I Measurement OF a Beamsplitter - Destroys Quantum Interference?

[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=

 

[ObjectivelyRational]

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

That paper looks amazing! Thank you very much!

I mean bouncing electrons off of tiny things like nanofabricated double slits and oil droplets etc... that's just the sandbox I'm interested in.

 

[ObjectivelyRational]

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

That's too bad. This "measurement collapse" issue and quantum gravity are two things that need to be to solved.Thanks Peter for your insights, you've helped resolve much of the confusion here,
hopefully nothing is left unresolved on this thread which could potentially mislead any unwary bystander.

Cheers!