Undergrad Measurement OF a Beamsplitter - Destroys Quantum Interference?

[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.

 

[ObjectivelyRational]

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.

Thanks but I cannot access the paper.

I suspect that the correspondence principle is conceptually antithetical to an objective collapse theory such as Penrose's. I have found in the past that arguments mathematically dismissing left over "probabilities" (one way or another) as insignificant to be very "hand wavy", especially in the face of the certainty (probability of 1) of classical phenomena. "Almost 1" never equals "1".

Is there any insight you can provide?

 

[ObjectivelyRational]

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.

By that logic:

If the trajectory of the electron is large enough that you can tell what way it went then you would not observe an interference "pattern" in the momentum of the disc, whether you measure the position of the electron with the screen or not.

I assume the opposite, the interference pattern forms because of the superposition prior to measurement, and it is not affected by the fact that you "could" measure the system, only measurement causes the collapse of the superposition to a certainty among probabilities.

Note that the measurement does not restrict the possible paths of the electron or the possible momenta of the disc, it just fixes it by measurement after the superposition is set up.In any case you are still refuting the veracity of 2 above, even in the case of electrons?

 

[DrChinese]

By that logic:

1. If the trajectory of the electron is large enough that you can tell what way it went then you would not observe an interference "pattern" in the momentum of the disc, whether you measure the position of the electron with the screen or not.

2. I assume the opposite, the interference pattern forms because of the superposition prior to measurement, and it is not affected by the fact that you "could" measure the system, only measurement causes the collapse of the superposition to a certainty among probabilities.

Note that the measurement does not restrict the possible paths of the electron or the possible momenta of the disc, it just fixes it by measurement after the superposition is set up.

In any case you are still refuting the veracity of 2 above, even in the case of electrons?

Well, yes and no. If the apparatus is modified to restrict possible paths in certain ways, then no measurement is required to cause interference to cease. This can be done with either electron or photon, a bit easier to describe for a photon.

Say you place polarizers over each slit in a double slit setup (which would normally produce the classic interference pattern). Then send photons through 1 at a time. If the polarizers are aligned parallel, there WILL be interference. If they are instead crossed, then there will be NO interference. That is because it would be conceptually possible to learn "which slit" information by testing polarization of the photons when they strike the back screen. But there need not be such a test, regardless the interference is destroyed.

 

[ObjectivelyRational]

Well, yes and no. If the apparatus is modified to restrict possible paths in certain ways, then no measurement is required to cause interference to cease. This can be done with either electron or photon, a bit easier to describe for a photon.

Say you place polarizers over each slit in a double slit setup (which would normally produce the classic interference pattern). Then send photons through 1 at a time. If the polarizers are aligned parallel, there WILL be interference. If they are instead crossed, then there will be NO interference. That is because it would be conceptually possible to learn "which slit" information by testing polarization of the photons when they strike the back screen. But there need not be such a test, regardless the interference is destroyed.

Speaking for the moment about your hypothetical set up...
It seems to me that your "modification" of the system (equipment) which wipes out the interference is the equivalent of preventing the superposition from occurring in the first place, but this is not the same as the measurement of something which is already in a superposition. There is a distinction.

I am proposing measuring a system already in a superposition to cause collapse to a specific state.

 

[PeroK]

I am proposing measuring a system already in a superposition to cause collapse to a specific state.

Do you believe there is a fundamental distinction between a particle that is in a "specific" state, and a particle that is in a superposition of two or more states?

 

[DrChinese]

1. Speaking for the moment about your hypothetical set up...
It seems to me that your "modification" of the system (equipment) which wipes out the interference is the equivalent of preventing the superposition from occurring in the first place, but this is not the same as the measurement of something which is already in a superposition. There is a distinction.

2. I am proposing measuring a system already in a superposition to cause collapse to a specific state.

1. I see it as being in a superposition still, it just isn't in a superposition that produces an interference pattern (when set at crossed polarizer settings).

2. As in your earlier example with the Beam Splitter: The disk does not contribute in any meaningful way to eliminating interference, regardless of how you measure it.

 

[ObjectivelyRational]

Do you believe there is a fundamental distinction between a particle that is in a "specific" state, and a particle that is in a superposition of two or more states?

I'm not sure I understand your question...

I think there is a fundamental difference between a particle when it has large probabilities across a wide variety of states in superposition, and a particle which upon measurement is found to be in one of those states. In one sense the state vector only tells you about outcomes... but if that is all there is to the physical state of the particle at that time.. it is a perfectly accurate "label" for what that particle actually is.

It is difficult to determine whether the particle itself is different in these two situations, prior to measurement, and at measurement, because QM does not provide (IMHO) a sufficient theory of measurement itself as a physical process, just what constitutes causation for the "outcomes" represented by the coefficient of each basis state.

Whatever the "particle" is or is doing, I think the science by which we study the particle, does have a huge asymmetry or asymptote, or singularity at the point of "measurement".

 

[ObjectivelyRational]

1. I see it as being in a superposition still, it just isn't in a superposition that produces an interference pattern (when set at crossed polarizer settings).

2. As in your earlier example with the Beam Splitter: The disk does not contribute in any meaningful way to eliminating interference, regardless of how you measure it.

1. I don't see the significance of this example. By placing different polarizers over the slits, its as if we have two different particle sources, ones with opposing polarizations, why would we even think they could constructively or destructively interfere with each other? I would assume we would get two single slit interference patterns (depending upon alignment... slightly spaced apart)

2. This is a bald assertion and not a reasoned answer which is what I am looking for.
How small would that floating disk in space have to be for you to take it (combined with the electron) as a "meaningful" enough entangled state?

Which of 1-6 above is an incorrect assumption (post #25)?

 

[PeroK]

I'm not sure I understand your question...

Whatever the "particle" is or is doing, I think the science by which we study the particle, does have a huge asymmetry or asymptote, or singularity at the point of "measurement".

This is not the case. A particle, upon measurement, is in an eigenstate of the observable measured. This is not a singularity. It's true that in the special case of position and momentum the eigenstates themselves are not physically realisable, hence the state is always a "wave packet" of eigenstates.

That's why many texts on QM (e.g. Sakurai's Modern QM, which I would highly recommend) start with spin, where the eigenstates are physically realisable and the (false) distinction between a particle before and after a measurement is not made.

 

[DrChinese]

1. I don't see the significance of this example. By placing different polarizers over the slits, its as if we have two different particle sources, ones with opposing polarizations, why would we even think they could constructively or destructively interfere with each other? I would assume we would get two single slit interference patterns (depending upon alignment... slightly spaced apart)

2. This is a bald assertion and not a reasoned answer which is what I am looking for.
How small would that floating disk in space have to be for you to take it (combined with the electron) as a "meaningful" enough entangled state?

Which of 1-6 above is an incorrect assumption (post #25)?

#6 is incorrect. No measurement of momentum of the the disk itself is going to eliminate interference effects. As before, no interference effects would ever be observed if it were otherwise.

Honestly, I am not even sure at this point what you are asking. You seem to be fixated on the relationship of a particular component of a macroscopic apparatus (BS or disc), and a quantum particle. Generally, they will not exhibit any meaningful degree of entanglement. And generally, no measurement of a property of the apparatus is going to affect the quantum particle in any observable manner.

 

[ObjectivelyRational]

This is not the case. A particle, upon measurement, is in an eigenstate of the observable measured. This is not a singularity. It's true that in the special case of position and momentum the eigenstates themselves are not physically realisable, hence the state is always a "wave packet" of eigenstates.

That's why many texts on QM (e.g. Sakurai's Modern QM, which I would highly recommend) start with spin, where the eigenstates are physically realisable and the (false) distinction between a particle before and after a measurement is not made.

Perfect... back to an eigenstate... makes sense.

 

[ObjectivelyRational]

#6 is incorrect. No measurement of momentum of the the disk itself is going to eliminate interference effects. As before, no interference effects would ever be observed if it were otherwise.

Honestly, I am not even sure at this point what you are asking. You seem to be fixated on the relationship of a particular component of a macroscopic apparatus (BS or disc), and a quantum particle. Generally, they will not exhibit any meaningful degree of entanglement. And generally, no measurement of a property of the apparatus is going to affect the quantum particle in any observable manner.

When is an apparatus macroscopic and when is it not?

How can you say there is no "meaningful entanglement" if conservation of momentum is conserved? What could you possibly mean by "meaningful entanglement", either there is entanglement or there is no entanglement.

What do you mean by "generally" no measurement of a property of the apparatus is going to affect the quantum particle? Again you seem to think the "apparatus" is somehow apart from the system, it is part of the system. The disc IS a particle of the system, its just bigger and/or heavier... but not necessarily so big that this physics hypothetical just goes away.

 

[PeroK]

When is an apparatus macroscopic and when is it not?

The disc IS a particle of the system, its just bigger and/or heavier... but not necessarily so big that this physics hypothetical just goes away.

Consider this. You may know about the statistics of "indistinguishable" particles and that you cannot identify an individual electron. The same must be true of hydrogen atoms. You cannot distinguish and identify one hydrogen atom from another. And, for any molecule. Hence of any cell(?). Hence for any red snooker ball? The statistics of red snooker balls are different from the statistics of electrons. As far as the game of snooker is concerned they are indistinguishable, but physically nature does not agree; and behaves as though it really does know one snooker ball from another.

So, at what point do objects become distinguishable? And, at what point, are they a finite collection of a specified number of indistinguishable elementary particles?

So, your question is at what point does QM go away and leave classical mechanics? And that is not an easy question. But, one thing is clear: a physicist is distinguishable from another physicist; any two beam-splitters are distinguishable; any two red snooker balls are distinguishable; but, any two electrons are not.

Figure that one out!

 

[PeterDonis]

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.

You are drawing inappropriate inferences from these three postulates combined. Basically you are assuming that, once we measure the photon to have hit at a particular point on the screen (by observing the dot it makes there), that pins down one particular trajectory for the photon, and therefore one particular recoil trajectory for the disc with the hole in it. But that is not correct. For any given point on the screen, there are many different photon trajectories that lead to it.

In other words, observing a photon at a particular point on the screen does not tell you the exact momentum exchanged between the photon and the disc with the hole in it.

 

[PeterDonis]

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.

@ObjectivelyRational I don't think you've taken proper notice of this early comment by @DrChinese. Combine this comment of his, just quoted above, with what I said in my previous post #49; and suppose we now add to the experiment that, every time we shoot a single photon through the apparatus, we very, very precisely measure the recoil of the disc with the hole in it. In other words, instead of the outcome of each run being "photon made a dot at some particular point on the screen", it is now "disc was measured to have a particular recoil, and photon made a dot at some particular point on the screen".

@DrChinese gave a number of reasons why this experiment would be extremely difficult to do in practice, and might not even be possible in principle. But as his quote above shows, if we suppose for the sake of argument that this experiment is possible, its result would be that the interference would disappear: i.e., that the pattern of dots on the screen after many runs of the experiment would no longer show diffraction. It would just be a single bright spot behind the hole in the disc, the combined effect of many small dots from individual photons.

Does this answer the question you were originally asking?

 

[ObjectivelyRational]

You are drawing inappropriate inferences from these three postulates combined. Basically you are assuming that, once we measure the photon to have hit at a particular point on the screen (by observing the dot it makes there), that pins down one particular trajectory for the photon, and therefore one particular recoil trajectory for the disc with the hole in it. But that is not correct. For any given point on the screen, there are many different photon trajectories that lead to it.

In other words, observing a photon at a particular point on the screen does not tell you the exact momentum exchanged between the photon and the disc with the hole in it.

Right, the angles subtended by the hole as viewed from the point on the screen present a number of possible trajectories, but that bundle of trajectories is a relatively narrow bundle. Given the very wide angles that the particle could be diffracted at (45 degrees left versus 45 degrees right) that would present a number of different sharp bundles of momentum which should correspond to those different points...

Now I have each position state corresponding to a bundle of If momentum states, which together conserve momentum... is this a kind of entanglement?

 

[Mentz114]

Right, the angles subtended by the hole as viewed from the point on the screen present a number of possible trajectories, but that bundle of trajectories is a relatively narrow bundle. Given the very wide angles that the particle could be diffracted at (45 degrees left versus 45 degrees right) that would present a number of different sharp bundles of momentum which should correspond to those different points...

Now I have each position state corresponding to a bundle of If momentum states, which together conserve momentum... is this a kind of entanglement?

You might find this paper linked to in this thread interesting. It analyses the conditions that can give interference in general.

 

[PeterDonis]

the angles subtended by the hole as viewed from the point on the screen present a number of possible trajectories, but that bundle of trajectories is a relatively narrow bundle

No, it isn't, because the photon might not be traveling at the speed of light, and might not travel in an exact straight line except for a possible bounce at the disc.

Now I have each position state corresponding to a bundle of If momentum states

No, you don't, because the dot on the screen is not an exact point; it's a small region. Exact position states (i.e., position at just a single point) are not physically realizable.

s this a kind of entanglement?

After the photon interacts with the disc, the states of the disc and the photon will be entangled, but the states involved in the entanglement are not quite those you describe.

 

[ObjectivelyRational]

@ObjectivelyRational I don't think you've taken proper notice of this early comment by @DrChinese. Combine this comment of his, just quoted above, with what I said in my previous post #49; and suppose we now add to the experiment that, every time we shoot a single photon through the apparatus, we very, very precisely measure the recoil of the disc with the hole in it. In other words, instead of the outcome of each run being "photon made a dot at some particular point on the screen", it is now "disc was measured to have a particular recoil, and photon made a dot at some particular point on the screen".

@DrChinese gave a number of reasons why this experiment would be extremely difficult to do in practice, and might not even be possible in principle. But as his quote above shows, if we suppose for the sake of argument that this experiment is possible, its result would be that the interference would disappear: i.e., that the pattern of dots on the screen after many runs of the experiment would no longer show diffraction. It would just be a single bright spot behind the hole in the disc, the combined effect of many small dots from individual photons.

Does this answer the question you were originally asking?

This comes close.. I think, or perhaps at one point it would have answered my question... and I'm somewhat disposed to agree.

I want to reassure myself that there is no artificial asymmetry in my own understanding...

If the apparatus is set up the same way every time a single particle is shot at the disc, and for the sake of argument we perform two kinds of tests,
A. for 10000 shots we quickly (after the interaction) place a screen far on the other side of the disc to intercept each particle after the interaction without touching the disc until after the measurement, and
B.for a different 10000 shots we quickly place a screen "super close" to the front side of the disc to intercept the recoiling disc without interacting with the particles on the other side until after the measurement of the disc...

In experiment A there should be a "interference pattern" of particle hits on the screen
In experiment B should there not also be an interference pattern in space or perhaps also in time?... maybe the screen is polled for a hit at a very fast rate

Now what if after every run of A we place a near screen to measure the disc... shouldn't there be pattern by virtue of A being an uneven distribution of location? Perhaps not technically an interference pattern but a collapsed correlation to the interference pattern of the particles?

Equally, if we put a screen out to catch the particles far out after each run of B, wouldn't there also be a pattern (perhaps not an interference pattern) corresponding to the interference pattern of the disc?

I think I might be getting ahead of myself... or confusing myself at this point.
thank you Peter you have given me much to think about.

 

[ObjectivelyRational]

You might find this paper linked to in this thread interesting. It analyses the conditions that can give interference in general.

Thank you! That looks interesting.

 

[PeroK]

[ suppose we now add to the experiment that, every time we shoot a single photon through the apparatus, we very, very precisely measure the recoil of the disc with the hole in it. In other words, instead of the outcome of each run being "photon made a dot at some particular point on the screen", it is now "disc was measured to have a particular recoil, and photon made a dot at some particular point on the screen".

Wouldn't you also need to know the initial momentum of the photon? Measuring the recoil on the disc would give you (at best) the change in momentum of the photon.

In any case, I found this paper (which looks quite interesting) and has a discussion of this with reference to the Bohr-Einstein debates.

http://iopscience.iop.org/article/10.1088/1742-6596/701/1/012007/pdf

 

[DrChinese]

How can you say there is no "meaningful entanglement" if conservation of momentum is conserved? What could you possibly mean by "meaningful entanglement", either there is entanglement or there is no entanglement.

What do you mean by "generally" no measurement of a property of the apparatus is going to affect the quantum particle?

I am going to forego discussion of your experiment itself, as I think PeterDonis, PeroK and others are addressing this. But there are a few things I'll comment on.

Entanglement is not binary, as in "it is" or "it isn't" entangled. There can be partial entanglement. And entanglement can occur between many objects, although there is a limit to "how entangled" they can be. For a maximally entangled pair of particles, there is "monogamy of entanglement." And there can be entanglement on some observables, but not on others.

The reason I use the word "generally" is that in quantum physics, there is almost always an exception to a general rule.

There is essentially no measurement of the momentum of the disc that will lead to the elimination of quantum interference effects of a photon (or an electron). Interference is observed by a series of position measurements. The photons' momentum is undefined in this situation. Sure there is conservation. But when you try to measure the disc's change in momentum due the photon's interaction with the disc, that value is relatively meaningless. You can't deduce a (unique) photon path taken from that. There are many photon paths that would yield the same number. (Interference remains.)

 

[PeterDonis]

Wouldn't you also need to know the initial momentum of the photon?

You have a reasonably narrow range for that because you know the relative locations of the source and the hole in the disc. That constrains the direction the photon has to travel to come from the source and pass through the hole.

 

[PeterDonis]

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

This is all speculative and has no prospect of being tested experimentally any time soon.

 

[Lord Jestocost]

Thanks but I cannot access the paper.

https://scholar.google.de/scholar?h...ntitative+statement+of+Bohr's+principle&btnG=