Measurement OF a Beamsplitter - Destroys Quantum Interference?

[ObjectivelyRational]

In those experiments demonstrating quantum interference which rely on a beam splitter to create a superposition of a photon taking different paths, what would happen if one made a sufficient "measurement" of the momentum of the beamsplitter itself? Would or should it destroy the interference pattern or quantum interference which depended upon the existence of the superposition of photon with itself?

Here I assume that the photon interaction with the beamsplitter conserves momentum and the superposition of the entire system includes entangled states of the photons with the beamsplitter... e.g. the state of the photon traveling along one leg of the apparatus is entangled with the state of the beamsplitter having momentum 1, while the state with the photon traveling along the other leg of the apparatus is entangled with the state of the beamsplitter having momentum 2.

If the beamsplitter is macroscopic (generally it is) how could it be in a superposition (momentum 1 and momentum 2) and what would be necessary to constitute a measurement sufficient to "collapse" the superposition, and would collapsing the superposition of the beamsplitter (as between momentum 1 and momentum 2) destroy the interference pattern down the line, which depends on the recombination of the quantum superposition of the photons, which would no longer occur?

 

[ObjectivelyRational]

Trying to change the title of the thread to "Measurement OF a Beamsplitter - Destroys Quantum Interference?" which is more accurate than the current title, but having difficulty doing so.

OK looks like the edit stuck this time.

Would appreciate ANYONE providing me with their best answer... I know there a lot of smart physicists here and this seems like a rather simple question.

 

[DrChinese]

Generally, there is nothing you are going to measure on the BS itself that will affect interference.

My assumption is that you are wondering if you could measure it so precisely that you could determine if a single photon went one way or the other. As long as it is producing interference, it won't register as going either way specifically. Quantum systems operate in the presence of "noise", impurities and the like all the time and still show quantum effects.

And the general rule is that a photon completely traveling through a medium is not going to impart any momentum to the medium.

 

[ObjectivelyRational]

Generally, there is nothing you are going to measure on the BS itself that will affect interference.

My assumption is that you are wondering if you could measure it so precisely that you could determine if a single photon went one way or the other. As long as it is producing interference, it won't register as going either way specifically. Quantum systems operate in the presence of "noise", impurities and the like all the time and still show quantum effects.

And the general rule is that a photon completely traveling through a medium is not going to impart any momentum to the medium.

I am assuming
1. one photon at a time is being sent
2. The paths are long enough (however long enough) to allow measurement of the beamsplitter while the photon in each state is traversing each long path (e.g. light-months or light-years long); and
3. The measurement of the momentum of the beamsplitter is sufficient to distinguish between momentum 1 and momentum 2. If the beamsplitter is e.g. floating in a vacuum and allowed to travel for a sufficient time for whatever measurement is used to detect the momentum - e.g. deflection of position (according to the same principle as a light sail) etc.

From your "general rule" it would appear one of momentium 1 and 2 imparted to the beamsplitter will be zero (transmission) while the other (reflection) will be non-zero. I generalize to simply momentum 1 and 2 without any reference to particular values, suffice to say the direction of the photon paths differ by 90 degrees in space, and hence the momenta imparted to the beamsplitter are actually different to conserve momentum in each case.

As in the OP measuring the beamsplitter should be such that the entangled state collapses, and we have only one beamsplitter state and only one path for the photon?

 

[DrChinese]

I am assuming
1. one photon at a time is being sent
2. The paths are long enough (however long enough) to allow measurement of the beamsplitter while the photon in each state is traversing each long path (e.g. light-months or light-years long); and
3. The measurement of the momentum of the beamsplitter is sufficient to distinguish between momentum 1 and momentum 2. If the beamsplitter is e.g. floating in a vacuum and allowed to travel for a sufficient time for whatever measurement is used to detect the momentum - e.g. deflection of position (according to the same principle as a light sail) etc.

From your "general rule" it would appear one of momentium 1 and 2 imparted to the beamsplitter will be zero (transmission) while the other (reflection) will be non-zero. I generalize to simply momentum 1 and 2 without any reference to particular values, suffice to say the direction of the photon paths differ by 90 degrees in space, and hence the momenta imparted to the beamsplitter are actually different to conserve momentum in each case.

As in the OP measuring the beamsplitter should be such that the entangled state collapses, and we have only one beamsplitter state and only one path for the photon?

There is no scenario I can think of which would support such a measurement as you envision. Not even in principle. Maybe someone else here knows of one. Photons are not billiard balls that bump things as they travel, imparting momentum in a classical fashion. And a Beam Splitter is designed to measure polarization, which commutes with momentum.

Keep in mind that there are all kinds of ways to change the path of a photon. Reflection in a mirror, for example. This does not cause a superposition to collapse. And entangled particles do NOT collapse to a specific state in any of those, including mirrors, fiber, wave plates, transparent media, etc.

And the obvious kicker is: how would you ever know the initial momentum of the BS in the first place?

 

[ObjectivelyRational]

Not even in principle. Maybe someone else here knows of one. Photons are not billiard balls that bump things as they travel, imparting momentum in a classical fashion.

Agreed, and I never stated or implied such. I observe only that momentum is conserved in the interaction between the photon and the beam splitter. The "state" of the two prior to the interaction has a total momentum, and this (for the law of conservation of momentum not to be broken) must be the same as the total momentum of the result of that interaction.

Your mention of "classical fashion" as though closed physical systems as "described by" QM do not conserve momentum... is this true?

And a Beam Splitter is designed to measure polarization

Ah, whether or not this is true, it is beside the point, but it may prove useful for a revised hypothetical. I am identifying the beamsplitter as that which interacts with the initial photon (P0) in a manner which we interpret as giving rise to a superposition (P1 and P2)... the photon following widely divergent paths 1 and 2. These widely divergent photons on different paths simply do not have the same momentum as each other, if we are to take these as "the same photon" in a superposition of two different states (P1, P2) arising from that same photon (P0) having an interaction with a BS (substitute whatever you would like here), implies two states for the photon - BS pair after the interaction:

|BS1>|P1> and |BS2>|P2>

each of which has the same total momentum of the original state prior to the interaction

|BS0>|P0>

Keep in mind that there are all kinds of ways to change the path of a photon. Reflection in a mirror, for example. This does not cause a superposition to collapse. And entangled particles do NOT collapse to a specific state in any of those, including mirrors, fiber, wave plates, transparent media, etc.

This goes back exactly to my OP. What do your examples from reality say about:
1. conservation of momentum
2. entangled states
3. the idea of "measurement" and "collapse" of a superposition of states

And the obvious kicker is: how would you ever know the initial momentum of the BS in the first place?

How does anyone's "knowing" the initial momentum have anything to do with the physical processes of measurement which causes collapse of the superposition?

 

[PeroK]

Your mention of "classical fashion" as though closed physical systems as "described by" QM do not conserve momentum... is this true?

Assuming that you do not know Quantum Theory well, I would say that the worst way to try to learn about QM is to consider how it applies to macroscopic objects.

There are, of course, important questions here for the consistency of QM - and the Copenhagen interpretation in particular. You could even say that Copenhagen explicitly gives an interpretation that applies to microscopic events but that, at some arbitrary and unspecified scale, is no longer a valid interpretation.

At the very least quantum effects are "washed out" at the macroscopic scale and the familiar laws of mechanics emerge. You ask about the effect of one photon on the state of a beam-splitter, which is no doubt being continuously assailed by photons from every direction; not to mention air molecules and/or vibrations from the Earth's surface.

Then there is the question of how you intend to measure the momentum of a beam splitter, accurate to the momentum of a typical photon?

 

[ObjectivelyRational]

Then there is the question of how you intend to measure the momentum of a beam splitter, accurate to the momentum of a typical photon?

I proposed conducting the experiment in 4. And yes it would require a perfect vacuum around the beamsplitter, a very lightweight beamsplitter (yet still macroscopic) and a very accurate way to measure deflection, and the time it would take for measurement might extend to a hundred million years and the divergent paths of the photons would extend across much of space...

the question is not so much about what we as humans can (and actually) literally do in an experiment, but
what the PHYSICAL UNIVERSE does.

when photons interact with things like beamsplitters, when superposition results from those interactions, and when measurement and "collapse" occurs and why...So assuming the superposition survives for the millennia required for the deflection (its possible), does "measurement" of that deflection cause the superposition to collapse?

 

[DrChinese]

...
This goes back exactly to my OP. What do your examples from reality say about:
1. conservation of momentum
2. entangled states
3. the idea of "measurement" and "collapse" of a superposition of states

How does anyone's "knowing" the initial momentum have anything to do with the physical processes of measurement which causes collapse of the superposition?

You would need to know the starting momentum M1 and the ending momentum M2 to determine the change in momentum due to the presence of the photon. I don't believe those quantities can be determined to a suitable degree of accuracy. And even if they could, I don't believe they would tell you anything about the path of the photon. But assuming all that was possible as you imagine: If you could deduce the path from the setup, regardless of whether you actually looked at the result, then there would be no interference.

 

[DrChinese]

... when photons interact with things like beamsplitters, when superposition results from those interactions, and when measurement and "collapse" occurs and why...

There is no objective way to determine when a superposition starts or ends, other than by assumption.

In a typical BS, the input photons are polarized at 45 degrees relative to the BS. In a Mach Zehnder Interferometer (MZI), the 2 output beams of the first BS are brought together through a second BS in such a way that the superposition is restored to a single path yielding no information about the path taken between BS1 and BS2. What can you objectively conclude in this case about the superposition? Was there collapse at any time?

 

[PeroK]

the question is not so much about what we as humans can (and actually) literally do in an experiment, but
what the PHYSICAL UNIVERSE does.

when photons interact with things like beamsplitters, when superposition results from those interactions, and when measurement and "collapse" occurs and why...

I can recommend:

https://www.goodreads.com/book/show/320449.Where_Does_The_Weirdness_Go_

One idea at the heart of Copenhagen is that the question of what the universe is doing while it is not being "measured" has no meaning. In fact, if you study electron spin, say, then this conclusion is effectively forced on you. Try looking for the Stern-Gerlach experiment. The opening section of the above book deals with this at length.

Also, Copenhagen does not (and cannot) say why the wave function collapses to an eigenstate of the observable. It's a postulate.

There are two fairly fruitless lines of enquiry here:

What is the universe really doing?
How do I explain the macroscopic world (mechanically) in terms of QM?

QM predicts what you will measure, if you carry out a measurement, but it does not say what a particle is doing while you are not measuring it. This is, in fact, the aspect of the theory that so disconcerted Einstein himself. But, time and experimental results have led almost inexorably to the conclusion that QM is correct in this respect.

 

[ObjectivelyRational]

If you could deduce the path from the setup, regardless of whether you actually looked at the result, then there would be no interference.

If our deductions from the setup is limited only by how long we have to wait before making a measurement of the position of the BS (impossible to measure unless there is enough deflection), then your statement implies that the experiment simply has to proceed long enough... then spontaneously once B1 and B2 are sufficiently different in position the superposition collapses?

Just a second... I think Penrose proposes such a mechanism... and a thought experiment.

Found a reference to it:
https://en.wikipedia.org/wiki/Penrose_interpretation

 

[ObjectivelyRational]

Just a second... I think Penrose proposes such a mechanism... and a thought experiment.

Found a reference to it:
https://en.wikipedia.org/wiki/Penrose_interpretation

So, if Penrose is correct, the interference pattern can exist as long as the states in superposition remain within some threshold difference of, and I'll paraphrase here, mass induced space time curvature from one another.. i.e. if the space-time curvatures are sufficiently different ... objective collapse occurs.

Here there is no "measurement" issue, and no subjective human "knowledge" or "deduction" issue. It would seem also that if the space-time curvatures are not different enough for the beamsplitters (or other optics mentioned by Dr.Chinese) as between the two states B1 and B2 (required to conserve momentum in each case) then they simply remain in superposition until the experiment is "concluded".

So in a way, Penrose answered my question.

Thanks Dr. Penrose!

 

[ObjectivelyRational]

There are two fairly fruitless lines of enquiry here:

What is the universe really doing?
How do I explain the macroscopic world (mechanically) in terms of QM?

Within the framework of a particular doctrinal approach, yes.

But reality is reality, and as physicists, the end goal is to identify it and describe it in as much detail as possible.

The universe is doing what it is doing, period. If something about what the universe is doing has any effect whatever upon us or our environment, we will be able to directly or indirectly measure and/or deduce it from its effects. The ghost like neutrino is a perfect example of the universe doing what it does in a way which is almost as if it didn't happen at all, except for our ability to study the universe to a point that it turns out to be fundamentally crucial. [If the interpretation of the superposition of states is correct, then the universe really is doing that (the loop holes for Bell's inequalities are all closed or almost all closed now?), and there's nothing fruitless in accepting that the universe IS doing what it is doing.]

So what the universe is doing is precisely what physicists study... and reality is only doing what it is "really" doing and it is doing nothing which it is not "really" doing, so its not fruitless at all.

As for using QM in the macroscopic "world" ... I agree that in its current form is not particularly great at scaling across all systems... but whatever physical science we end up with when complete and when it correctly describes the actual physical world (or approaches this), it will be the one which can describe reality in its entirety and at all scales, (even if the science itself looks a bit like a patchwork).

There is much work to be done.. and that's a good thing for physicists.

 

[DrChinese]

1. If our deductions from the setup is limited only by how long we have to wait before making a measurement of the position of the BS ...

the experiment simply has to proceed long enough...

1. Notice how quickly things switched from measuring the momentum change in the BS, to measuring the position change. These are NOT equivalent! Clearly, a precise position measurement of a quantum object leaves its momentum completely uncertain. That makes it impossible to measure a difference in momentum of the system due to any interaction with other objects.

Please re-consider the MZI. It is fundamental to its operation that what you envision measuring will NOT cause collapse, and will not cause the interference to disappear. As far as the apparatus knows, you are attempting to measure momentum.

2. I do not understand your references to the length of time the experiment runs. That photon flies by pretty fast.

 

[Lord Jestocost]

Regarding the OP, maybe the following might be of help:
Quantum Processes Systems, and Information by B. Schumacher, et al. Section 10.4.

 

[ObjectivelyRational]

1. Notice how quickly things switched from measuring the momentum change in the BS, to measuring the position change. These are NOT equivalent!

Measuring momentum by measuring position change is somehow not a measure of momentum?

That's equivalent to saying "measuring speed" (of something) cannot mean "measuring times and positions" of that something.
It defies logic to impose upon the words "measuring momentum", the non measurement of position, time, and mass of the object... (for those laypersons p=mass*velocity = mass*delta_vector position/delta_time).

"Measurement of X" does not mean direct Mystical Revelation of X.

As for the rest of your post, I see that my relying on a specific concrete experiment to discuss fundamentals is not always useful for having a discussion.

The abstract idea posed is that "classical" objects interacting with "quantum" objects must conserve certain quantities, and that if the "quantum" part is in a superposition which consists of two different values of that conserved quantity, the "classical" part must also (according to the Copenhagen interpretation) exist in a superposition. Also, if measurement of the "quantum" part, is sufficient to collapse the superposition, of everything, so too should SOME kind of measurement IN PRINCIPLE of the "classical" part... i.e. in whatever "respect" the classical part is in a superposition, sufficient measurement of THAT quantity (of the classical part) should collapse the whole thing... at least if one believes the Copenhagen interpretation (rather than the answer provided by Penrose).

 

[PeroK]

(for those laypersons p=mass*velocity = mass*delta_vector position/delta_time).

In QM, we have $p = -i\hbar \frac{d}{dx}$.

What you do have is:

$\langle p \rangle = m \frac{d\langle x \rangle }{dt}$

You really do need to learn some QM. You cannot simply apply classical mechanical thinking to the issue!

 

[ObjectivelyRational]

Regarding the OP, maybe the following might be of help:
Quantum Processes Systems, and Information by B. Schumacher, et al. Section 10.4.

The quantum state of the nonrecoiling and recoiling mirrors are "almost indistinguishable". That' almost an answer...

 

[DrChinese]

Regarding the OP, maybe the following might be of help:
Quantum Processes Systems, and Information by B. Schumacher, et al. Section 10.4.

Great reference. They look into the momentum question specifically, and conclude (for an MZI):

"The unroiling and recoiling mirror states are almost indistinguishable, and the photon is informationally isolated, just as originally supposed."

The MZI wouldn't work if it were otherwise.

 

[ObjectivelyRational]

In QM, we have $p = -i\hbar \frac{d}{dx}$.

What you do have is:

$\langle p \rangle = m \frac{d\langle x \rangle }{dt}$

You really do need to learn some QM. You cannot simply apply classical mechanical thinking to the issue!

No need to get snarky! :)

That's the expectation value of momentum which is analogous to its classical equivalent...

 

[PeroK]

No need to get snarky! :)

That's the expectation value of momentum which is analogous to its classical equivalent...

Okay, but clearly, if you have a particle that is:

1) At position $x = 0$ at $t =0$
2) At position $x = 5$ at $t =1$
3) Has a momentum of $p = 5m$ (during the first second). Where $m$ is its mass.

Then you have a classical model of the particle's motion. That is not a QM model of the particle.

The QM model is governed by the wave-function (or, more generally, the state of the particle).

 

[ObjectivelyRational]

Suppose you have a single diffraction hole in a thin disc floating in a vacuum

You shoot photons (or electrons) at it one at a time from a great distance.

There is an interaction at the disc and diffraction occurs.

The state of the photon (or electron) after interacting with the disc is in a superposition.

The disc will also be in a superposition including states with transverse momenta appropriate to those transferred by the states of the photon in superposition, and the states of the disc will be appropriately entangled with the states of the photon (or electron)IF at some great distance at some later time we choose to place a screen behind the disc to cause a "measurement", the position of the photon (or electron) will collapse and become fixed, as will the particular state of the disc with its appropriate transverse momentum matching the deflection of the photon (or electron) as measured on the screen (position on the screen corresponding to the actual transverse momentum now "collapsed" to identity).

IF however, we forego interposing the screen to collapse the photon (or electron) states, we choose instead to measure, at some later time, the disc, there should be a way to do so IN PRINCIPLE, in a manner which causes it to collapse to a fixed transferred momentum... (in the same way deciding to intervene with the screen measured the photon (or electron)) collapsing the whole shebang.

ALSO in principle we are perfectly correct to assume that we can forego any measurement of either the disc or the photon (or electron)... in which case collapse of neither the disc and the photon (or electron) occurs until some other uncontrolled factor intervenes.

 

[zonde]

You can observe interference with static experimental setup and coherent photon beam. If you let some experimental equipment drift around too much then experimental setup will not be static enough. In other words original coherent photon beam will not remain coherent after interacting with equipment at different positions. But I do not see that it has anything to do with measurement of experimental equipment's positions.

 

[ObjectivelyRational]

You can observe interference with static experimental setup and coherent photon beam. If you let some experimental equipment drift around too much then experimental setup will not be static enough. In other words original coherent photon beam will not remain coherent after interacting with equipment at different positions. But I do not see that it has anything to do with measurement of experimental equipment's positions.

Hmm I think maybe I should be more specific so we can investigate exactly what is going on, I'll list the assumptions associate with the "Disc Scenario" above:

1. A coherent photon beam can be set up to send photons "one at a time"
2. A disc with a hole in it can cause diffraction of a single photon into a "superposition" of states (which could be measured on a screen as an interference pattern if performed over and over with single photons).
3. The interaction of the disc and each photon conserves momentum
4. Due to 3 and 2, the disc must also be in a superposition of states, each state entangled with a corresponding photon state, so that each combined "disc-photon" state conserves momentum.
5. Making a "measurement" (whatever that means) on the photon part of the combined state collapses the entire state.
6. Making a "measurement" (whatever that means) on the disc part of the combined state collapses the entire state

We can now make reference to things specifically which conflict with your experience and knowledge.

 

[zonde]

2. A disc with a hole in it can cause diffraction of a single photon into a "superposition" of states (which could be measured on a screen as an interference pattern if performed over and over with single photons).

I have problems with this assumption. I do not see that this assumption can be justified as part of consistent interpretation.
So maybe you should look at other answers from people who probably have no problems with this assumption.

 

[ObjectivelyRational]

I have problems with this assumption. I do not see that this assumption can be justified as part of consistent interpretation.
So maybe you should look at other answers from people who probably have no problems with this assumption.

Double or single slit diffraction -interference patterns... I have never heard that one need only reduce the intensity to single particles (photons or electrons) for the quantum behavior/ interference patterns to disappear...

Also, I was under the assumption that (assuming we insert a screen) one cannot know where the particle will hit the screen until it has done so (in essence it has no definite path until it is measured) we only know the probabilities of where it will land... meaning it is in a superposition until there is a measurement.

Can you be more specific about what needs to be adjusted in the assumption that you have problems with?

 

[zonde]

Double or single slit diffraction -interference patterns... I have never heard that one need only reduce the intensity to single particles (photons or electrons) for the quantum behavior/ interference patterns to disappear...

This of course is not the case as plenty of experiments have demonstrated interference with very low intensity beams.

Can you be more specific about what needs to be adjusted in the assumption that you have problems with?

Fair request, but I'm not sure what answer to give. I would say it's safe to assume that photon interference is indirect interaction between photon and ensemble.
Anyways there are experiments that observe interference between photon beams from two separate sources, for example:
https://journals.aps.org/pr/abstract/10.1103/PhysRev.159.1084
You can look if particular assumption is consistent with some interpretation of such experiment.

 

[ObjectivelyRational]

This of course is not the case as plenty of experiments have demonstrated interference with very low intensity beams.

Fair request, but I'm not sure what answer to give. I would say it's safe to assume that photon interference is indirect interaction between photon and ensemble.
Anyways there are experiments that observe interference between photon beams from two separate sources, for example:
https://journals.aps.org/pr/abstract/10.1103/PhysRev.159.1084
You can look if particular assumption is consistent with some interpretation of such experiment.

Granted, however,
even IF it is a fact that "different" photons can interfere, how would that logically bear upon what we observe about individual photons, or individual electrons, sent one at a time, which do form interference patterns.

Would it be a cleaner hypothetical to restrict the particle to an electron (and not a photon)?

 

[zonde]

even IF it is a fact that "different" photons can interfere, how would that logically bear upon what we observe about individual photons, or individual electrons, sent one at a time, which do form interference patterns.

Well, it is basically the same experiment as photons anyways are sent one at a time from either source, just with small difference that it is not one source but two independent sources.
So why there should be two different interpretations for two very similar experiments? And even more than that, one experiment can be seen as more specific subset of the other experiment.

Would it be a cleaner hypothetical to restrict the particle to an electron (and not a photon)?

Maybe. But I know a lot more different experiments with photons than with electrons or other massive particles, so I prefer photons.

 

[ObjectivelyRational]

So why there should be two different interpretations for two very similar experiments? And even more than that, one experiment can be seen as more specific subset of the other experiment.

I'm not sure what you mean, and I have yet to be convinced of the truth of what you mean. Please explain.

 

[zonde]

I'm not sure what you mean, and I have yet to be convinced of the truth of what you mean. Please explain.

Let's say we mix two photon beams on a beamsplitter and look for interference pattern. And we have two modifications of that experiment. In one case two beams come from the same source but original beam is split into two beams by beamsplitter. And in the other case we have two beams coming from two independent sources.
In case with one source, two beams are similar because they originate from the same source. In case of two sources, beams can be very different of course, and then we would not observe any interference pattern. But by doing careful arrangements of experimental setup we can approach such similarity that we start to observe interference pattern. So we kind of approach limiting case of single source setup. That way single source setup can be viewed as special case in a range of many different modifications of the same two sources experiment.

 

[Lord Jestocost]

Making a "measurement" (whatever that means) on the disc part of the combined state collapses the entire state

Regarding the measurement on the "disc part" and its consequences, have a look at "Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr's principle" by William K. Wootters and Wojciech H. Zurek.

 

[ObjectivelyRational]

I suppose it is interesting to speculate what would happen in a different experiment and why. Rather than complicate the issues by thinking of other experiments, I am engaged in the exercise of thinking of what would happen in the particular hypothesized experiment.

 

[zonde]

I suppose it is interesting to speculate what would happen in a different experiment and why. Rather than complicate the issues by thinking of other experiments, I am engaged in the exercise of thinking of what would happen in the particular hypothesized experiment.

Well, I gave my answer. If the drift of experimental equipment is large enough that you can tell what way went the last photon you would not observe interference pattern, whether you measure position of beamsplitter or not.