Momentum transfer to mirror in Mach–Zehnder interferometer ?

It is said that there is interference in Mach–Zehnder 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) - photons coming from different slit, excitate different pixel on its matrix ...

 

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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.

 

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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.
So I would say that even in vacuum, there would be interference ...

 

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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

http://en.wikipedia.org/wiki/Wheeler's_delayed_choice_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 ...

 

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.

Fundamentally impossible to have occurred you mean?

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 ...

 

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.

 

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... ?

 

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.

 

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)

 

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

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

 

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.

What classification? If you mean that "completely indistinguishable" and "perfectly distinguishable" are just two extremes in a spectrum, then I never said otherwise.