Why do orthogonal polarizers at slits eliminate interference pattern?

[ChadGPT]

TL;DR Summary

More of a wave optics question. Is it the case that the two waves from each slit cannot interfere at all, resulting in two superimposed single slit diffraction envelops at the screen? Or is it that the positive and negative diagonal components create a fringe and anti fringe interference pattern superimposed on the screen?

1) Very simple setup: a light source sends single photons towards a double-slit setup. After slit A there is a horizontal polarizer, and after slit B there is a vertical polarizer. Finally, there is a back screen.

In this setup we will see no interference pattern, despite the fact that there are no detectors and thus no which-way data being obtained. There are many explanations for why we get no interference pattern at the screen, and I am trying to figure out which is correct.

2) Very simple quantum erasure: Exact same setup, but now we place a 45º diagonal polarizer before the back screen.

Now the interference pattern reappears! And, interestingly, if we place a -45º diagonal polarizer before the back screen instead, we get an "anti-fringe" interference pattern instead.

THE QUESTION: There seems to be two possible explanations of what is going on here: The first explanation is that, when the waves from each slit are orthogonally polarized they cannot interact with each other because their electomagnetic oscillations are perpendicular to each other. Thus, what we see at the back screen is two single-slit diffraction envelopes superimposed onto each other. Placing the diagonal polarizer before the screen transforms the wave oscillations so that they once again interact, reproducing the interference pattern at the back screen. The second interpretation is that the diagonal components of both waves are always able to interact. 50% of the time the 45º components interact, producing a fringe interference pattern, and 50% of the time the -45º components interact, producing an anti-fringe interference pattern. When these two interference patterns are superimposed over each other, they produce what looks like a particle pattern at the back screen. When a diagonal polarizer is placed before the back screen, it blocks one of the two diagonal component oriented possibilities from reaching the back screen, allowing only the others through. So if a 45º diagonal polarizer is placed before the back screen, then all -45º diagonal component oriented photons will not reach the back screen, and what ends up on the back screen is all of the 45º diagonal component oriented photons, producing a fringe interference pattern.

Maybe there are more options I'm not aware of, but what is actually going on here?

 

[PeterDonis]

More of a wave optics question.

In which case it's not a QM question. Which theory do you want to use to discuss your question? If it's classical wave optics, it belongs in the classical physics forum, not the QM forum. If it's QM, then it's not a wave optics question, it's a QM question.

 

[anuttarasammyak]

Now the interference pattern reappears! And, interestingly, if we place a -45º diagonal polarizer before the back screen instead, we get an "anti-fringe" interference pattern instead.

Thanks, It is new to me. Is "anti-fringe" black-and-white oppisite pattern to fringe ?

 

[ChadGPT]

In which case it's not a QM question. Which theory do you want to use to discuss your question? If it's classical wave optics, it belongs in the classical physics forum, not the QM forum. If it's QM, then it's not a wave optics question, it's a QM question.

Well, it's how classical wave optics affects a QM experiment. But since the core of the issue is relative to how a QM experiment behaves, I thought the QM forum was best. If you disagree, I'll move it to the classical physics form. I'd say it could be in either.

 

[ChadGPT]

Thanks, It is new to me. Is "anti-fringe" black-and-white oppisite pattern to fringe ?

Yes, anti-fringe is an interference pattern where the peaks and troughs are opposite to the usual "fringe" interference pattern we are used to seeing.

 

[PeterDonis]

it's how classical wave optics affects a QM experiment

Classical wave optics doesn't apply if we are analyzing a QM experiment.

the core of the issue is relative to how a QM experiment behaves

Ok, then we'll keep the thread in this forum. But bear in mind what I said above.

 

[PeterDonis]

a light source sends single photons towards a double-slit setup. After slit A there is a horizontal polarizer, and after slit B there is a vertical polarizer. Finally, there is a back screen.

In this setup we will see no interference pattern

Yes.

despite the fact that there are no detectors and thus no which-way data being obtained

Wrong. The polarizers, since they are set at orthogonal polarizations, are giving which-way data. The fact that we don't have a device that can record that data for us to review later doesn't mean the data isn't there. It is precisely the fact that the polarizers are giving which-way data (even though it gets thrown away without humans reading it) that removes the interference pattern.

There are many explanations for why we get no interference pattern at the screen

Please cite actual references for this claim. The only explanation I have seen in the literature is the one I just gave above.

Exact same setup, but now we place a 45º diagonal polarizer before the back screen.

Note that it's not as simple as your description makes it sound; we have to make it so every possible location on the back screen that could record the impact of a photon, has a 45 degree diagonal polarizer in front of it.

Now the interference pattern reappears!

Yes, because the diagonal polarizer, since it is (a) oriented halfway between the two polarizers at the slits, and (b) oriented the same way for all photons, removes the which-way information that the horizontal and vertical polarizers created.

if we place a -45º diagonal polarizer before the back screen instead, we get an "anti-fringe" interference pattern instead.

If you want to look at it that way, yes: this polarizer is oriented 90 degrees different from the first 45 degree polarizer, so it changes all of the phases by that amount relative to the first polarizer, which reverses the pattern.

There seems to be two possible explanations of what is going on here

Both of your proposed "explanations" are based on an invalid model. See below.

The first explanation is that, when the waves from each slit are orthogonally polarized they cannot interact with each other because their electomagnetic oscillations are perpendicular to each other.

There are no "electromagnetic oscillations" in a quantum model. As I said in my previous post, you can't use a classical wave model to analyze a quantum experiment.

what we see at the back screen is two single-slit diffraction envelopes superimposed onto each other.

This is true, but not for the reason you give. The correct reason is that the two polarizers at the slits give orthogonal polarizations, which means they give complete which-way information about which slit each photon went through.

Placing the diagonal polarizer before the screen transforms the wave oscillations

There are no "wave oscillations". See above. As I said above, the diagonal polarizer removes the which-way information.

The second interpretation is that the diagonal components of both waves are always able to interact.

Again, there are no "waves" here. See above.

 

[ChadGPT]

If you want to look at it that way, yes: this polarizer is oriented 90 degrees different from the first 45 degree polarizer, so it changes all of the phases by that amount relative to the first polarizer, which reverses the pattern.

There are no "electromagnetic oscillations" in a quantum model.

There are no "wave oscillations".

Again, there are no "waves" here.

thank you. I'm left wondering, however, if there are no waves or wave oscillations, what then we are talking about when we say the beam is horizontally/vertically polarized, or that the "phases" shift. I was under the assumption that what it means for the beam to be horizontally or vertically polarized is that its wave oscillations are oscillating either horizontally or vertically. And when you say the -45º diagonal polarizer is oriented 90º relative to the 45º polarizer, isn't that referring to the oscillations of the wave?

Perhaps you mean that in QM we are actually talking about "probability waves" rather than physical electromagnetic waves. Yet still, whether it is EM or probability, wave optics seem to be in play, as evidenced by the resulting "anti-fringe" pattern when the phase is shifted 90 degrees by the -45º diagonal polarizer being in place instead of the 45º one. That can only happen because the phase relationships between the two interfering beams are changed such that where two troughs used to meet now two peaks meet, etc.

My underlying question is this: We know what we should expect to see if the orthogonal polarizers are causing collapse. But should we expect to see anything different if the orthogonal polarizers are not causing collapse? To me it seems like we should expect to see the same results on the back screen in both cases.

 

[PeterDonis]

if there are no waves or wave oscillations, what then we are talking about when we say the beam is horizontally/vertically polarized, or that the "phases" shift

We are talking about properties of the quantum state that describes the photons. Different polarizations correspond to different spin properties of the quantum state. Different "phases" correspond to different phases of the quantum state.

I was under the assumption that what it means for the beam to be horizontally or vertically polarized is that its wave oscillations are oscillating either horizontally or vertically. And when you say the -45º diagonal polarizer is oriented 90º relative to the 45º polarizer, isn't that referring to the oscillations of the wave?

Not in QM, no. In a classical wave model, yes, but as I've already said, you can't use a classical wave model to analyze a QM problem.

Perhaps you mean that in QM we are actually talking about "probability waves" rather than physical electromagnetic waves.

No, in QM we are talking about quantum states. Those states are used in QM to predict the probabilities for things, but they aren't "probability waves". A better term would be probability amplitudes.

whether it is EM or probability, wave optics seem to be in play

Not classical wave optics, no, not if you are using QM to analyze the experiment.

Note that you do not need QM to explain the interference pattern itself: Thomas Young explained it quite well in the early 1800s using a classical wave model of light. Even some of the things you can do with polarizers to affect the pattern can be explained using a classical wave model of light.

What the classical wave model cannot explain is why, if you make the intensity of the light low enough, the light appears on the detector screen as individual dots, one at a time, not as a very faint version of the pattern you see when the intensity is high. At low intensity the pattern only builds up over time as the combination of impacts of many dots. That is the key fact that requires QM.

Of course, once you know you need QM, you can use it to explain all the other stuff too, using probability amplitudes. Feynman's book QED gives a good layman's discussion of how to do this for light using the path integral formulation of QM, as well as explaining how this model also leads to the classical behavior you're familiar with, under the conditions where that behavior is observed.

We know what we should expect to see if the orthogonal polarizers are causing collapse. But should we expect to see anything different if the orthogonal polarizers are not causing collapse?

Whether or not "collapse" is an actual physical process depends on which QM interpretation you adopt. Interpretation discussions belong in the interpretations subforum, not this one.

As far as experimental predictions go, QM only makes one prediction for a given scenario, and that is the same regardless of what interpretation you adopt.

 

[ChadGPT]

We are talking about properties of the quantum state that describes the photons. Different polarizations correspond to different spin properties of the quantum state. Different "phases" correspond to different phases of the quantum state.

Okay, so then we can say that the polarizers are affecting the spin properties of the quantum state in way that it at least similar to classical wave mechanics, such that if there are orthogonal polarizers at the slits and a -45º polarizer before the back screen we see an anti-fringe interference pattern rather than a fringe interference pattern because of the 90º phase shift.

Whether or not "collapse" is an actual physical process depends on which QM interpretation you adopt.

As far as experimental predictions go, QM only makes one prediction for a given scenario, and that is the same regardless of what interpretation you adopt

What I mean is that either 1) what removes the interference pattern is the fact that the polarizers are determining which-way data, or 2) what removes the interference pattern is the fact that the polarizers are altering the spin properties of the quantum state such that no interference pattern can appear anyway.

My question has to do with possibility 2). For argument's sake, or theoretically, assume that the orthogonal polarizers revealing which-way data does not remove the interference pattern. In such a hypothetical scenario, would we still, nevertheless, see no interference pattern at the back screen? (of course I mean in the setup with just orthogonal polarizers at the slits and no diagonal polarizer before the screen).

I think you would still see no interference pattern, either because A) the two orthogonally polarized beams simply cannot interact, such that we will see two single-slit diffraction patterns superimposed on top of each other at the back screen, or because B) the diagonal components of the two beams interact producing a fringe interference pattern 50% of the time and an anti-fringe interference pattern 50% of the time, such that we will see both interference patterns superimposed over each other at the back screen, which again removes the interference pattern since they cancel each other out.

Perhaps someone else can give this question a go, Peter, if you don't know.

 

[PeroK]

Perhaps someone else can give this question a go, Peter, if you don't know.

I'll try a simpler explanation. Interference involves the superposition (addition) of two wavefunctions with complex probability amplitudes. If the wavefunctions are identical in other respects and the amplitudes are opposite, then you get totally destructive interference. Likewise, if the amplitudes are equal, you get constructive interference. Otherwise, you get something in between.

If the wavefunctions are different, then you get a cross term in the probability when you add them together (invacsuperposition) And, in particular, if the two wavefunctions have orthogonal spin states, then the cross term is zero and there is no interference.

So, it's all about what happens when you add two wavefunctions together.

 

[ChadGPT]

I'll try a simpler explanation. Interference involves the addition of two wavefunctions with complex probability amplitudes.

Yes!

If the wavefunctions are identical in other respects and the amplitudes are opposite, then you get totally destructive interference.

Right, so an "anti-fringe" interference pattern, where the maximums and minimums are reversed from the usual interference pattern.

Likewise, if the amplitudes are equal, you get constructive interference.

Yes, the regular "fringe" interference pattern.

Otherwise, you get something in between.

Yes.

If the wavefunctions are different, then you get a cross term in the probability when you add them together.

So now we are talking about other than amplitudes; as in not identical "in other respects." Is that right? Do the polarizers affect the amplitudes or just the other aspects? or both?

And, in particular, if he two wavefunctions have orthogonal spin states, then the cross term is zero and there is no interference.

Do orthogonal polarizers at the slits result in orthogonal spin states? By spin states does this equate to something like "polarization"? When there is no cross term is this like saying the two wave functions do not interact?

So, it's all about what happens when you add two wavefunctions together.

Okay, I think we're getting somewhere. So say you have a coherent beam of single photons incident on a double slit with orthogonal polarizers at the slits. I assume this results in the two wave functions from the slits having orthogonal spin states. If they have orthogonal spin states I assume they cannot interact so they cannot produce an interference pattern, and what we see at the screen will be two single-slit diffraction envelopes superimposed over each other. Is that right?

Now if we add the 45º diagonal polarizer before the back screen, I assume this alters both wave functions such that there is now a cross term when they reach the back screen, presumably because the diagonal polarizer altered the spin states? And this is why the interference pattern is recovered. Is that right?

Do the polarizers affect the amplitudes at all? Are the spin states and amplitudes related in some way?

 

[PeterDonis]

Okay, so then we can say that the polarizers are affecting the spin properties of the quantum state

Yes.

in way that it at least similar to classical wave mechanics

Somewhat, yes. But remember that we are dealing with photons, not classical waves, because you've chosen to use QM to analyze this experiment, not classical wave optics.

What I mean is that either 1) what removes the interference pattern is the fact that the polarizers are determining which-way data, or 2) what removes the interference pattern is the fact that the polarizers are altering the spin properties of the quantum state such that no interference pattern can appear anyway.

These aren't two different possibilities. They are just two different ways of saying the same thing. Determining which-way data is altering the spin properties of the quantum state so no interference pattern can appear.

My question has to do with possibility 2).

There is no possibility 2). See above.

For argument's sake, or theoretically, assume that the orthogonal polarizers revealing which-way data does not remove the interference pattern

There's no point in assuming something that contradicts the laws of physics. The laws of physics say that the which-way data does remove the interference pattern. That's the only theory we can use. We can't say anything about what would happen in some hypothetical universe where that wasn't the case, because we have no theory to tell us what would happen. You could make up anything you like. We don't do that here.

 

[PeterDonis]

If they have orthogonal spin states I assume they cannot interact

There is no "interaction" anywhere here. What is absent in the case of the orthogonal polarizers is interference between the two wave functions coming from the two slits. ("Two wave functions" is actually a misnomer--there is only one wave function for each photon, with two terms in it, one for each slit. But for this particular case, thinking of it as "two wave functions" is a good enough approximation.) "Interference" is defined just as @PeroK defined it. It has nothing to do with "interaction": there is only one photon at a time and it doesn't interact with anything else.

 

[anuttarasammyak]

As for fringe and anti-fringe

Yes, anti-fringe is an interference pattern where the peaks and troughs are opposite to the usual "fringe" interference pattern we are used to seeing.

Right, so an "anti-fringe" interference pattern, where the maximums and minimums are reversed from the usual interference pattern.

Thanks. Is there a rule that +45 is fringe and -45 is anti-fringe? Or we don't know which one is fringe but are sure that one is fringe and the other is anti-fringe ?

 

[PeterDonis]

Is there a rule that +45 is fringe and -45 is anti-fringe?

Which one is called "fringe" and which "anti-fringe" is an arbitrary choice.

 

[anuttarasammyak]

Which one is called "fringe" and which "anti-fringe" is an arbitrary choice.

Thanks. If we define fringe so that the ordinary Young experiment pattern of mid slits position has a peak, does anti-fringe appear in -45 degree arrangement ? and is it 45 degree of right turn or left turn from vertcal line ?

 

[anuttarasammyak]

1) Very simple setup: a light source sends single photons towards a double-slit setup. After slit A there is a horizontal polarizer, and after slit B there is a vertical polarizer. Finally, there is a back screen.

Do incdent lights have condition on polarization ? For an example if incident light is horizontally polarized, there appears no interference pattern on the screen in your arrangements explained.

 

[PeroK]

PS you have to understand how a superposition of QM wavefunctions produces non classical behaviour in the first place. E.g. by studying wave mechanics and doing problems. It only happens because of the details of the mathematical formalism. You need to look at what wavefunctions are being combined in a superposition to determine what the interference effects are. Phrases like "which way" information are just heuristic short cuts once you have established how the formalism manifests itself. The words themselves are not enough.

 

[ChadGPT]

Do incdent lights have condition on polarization ? For an example if incident light is horizontally polarized, there appears no interference pattern on the screen in your arrangements explained.

Interesting point. True. But what if the photon sent to the slits is in a superposition of both horizontal and vertical polarization? Then there is an interference possible because the wave function still passes through both slits.

About the fringes: The fringe is first below, and the anti-fringe second.

My fundamental interest is this:

Scenario A: The orthogonal polarizers determining which-path information removes the interference pattern, and if the orthogonal polarizers determining which-path information did not remove the interference pattern we would see an interference pattern with them in place, rather than no interference pattern.

Scenario B: The orthogonal polarizers determining which-path information removes the interference pattern, and if the orthogonal polarizers determining which-path information did not remove the interference pattern we still would NOT see an interference pattern anyway with them in place, simply due to the affects of the polarizers.

I suspect Scenario B is correct. What I want to know is 1) Is Scenario B correct? and 2) What explains why we still wouldn't see an interference pattern if the wave function is not "collapsed" by the polarizers?

There's no point in assuming something that contradicts the laws of physics. The laws of physics say that the which-way data does remove the interference pattern. That's the only theory we can use. We can't say anything about what would happen in some hypothetical universe where that wasn't the case.

I totally disagree. First of all we don't have the complete laws of physics, we have models described by our current theories of what we think the laws of physics are like. And there is plenty of reason to assume things beyond or outside of our current theories. If we are forbidden from assuming anything outside of our current theories, we can never advance science. To get beyond Newtonian physics we had to assume something that contradicted what Newtonian physics said was the laws of physics. The fact that what was assumed turned out to be true was valuable because it told us Newtonian physics wasn't the full picture. Assuming something outside of what our current theories tell use is essential for progress, and learning that an alternate model or hypothesis is false is still valuable because it strengthens the support for the current model. Physics is still in progress, not settled. All of our models are simply the best we have for now, and are open to being replaced in the future by a better model with better predictions and which better explains the available facts. There is nothing wrong with assuming something that contradicts our current models/theories.

 

[sophiecentaur]

About the fringes: The fringe is first below, and the anti-fringe second.

That diagram doesn't mean much to me, without more details about the polariser.

If you have a linear polariser and you rotate its polarisation plane, why would the fringe pattern shift? The path differences through the slit apparatus are the same for both polarisations and the patterns should be the same. So where does your idea come from?

 

[DrChinese]

...

My underlying question is this: We know what we should expect to see if the orthogonal polarizers are causing collapse. But should we expect to see anything different if the orthogonal polarizers are not causing collapse? To me it seems like we should expect to see the same results on the back screen in both cases.

I didn't see a reference anywhere. This is the quantum version of the described experiment, built up a single photon at a time:

Young's double-slit experiment with single photons and quantum eraser

See in particular figures 8, 9, 10 for results. The theory is in section II.

 

[sophiecentaur]

I didn't see a reference anywhere. This is the quantum version of the described experiment, built up a single photon at a time:

Young's double-slit experiment with single photons and quantum eraser

See in particular figures 8, 9, 10 for results. The theory is in section II.

Perhaps you could help me with this. I find it hard to tear myself away from RF and Antennas. I gather from the description of the experiment (fig 1) that an extra polariser is inserted into one of the slits (the quantum erasor). This has the effect of slewing the pattern. (?) which is far les controversial than an "anti-fringe".

I could achieve a similar thing at RF by a half cycle phase shift in one of two co-phased dipoles which would slew the main beam. To make the RF experiment more photon-like I could generate circular polarised signals by replacing the two dipoles with two pairs of spaced, orthogonal dipoles - with a max in the boresight direction. That would produce a max again on boresight.

I could then replace one of the CP pairs with a single dipole. This would cause a phase shift in one of the paths which would result in a slewed beam (and possibly a pattern with reduced 'contrast').

So classical wave theory doesn't seem too removed from the single photon experiment except that there seems to be a built-in slew for one sense of CP (photons). Can you reconcile this apart from just saying quantum is different. I'm not trying to trip people up; I can just see an apparent contradiction which can very likely be explained.

PS I know this thread is is the QM forum but I feel that I've read this QM concept turning up in the Classical fora. If this actually happens, there should be a massive caveat to avoid confusing people who just want to know about Young's Slits.

 

[PeroK]

Interesting point. True. But what if the photon sent to the slits is in a superposition of both horizontal and vertical polarization?

Then do the maths and you'll get the answer. Note that an interference pattern is not an all or nothing phenomenon. You can have a mixture of interference and non-interference depending on the scenario.

You can ask about as many scenarios as you want but you won't understand a thing about QM without understanding the maths of interference. QM is just like a set of puzzles for the Sunday papers!

Also, you can complain all you like about the laws of physics being incomplete, but that is a hollow excuse for not putting in the effort to learn QM properly.

 

[ChadGPT]

If you have a linear polariser and you rotate its polarisation plane, why would the fringe pattern shift?

That is essentially my question. I assume that whatever explains the fringe pattern shifting will also answer my question regarding scenario B above.

So where does your idea come from?

This experiment can be done in one's kitchen using a laser pointer and a few polarizing films from Amazon.

See here as an example: https://physics.stackexchange.com/q...-other-v-of-a-youngs-double-slit-if-my-source

Also, you can complain all you like about the laws of physics being incomplete, but that is a hollow excuse for not putting in the effort to learn QM properly.

That our models of the laws of physics are incomplete was not intended as an excuse for not needing to learn QM maths. It was intended to express why I disagree with the idea that one cannot posit what-ifs that contradict our current models.

 

[PeroK]

Here's my thought for the day. Imagine if we did Newtonian physics like this? Just questions and answers without interest in the calculations or underlying laws of physics.

What would happen if I dropped an object from the roof of my house? And what would happen if I dropped it off a cliff.

And what would happen if it threw the object up at 45 degrees? Would it keep going upwards or would it eventually fall to Earth?

What would happen if I threw the object down towards the ground? Would it get there quicker.

If I threw the object fast enough would it orbit the Earth?

Etc.

And, after a thousand such questions, there is some sort of understanding of projectile motion.

 

[PeterDonis]

what if the photon sent to the slits is in a superposition of both horizontal and vertical polarization? Then there is an interference possible because the wave function still passes through both slits.

No, there isn't. Only the horizontal part passes through one slit and only the vertical part passes through the other. That is exactly the scenario you described in your OP, and as you said in your OP, doing this removes the interference pattern.

 

[PeterDonis]

It was intended to express why I disagree with the idea that one cannot posit what-ifs that contradict our current models.

You can disagree with it all you want; that doesn't change how we do things here at PF. Here at PF we require you to have a model that is backed by published peer-reviewed research. Just making up a scenario that contradicts current models is not sufficient; you have to have an alternate model that meets those requirements, that we can use to derive predictions. You don't.

 

[PeterDonis]

The thread topic has been sufficiently discussed. Thread closed.