you get a nice clear interference pattern. At the opposite extreme, if \psi has a narrow shape and \Delta is larger than its width, then \psi^{*}(p-\Delta) \psi(p+\Delta) \approx 0 everywhere, the correlation function is pretty much 0, and you get little or no visible interference.

* In general, it could be in an entangled state with the rest of its environment.


Models representing our knowledge doesn't longer have to be local - we have for example classical analogue of EPR: we know that there is red and blue ball, which in some deterministic but unknown way are send in opposite directions - now in model representing our knowledge, getting know one color means we immediately (faster than light) get know the second color.
This is in no way an analogue of EPR. You're just describing a classical correlation produced at a common source, which in itself didn't trouble the EPR authors and would normally be considered a perfectly local phenomenon. The problem with EPR isn't that the result of a measurement made in one place can "determine" the result of a distant measurement. The problem in EPR is that the choice of which measurement is made in one place apparently has an instantaneous influence on the distant system.


If we want to talk about objective - fundamental quantum mechanics, there is no longer environment and so there is no longer measurements Heisenberg principle applies to - we can forget about this principle for a moment.
No, we can't because as I said before, Heisenberg uncertainty is not a feature of the measurement process. The fact that position and momentum are Fourier conjugate is an integral part of what you keep calling "fundamental quantum mechanics". Of course that has implications for "practical quantum mechanics" - it means in practice we can't simultaneously measure a particle's position and momentum. But according to "fundamental quantum mechanics", that's because such a state simply does not exist. The difference between "PQM" and "FQM" is that the former treats the Born rule and wavefunction collapse as postulates while the latter tries to give an explanation of the measurement process in terms of the remaining postulates of the theory. The distinction between the two has nothing to do with Heisenberg uncertainty. That just follows from the commutation relations that position and momentum are postulated to have, even in "FQM". If you ignore it, you're not doing any kind of quantum mechanics any more.

About measuring momentum ...
Standard picture of localized objects in quantum mechanics is through wave packets - while momentum measurement, probability distribution among values is e.g. a gaussian.
The problem with standard QM description is that such wave packet increase its width while evolution, what suggests that observed by us photons created by deexcitations of single atoms in another galaxy, increased its shape to macroscopic one ... while we know that such photons still excitate single atoms, small delay on one path in MZ interferometer destroys interference, we don't observe 'fuzzying' of particle's charge, particles in scatterings are observed as having extremely small fixed radius/shape - that means photons, particles maintain their shape - are solitons - there is required some nonlinearity in quantum mechanics.
And similarly with macroscopic objects - QM doesn't make that e.g. meteorites, mirrors increase their width while evolution.

So let's return to our mirror - if we ask about its momentum, there is indeed some probability distribution among possible outcomes, but this uncertainty is only property of our measurement (physics knows precisely the whole Fourier transform) - if we would like to use it to estimate mirror's position in future or past, we would have to multiply this uncertainty of our knowledge by the delay - in such model representing our knowledge, mirror would abstractly became wider.
But in real physics mirror maintain its shape - is moving with some exact velocity, like the peak of Fourier transform (we don't know) and it's this exact velocity what is affected by momentum transfer from our photon.
Now while measuring mirror's position after some chosen delay, there is some uncertainty, but if physics not us made the evolution - this uncertainty doesn't grow with chosen delay. So we can choose this delay large enough (like a year) to make this uncertainty negligible.

Heisenberg's principle assumes linear QM - nonlinearity making that width of wave packets isn't in fact growing, makes we can bend this principle (there is a chapter about modified uncertainty principle because of unavoidable nonlinearities in Croca's book).
To summarize - you would be right if only physics(FQM) would be linear ... but fortunately it's not our case :)

The problem in EPR is that the choice of which measurement is made in one place apparently has an instantaneous influence on the distant system.
But PQM we are able to use isn't the fundamental theory, but only a model representing our limited knowledge (like quantum mechanics of Schroedinger's cat as observer) - so your sentence means only that our measurement has influence on our knowledge about distant system - exactly as in two balls analogue I gave.
Can you prove that in not our model, but real physics (FQM) our measurement still "has an instantaneous influence on the distant system"?
Now particles (against PQM) maintain their shape - are solitons - are much more complicated than classical scenarios considered in Bell's argumentations - soliton interfere with itself - it would go one path in MZ interferometer, but Fourier transform says that there is also some its 'shadow' (called theta wave in Croca's paper) carrying some information through the second path ...


The fact that position and momentum are Fourier conjugate is an integral part of what you keep calling "fundamental quantum mechanics".
Generally Fourier transform is useful mathematical tool to solve simple linear PDEs or approximate more complicated ones.
It's integral part of PQM - usually linear approximation representing our knowledge, allowing to e.g. say that if we know only momentum of particle, according to our knowledge it could be at any point of universe (constant amplitude), but we know something about this subset of scenarios our knowledge allow us to restrict to - with given (phases of wavefunction) expected relative phases of scenarios being now in given points.
But how do you see it in real physics (FQM), in which particles are quite well localized and maintains their shapes?

The problem with standard QM description is that such wave packet increase its width while evolution, what suggests that observed by us photons created by deexcitations of single atoms in another galaxy, increased its shape to macroscopic one ... while we know that such photons still excitate single atoms
First of all, the fact that photons can be delocalized doesn't mean that they can interact with a large number of atoms simultaneously. The interaction is still point-like. The delocalization just means that someone in the distant galaxy couldn't predict in advance which atom the photon would finally interact with. Second, the wavepacket associated with a photon travelling in a vacuum doesn't necessarily have to increase in width. A single free photon's wavefunction is governed by the massless Klein-Gordon equation, which has solutions of the form f(x \pm ct) for arbitrary fixed functions f (this is a property unique to massless particles). Finally, while the speed of light is a constant in a vacuum, in matter it can depend on frequency and polarisation. Consequently, wave packet dispersion does occur in optical fibers for instance, and this has to be accounted for in the telecommunications industry, both for classical light pulses and individual photons.


that means photons, particles maintain their shape - are solitons - there is required some nonlinearity in quantum mechanics.
See above. The Klein Gordon equation - a linear differential equation - has propagating solutions of fixed shape.


And similarly with macroscopic objects - QM doesn't make that e.g. meteorites, mirrors increase their width while evolution.
We wouldn't expect to observe dispersion in that case anyway: the dispersion predicted by QM for macroscopic objects is tiny. To illustrate, suppose you prepare a 1 kg object whose center of mass is delocalized with an uncertainty of an ångström (10-10 m). In that case an easy calculation will tell you that you might have to wait up to six million years for that uncertainty to grow by another ångström. And that's assuming you leave that 1 kg object in a vacuum in isolation (so it doesn't interact with anything) for all that time.


But in real physics mirror maintain its shape

Now while measuring mirror's position after some chosen delay, there is some uncertainty, but if physics not us made the evolution - this uncertainty doesn't grow with chosen delay.
Do you think you're God? Do you believe you have some sort of special, direct knowledge about "real physics" that the rest of us don't have access to? If not, you have no basis for claiming that the mirror's center of mass won't disperse. You're just assuming that doesn't happen.


So we can choose this delay large enough (like a year) to make this uncertainty negligible.
Again, just to give you an idea, a photon with a wavelength of say 550 nm (in the green range) has a momentum of about 1.2x10-27 kg m/s. If it transferred all its momentum to the 1 kg object I mentioned above, it would change its velocity by about 1.2x10-27 m/s. In the six million year period I referred to above, that would cause it to move about 2.3x10-13 m. Compare with the fact that the uncertainty in its position is supposed to grow by about 10-10 m in that time.


To summarize - you would be right if only physics(FQM) would be linear ... but fortunately it's not our case :)
Quantum mechanics, to the best of our ability to test it, is linear. The dispersion associated with macroscopic objects that QM predicts is far too small to be ruled out by everyday observation.


But PQM we are able to use isn't the fundamental theory, but only a model representing our limited knowledge (like quantum mechanics of Schroedinger's cat as observer) - so your sentence means only that our measurement has influence on our knowledge about distant system - exactly as in two balls analogue I gave.
Can you prove that in not our model, but real physics (FQM) our measurement still "has an instantaneous influence on the distant system"?
EPR was originally about quantum mechanics. Bell's theorem is not. Bell showed that the type of non-locality the EPR authors were bothered by could be measured just from certain statistical properties of the predictions QM makes, without reference to the details or "mechanism" of the theory. It's a very general result.

The interaction is still point-like. The delocalization just means that someone in the distant galaxy couldn't predict in advance which atom the photon would finally interact with.
I completely agree - the interaction is point-like, bet we are not able to e.g. identify concrete excitation-absorption couples. Our measurement capabilities are limited and it is build in as integral part of practical quantum mechanics we use.

Second, the wavepacket associated with a photon traveling in a vacuum doesn't necessarily have to increase in width. A single free photon's wavefunction is governed by the massless Klein-Gordon equation(...)
I'm not sure about K-G which is quite limited, but in Schroedinger's equations wave packets (http://en.wikipedia.org/wiki/Wave_packet) grow in size approximately linearly with time - it cannot describe e.g. proton which in scattering experiments isn't blurred, but always gives similar results - it's shape and structure is maintained (what being soliton means) - and we don't need to be god to know it.

About the mirror, it could weight 1 mg ... but generally I have never claimed that it's a practical experiment.
What is important is if there is (unknown) 'wavefunction of mirror', it will have a bit larger momentum after reflecting photon.
We cannot know this wavefunction precisely, but shouldn't Physics 'know' it exactly? (God if you prefer)
If yes, scenarios with different paths of photons are objectively distinguishable.
If not - physics didn't noticed the difference after one reflection, succeeding reflections should be also ignored - momentum conservation would be violated, solar sails couldn't work ...

Bell showed that the type of non-locality the EPR authors were bothered by could be measured just from certain statistical properties of the predictions QM makes, without reference to the details or "mechanism" of the theory. It's a very general result.
It's very general result ... for classical particles - one particle goes that way/spin and the second the other ...
But for solitons it's not the end of the story!
When soliton meets an obstacle (half-silvered mirror), it is reflected or transmitted ... but there is also created some complicated wave, traveling the second way ('theta wave').
It's why we observe (e.g. for fluxons) and expect interference for solitons - it's clear that plane waves interfere in MZ interferometer configuration because of going simultaneously through both paths, so use Fourier transform to decompose soltion into plane waves - soliton has to go one path, plane waves of its mathematical decomposition goes also the second one - there is some low energy wave carrying information for interference going through the second path ...
So EPR using solitons means that there are send particles of some concrete spin configuration (classical picture), but additionally with each particle there travel 'a reminiscence' of Fourier decomposition of the second one - soliton have wave picture like in QM.

I completely agree - the interaction is point-like, bet we are not able to e.g. identify concrete excitation-absorption couples. Our measurement capabilities are limited and it is build in as integral part of practical quantum mechanics we use.
It's got nothing to do with "practical quantum mechanics". I've never heard of this "practical quantum mechanics" you keep talking about. I know that textbook QM typically treats measurement as a postulate, but that's it, and it's an issue that's completely tangential to the topic you started in this thread.


I'm not sure about K-G which is quite limited, but in Schroedinger's equations wave packets (http://en.wikipedia.org/wiki/Wave_packet) grow in size approximately linearly with time
Only for massive particles. For photons in a vacuum, E = pc, which means that \omega = c k. All the possible Fourier modes have the same phase velocity, and it's possible to build up wavepackets that don't disperse from these modes. For massive particles, and for photons in a medium, the different modes don't all have the same phase velocity. That's what causes dispersion. Even there, keep in mind that's only necessarily true for free particles. The Schroedinger equation with a potential term is still linear (the superposition of two solutions is still a solution), yet it's capable of describing bound states like atoms which don't grow over time.


About the mirror, it could weight 1 mg ...
And where would that get you? A lighter mirror would be more sensitive to an impact by a photon, but its positional uncertainty would also grow faster. Same result.


We cannot know this wavefunction precisely, but shouldn't Physics 'know' it exactly?
As far as "physics" is concerned, you don't get one wavefunction or the other. You get a superposition in which the two possible wavefunctions are entangled with the corresponding photon paths. If the wavefunctions have little or no overlap, the entanglement is strong and the two photon paths taken in isolation look like they're only probabilistically superposed. If the overlap is high, the entanglement is weak and the two photon paths taken in isolation look more like they're in a quantum superposition.

As for what happens to the entangled state when someone "observes" the interference pattern, that's an issue I'll leave between you and your favourite QM interpretation. It's got nothing to do with the conditions necessary for interference though.


It's very general result ... for classical particles - one particle goes that way/spin and the second the other ...
Actually, there's nothing in Bell's theorem that limits its applicability to classical particles.

Practical quantum mechanics is the one we are able to use, for example always with neglected some interacting environment - essential parameters to which our model doesn't have access to - so it has to have hidden statistical(/Feynman) ensemble among these parameters/scenarios going there ...
Another property is that against standard Schroedinger's equations, different modes interact with each other, what is essential part of QFT - our physics is nonlinear ... and it make that e.g. proton as wave packet isn't increasing its width, but always while scattering shows similar structure.
And if physics doesn't distinguish between situation in which mirror reflected photon and situation in which it didn't, it should also ignore succeeding single photons - it would would finally sum up to macroscopic violation of momentum conservation.

About Bell inequalities arguments, they works on concrete classical past states of particles, forgetting about that there is also a lot of information carried in very complicated way through the field - to see that particles maintaining shape (solitons) behave like in quantum mechanics, we have to decompose them into plane waves - it's also how we represent particles in QFT, but starting with that picture make it difficult to control their topological properties (e.g. electric field around charge is topological singularity).

Correlations in QM violate Bell inequalities because of Born rules saying that to translate amplitude we are adding, into probabilities of events, we have to square it (... like in classical Malus law).
If we want to work on concrete scenarios - remember that PQM represent our knowledge: statistical or Feynman ensemble among possible scenarios - trajectories of particles, which eventually can be branched (Feynman diagrams), we have to remember that these included scenarios don't end in this moment, but goes further into the future - if we want to translate their amplitudes into probabilities of events on constant time cut, we have to remember that they go toward both past and future from this selected moment - to get given scenario in this moment, we have to 'draw it' twice, getting squares relating amplitudes and probabilities.
These squares required to translate ensemble among 4D scenarios into situation in single moment - probability on constant time cut, are mathematically clearly seen in the simplest case - uniform ensemble (9th page of the presentation (http://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B7ppK4I%20yMhisYmI3YTAzNzYtMDkyNy00ZDAxLTg1 NGEtOTg4NWNkYzU3M%20jQ1&hl=en)). Here in recent Goyal, Knuth, Skilling paper (http://philipgoyal.com/papers/research/assets/FeynmanRulesPRA2010.pdf) is kind of similar derivation of Born rules: through translating ensemble among scenarios into constant time cuts.
If scenarios we take ensemble among wouldn't go into the future, but just ends now, the power relating amplitudes and probabilities would drop to one, making that Bell inequalities were fulfilled ... but such model leads to nonsenses.

Practical quantum mechanics is the one we are able to use, for example always with neglected some interacting environment - essential parameters to which our model doesn't have access to - so it has to have hidden statistical(/Feynman) ensemble among these parameters/scenarios going there
I don't know why you keep going on about this. In principle you can give a full fundamental desctiption of the photon + mirror (+ rest of the universe) if you want. If you do that, you find that the strength of the interference depends on the overlap of the final states of the mirror (+ universe) associated with each possible photon path.


Another property is that against standard Schroedinger's equations, different modes interact with each other, what is essential part of QFT - our physics is nonlinear ...
You're confusing nonlinearity of the classical equations of motion with nonlinearity of the Schroedinger equation. QFTs use Lagrangians with associated nonlinear EOMs which produce interactions, but they still use linear QM in the sense of the superposition principle: the superposition of two states that are solutions of a QFT is still a solution. It's the same with "ordinary" quantum mechanics: you can use a Hamiltonian which implies nonlinear classical EOMs - and you need such a Hamiltonian to describe eg. a bound atom - but the Schroedinger equation itelf is still linear: the superposition of two atomic state vectors is still a possible atomic state.


And if physics doesn't distinguish between situation in which mirror reflected photon and situation in which it didn't ...
You're still missing the point of what I said: "physics" doesn't care about categorising the final states of the mirror as objectvely "indistinguishable" or "distinguishable". "Physics" cares about the overlap of the final states. In "physics", that's what determines the strength of interference. Not whether they're "objectively distinguishable" in the simplistic sense you keep referring to.