Interference fringes, what if you sample them?

[DrChinese]

Quantum interference doesn't magically disable the function of telescopes.

Optical telescopes are not going to be able to see many quantum events. In this case: you cannot see which slit a photon passes through because, by definition (or rule or whatever), path interference cannot occur when you can. The only imaging related to the 2 slits you will see is the portion of detections for which interference did NOT occur. That will be some, and you could possibly resolve that at some level. But not the ones that interfere with themselves. That information simply is not present because it does not exist.

 

[David Byrden]

Let me spell out what happens to a single photon in the telescope:

1. Two lobes of its wave function pass through the slits (call them A and B)
2. A portion of lobe A impacts the entire lens glass
3. Simultaneously a portion of lobe B impacts the lens
4. If the lens were opaque they would be absorbed, and interference would begin here and we would see fringes on the lens
5. But no, it's not opaque, so both lobes pass through the glass
6. Within the telescope, both lobes are focused onto separate points on the imaging plane
7. They are no longer interfering because they no longer overlap
8. The imaging plane can tell which slit the photon used, by the position where it is absorbed

Does anybody disagree?

David

 

[Vanadium 50]

You really should read about how telescopes work.

You really don't want to take this tone with people who are trying to explain things. I am beginning to think your intent was never to ask a question but rather to push your own iconoclastic view. If that's not your intent, you might be less aggressive.

Consider a case where you have slits separated by a distance d, with a screen at a distance D away and at a point x on that screen. If you are at the first bright fringe, the condition is $x \approx \lambda D/d$. If you then position a telescope at x and look back at the source, you cannot resolve an angle $\lambda/d$ or smaller. These are the exact same conditions.

It doesn't matter how cleverly you make or position the telescope, since this is a property of the light you are using.

 

[DrChinese]

The wave interference does not begin at the point it enters the lens. It occurs at many spots prior, and in fact it would be incorrect to limit the paths taken to one or two particular ones. You are treating quantum objects like classical ones, and that will always get you in trouble - at least in the quantum forum.

If you study quantum reflection, how index of refraction changes the direction of light, Mach-Zehnder Interferometers, etc. you will see that all possible paths contribute to the final results. You are attempting to oversimplify something that is a complex subject. Before you speculate, I would recommend you beef up your understanding.

 

[Charles Link]

The wave interference does not begin at the point it enters the lens. It occurs at many spots prior, and in fact it would be incorrect to limit the paths taken to one or two particular ones. You are treating quantum objects like classical ones, and that will always get you in trouble - at least in the quantum forum.

If you study quantum reflection, how index of refraction changes the direction of light, Mach-Zehnder Interferometers, etc. you will see that all possible paths contribute to the final results. You are attempting to oversimplify something that is a complex subject. Before you speculate, I would recommend you beef up your understanding.

To the OP: @David Byrden If you study interferometers, even at the classical level, I think you will find the results are quite phenomenal: It is simply amazing that the presence of the second beam can cause all of the energy to wind up at one receiver, while with a single beam, there is a 50-50 energy split. (This phenomenal interference and wave behavior can be explained completely using the Fresnel coefficients for the amount of amplitude reflection that occurs from the beamsplitter, along with a little algebra to sum the waves).

 

[David Byrden]

You really don't want to take this tone with people who are trying to explain things.

Tell me, do you think that his explanation was correct?
The notion that all photons passing through a chosen point on the telescope lens will all meet up at a single point on its image plane - do you agree with it?
It would make my "thought experiment" look like rubbish - but is it true?

I am beginning to think your intent was never to ask a question but rather to push your own iconoclastic view.

I did ask a question about QM, and zonde effectively answered it (post 22).
Than, to my astonishment, my high school understanding of optics and telescopes was questioned by two people.
What kind of tone are you using with me? Quote: "You might want to review that"

Consider a case where you have slits separated by a distance d, with a screen at a distance D away and at a point x on that screen. If you are at the first bright fringe, the condition is $x \approx \lambda D/d$.

That's equivalent to the second equation that I wrote in post 28.
But OK, let's use your notation.
D is the screen distance, x is the fringe spacing, and so on.

If you then position a telescope at x and look back at the source, you cannot resolve an angle $\lambda/d$ or smaller.

That's odd - where are D and x ?
Why did you introduce them, if you're not using them now?

But let's assume you are correct here. A telescope can resolve angles greater than λ / d
Let's take a slit spacing of 0.1mm as an example.
And we'll use a red laser as the source.

You're telling me that a telescope can resolve the slits if the screen is closer than about 1.5cm from the lens.
And you're telling me that the lens diameter has no effect at all.
So, I might as well use a tiny lens, such as we find in a phone. Put the screen 12mm away, and there we are!
You're promising me that it will work !

I must ask you, where did you get that limit, λ / d

David

 

[Charles Link]

Tell me, do you think that his explanation was correct?
The notion that all photons passing through a chosen point on the telescope lens will all meet up at a single point on its image plane - do you agree with it?

@David Byrden The QM description of summing wave amplitudes over all possible paths, if I understand it correctly, is very much like diffraction theory. I have a better understanding of the classical (diffraction) description, but I do believe @DrChinese has considerable expertise in this (QM) area. I strongly recommend you study his explanations in detail before coming to the conclusion that they are anything but completely accurate.

 

[berkeman]

Thread is closed for Moderation...

Thread is re-opened.

 

[bhobba]

A telescope performs a Fourier transform on the incoming photon pattern

It does not. I do not know a lot about optics, but do know a bit about QED and a fair bit about Fourier Transforms and that is not what a telescope does. In fact what it does is quite complicated and requires a solid state physicist to fully explain but here is an overview. When a "photon" gets to a material, it is absorbed by the material. The material then sets up an internal electromagnetic vibration called a phonon (its what is known as a quasi-particle). The phonon has a less-than-light velocity that depends on the properties of the material. When the phonon reaches the "other side" of the material, it may create a new photon that then goes out and travels off at the speed of light.

We have a rule here - when you make a statement you need to be able back it up. Now precisely what do you have to back your statement up?

A bit of friendly advice from a mentor - around here, unless you are 100% sure about what you write, best to listen to what others say.

Thanks
Bill

 

[David Byrden]

When a "photon" gets to a material, it is absorbed... phonon...may create a new photon

Ah, but look at the bigger picture, Bill. That description covers only a single photon passing through a transparent material of undefined shape. But I'm talking about the pattern of photons processed by a telescope.
Let me explain where the Fourier transform comes into it:

Here's a very simple telescope, with one lens. Real telescopes have more lenses and mirrors, but they're essentially doing the same thing.
Incoming photons are focussed by the lens (on the left) to an image sensor (on the right).

The coloured lines represent the paths of individual photons.
All of the photons from a source are near parallel, so e.g. the photon paths "a1" and "a2" are from a "red source".

The telescope focusses light such that we get distinct images of the "red source" and "green source" on the image plane.
Notice that all of the photons collected from a source, from the whole surface of the lens, are brought to a single point.

Now: how is that a Fourier transform?

The incoming photons can be described as a function of position and momentum.
Photons from different sources have different momentum vectors. But they may have the same position - for example, a2 and b2 pass through the same point on the lens.

At the image plane, the momentum of the photons has been transformed into position (light from different sources goes to different points)
The position has been transformed into momentum (light from different parts of the lens arrives at different angles).
I'm sure you will recognise that's the essence of what a Fourier transform does!

The field of Fourier Optics, where we manipulate light using concepts from Communications Theory, is a fascinating one. There's an introduction here;
https://en.wikipedia.org/wiki/Fourier_optics

And that's what I referred to earlier.

Finally; my example telescope is handling an ensemble of photons, a "pattern" as I called it, but we're talking about quantum events here. What will happen with a single isolated photon?
To answer that, I call upon a wonderful property of photons. They don't affect each other.
The behaviour of a huge ensemble of photons arriving together, is the same as if they arrive one by one and we slowly accumulate the image. Every description of the Young's experiment will remind you of that.
And it's important to understand why that is; it's because the Wave Function of the single photon behaves as an ensemble of photons would. The Wave Function impacts the whole of the lens, it gets focussed as I described, and it defines the single photon's probability distribution to match exactly the image that a large ensemble of photons would form.

Has anybody any questions?

David

 

[bhobba]

Has anybody any questions?

The above is full of so much misinformation I do not know where to start. For example for photons position is not an observable:
https://www.physicsforums.com/threads/why-no-position-operator-for-photon.906932/

Really I should delete it , but I will give you one more chance to start listening instead of lecturing about what you do not know. This is a formal warning in my capacity as a mentor. Ignoring it will mean stronger action.

Thanks
Bill

 

[Vanadium 50]

Let's sweep aside some brush. This has nothing to do with QM; it's pure optics. This doesn't even really have anything to do with interference. Fundamentally, the claim is that one can beat the diffraction limitation for optics via clever construction and/or placement of a telescope. This is what we should be focusing (no pun intended, mostly) on.

This is impossible because the limitation is not a property of telescopes; it's a property of light.

Furthermore, there are zillions of pictures out there that show diffraction limitation. It's a real thing.

 

[David Byrden]

...the claim is that one can beat the diffraction limitation...
...This is impossible because the limitation is not a property of telescopes; it's a property of light.

Yes, you're right, there is a limit to attainable resolution for telescopes.
But the question is, will that limit prevent me doing what I proposed to do?
What is its actual size?

You posted an equation :

... slits separated by a distance d, with a screen at a distance D away and at a point x ...
...you cannot resolve an angle λ/d or smaller.

I'm sorry but I can't make sense of that.
I calculated that it's not a show-stopper at certain scales, but you insist that it is.

I have to ask you again, could we have a source for that equation?

David

 

[David Byrden]

I will give you one more chance to start listening instead of lecturing about what you do not know.

I'm not sure what you are saying. Is it;

[1] classical approximations of QM phenomena are not wanted in this forum,
or
[2] lens don't create the results you described
or
[3] other ?

David

 

[zonde]

This is impossible because the limitation is not a property of telescopes; it's a property of light.

Aperture of a telescope certainly is a factor in determining diffraction limit. https://en.wikipedia.org/wiki/Airy_disk
Here is reference for experiment described by David Byrden: https://arxiv.org/abs/quant-ph/0701027
In this experiment two pinholes produce two well resolved peaks in the image behind the lens.

 

[bhobba]

classical approximations of QM phenomena are not wanted in this forum,

What you are talking about has nothing to do with QM. It can all be explained with classical physics. But you insist on introducing QM into it and in doing that end up promulgating misinformation. For example you speak of individual photon paths - in QM there is no such thing - and that is just one of many errors in what you write. I am asking you to listen to what others in this thread are telling you rather than try to tell them and get it completely wrong.

Ah, but look at the bigger picture, Bill.

In other words ignore what is going on Quantum Mechanically, which is very complicated, and delve into something you have concocted yourself. As I said you really need a solid state physicist to sort this out using QM. We have some people here with that background, but its way beyond a B level thread nor is there is any gain in doing so since its all capable of being explained using classical physics.

Really this thread should be moved out of the QM forum and into the classical physics forum, but for now I will leave it here and see how it progresses.

Thanks
Bill

 

[David Byrden]

I am asking you to listen to what others in this thread are telling you rather than try to tell them and get it completely wrong.

Vanadium has been telling me, since post #5 on page 1, that the experiment can't work.
He or she has used strong language without reprimand.
And has implicitly painted me as a fool, unable to understand a two-term equation or check external resources.

I have listened and asked for clarification, to no end.

As moderator, and as a person capable of understanding QFT, would you now please step in?

David

 

[bhobba]

As moderator, and as a person capable of understanding QFT, would you now please step in?

He has done nothing wrong IMHO. However you are not listening to what others, including him, are telling you and instead post misinformation. This has lead to a thread that is not going anywhere. Because of this the thread will now be locked and the mentors will discuss any further action.

Thanks
Bill

 

[berkeman]

After further Mentor discussions, this thread will remain closed. Thank you everyone for trying to help the OP learn.