B Yet another double slit thought experiment...

[PhysicsIsReallyFun]

Consider the double slit experiment where electrons are used as the media that travels through the slits. A beam of photons is directed across one of the slit. On the other side of the slit there is a detector that can let us know which slit through which electrons pass.

What happens if the detector is on?
What happens if the detector is turned off?
What happens of the detector is moved from the location but left on?

Finally, move the detector 1 light minute from the slit but still in a location to detect the electrons. Send 1 electron through at a time but don't send the next electron until the last one registered at the detector, then send the next, wait a minute again, repeat enough times to develop a pattern. What type of pattern develops?

If there is no interference pattern then there seems to be a retro-causality problem with the electrons going back in time and changing their behavior. ie they didn't know they were being detected until a minute after hitting the screen.

If there is no interference pattern then we know which slit each electron went through to form the interference pattern.

 

[Nugatory]

A beam of photons is directed across one of the slit.

There's no such thing as "beam of photons", but there's a fair chance that you're thinking about a beam of light.
Whatever this beam is, it's not clear how it matters because you don't mention it again anywhere in your post (but I will take a guess below).

And with that said, the on/off state and location of the detector is irrelevant. If there is an interaction at the slit that affects the state of the electron in such a way that it is possible to determine which slit it went through then no interference pattern will develop.
You may be thinking that the electrons will interact with and change the beam of light, and the detector works by looking for these changes. If that's what you're thinking.... the interaction between the electron and the light beam at the slit is sufficient to eliminate the interference pattern. The state of the system changes if the electron interacts with the light, this can only happen at the slit where the light is, in principle the change is detectable, therefore in principle we can determine which slit the electron went through so no interference pattern.

 

[PhysicsIsReallyFun]

A "beam of photons" refers to a collection of photons, the fundamental particles of light, traveling together in a defined direction, which can be characterized by its intensity, energy, and other properties

 

[PhysicsIsReallyFun]

If the interaction at the slit is the determining factor for an interference to occur or not occur then there is no strangeness to the double slit experiment.

But it is deeper than that as indicated by the quantum eraser experiment since if information is gained and lost the interference pattern remains. Meaning the entire apparatus might be entangled.

I was thinking of a method to isolate the effect but I didn't think it through carefully enough.

I guess I could state my question more specifically like this.

If single electrons fired sequentially are used in the experiment, what amplitude and/or frequency of light would be required to collapse the electron wave function? Is stray light in the room enough? What is the threshold? Does the wave function collapse upon interaction with the light or after it has reached some sort of detector?

 

[weirdoguy]

A "beam of photons" refers to a collection of photons, the fundamental particles of light, traveling together in a defined direction

And there is no such thing in QM, because masless particles with spin 1 or higher have no position operator, and there may be other additional reasons. But, you can talk about light, like laser light

 

[PeroK]

If single electrons fired sequentially are used in the experiment, what amplitude and/or frequency of light would be required to collapse the electron wave function? Is stray light in the room enough? What is the threshold? Does the wave function collapse upon interaction with the light or after it has reached some sort of detector?

If you watch Feynman's Messenger lecture on QM, he covers this point. If the light source is too weak to detect an electron, then it doesn't affect the experiment. As the source is intensified, a percentage of the electrons get detected and theoretically you get a mixture of the double-slit pattern with two single-slit patterns. Theorectically, if you detect every electron, then you get two single-slit patterns.

I say theorectically, because detecting electrons with an intense light source in this way will also disrupt the path of the electrons - deflecting them at some random angle and ruining the experiment.

A theoretically cleaner approach is to close one slit of the other (perhaps randomly) and the fact that one slit is closed means the electron is either lost to the experiment or passes through the only open slit.

Wave function collapse is not a physical process. It's part of the mathematical calculations within QM. Your question, however, touches on the measurement problem - which asks what defines a macroscopic detector, as opposed to fundamental interactions?

 

[PhysicsIsReallyFun]

If you watch Feynman's Messenger lecture on QM, he covers this point. If the light source is too weak to detect an electron, then it doesn't affect the experiment. As the source is intensified, a percentage of the electrons get detected and theoretically you get a mixture of the double-slit pattern with two single-slit patterns. Theorectically, if you detect every electron, then you get two single-slit patterns.

I say theorectically, because detecting electrons with an intense light source in this way will also disrupt the path of the electrons - deflecting them at some random angle and ruining the experiment.

A theoretically cleaner approach is to close one slit of the other (perhaps randomly) and the fact that one slit is closed means the electron is either lost to the experiment or passes through the only open slit.

Wave function collapse is not a physical process. It's part of the mathematical calculations within QM. Your question, however, touches on the measurement problem - which asks what defines a macroscopic detector, as opposed to fundamental interactions?

Yes, thank you. I have read that paper. I am trying to get a handle on the conditions that trigger an "interaction," which provides or doesn't provide which-way information and furthermore if the behavior of the electron changes at that moment or at a later time if there was somehow a way to delay the which-way information to the "detector" that provides that information.

 

[PhysicsIsReallyFun]

And there is no such thing in QM, because masless particles with spin 1 or higher have no position operator, and there may be other additional reasons. But, you can talk about light, like laser light

And yet a beam of light is still a beam of light. But seriously I'm referring to the wave nature of the EM field in that changes are detectable even to the naked eye if the conditions are right.

 

[weirdoguy]

And yet a beam of light is still a beam of light.

Yes, what we were trying to say is that photons are not like a little billard balls that constitutes every light beam. They are way more compicated than that, mainly because they are massless and thing get heavy with that. For massive particles "billard ball" intuition sometimes works.

 

[Nugatory]

And yet a beam of light is still a beam of light. But seriously I'm referring to the wave nature of the EM field in that changes are detectable even to the naked eye if the conditions are right.

Yes, which is why it is better to say “beam of light” than to say “beam of photons” and hope that your audience will know what you really mean.

But the relationship between photons and electromagnetic radiation is a digression in this thread, it might be best to start a new thread (or search some of our older threads on the subject) for that question.

 

[PeroK]

Yes, thank you. I have read that paper. I am trying to get a handle on the conditions that trigger an "interaction," which provides or doesn't provide which-way information and furthermore if the behavior of the electron changes at that moment or at a later time if there was somehow a way to delay the which-way information to the "detector" that provides that information.

In general, you have an electron and an EM field and the state of the electron evolves, partly as a free-particle, and partly due to the EM field. In this case, we are talking about potential "collisions" between a photon and the electron. The interaction is always there, but the outcome is probabilistic. Eventually an electron interacts with a detector screen and the probability distribution for position depends on the evolution of the wave-function through the double-slit and the through the EM field.

Which-way information, although a useful heuristic, is not the full story as far as QM is concerned. The problem with your analysis, is that you analyse the scenario in terms of definite events at definite points in time. Whereas, what QM predicts is a correlation between photon detections and electron detections. Under certain circumstances, an experiment appears to proceed classically, or semi-classically, but those are just special cases, where we can ignore the full QM picture and explain things with a simple semi-classical heuristic - like "which-way" information. Eventually, these experiments can only be fully understood by taking a fully QM approach to the analysis.

 

[Nugatory]

…. and furthermore if the behavior of the electron changes at that moment or at a later time

The behavior of the electron is that it makes a dot on the screen.

Quantum mechanics allows us to calculate the probability of that dot appearing at any particular point on the screen based on the overall experimental setup (configuration of slits, intensity of light beam at slit, ….) but says nothing about what might be going on unseen before the dot appears. It’s a black box: configuration and other initial conditions go in, probabilities come out.

 

[DrChinese]

Does the wave function collapse upon interaction with the light or after it has reached some sort of detector?

I think you missed the part Nugatory mentioned about the which-slit detector. That detector has no function in this kind of experiment. If there is anything in a double slit experiment that has the potential to provide such information, then the interference pattern on the back screen is reduced accordingly. (Note that it is not either-or, it is variable.)

Consequently the position of such detector has no relevance. If you want to better understand the quantum issues involved in an actual experiment, I recommend studying the following paper on the DSE using photons:

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

https://www.researchgate.net/publication/261011417_Young's_double-slit_experiment_with_single_photons_and_quantum_eraser
(Scroll down a bit to see full paper)

 

[PhysicsIsReallyFun]

I think you missed the part Nugatory mentioned about the which-slit detector. That detector has no function in this kind of experiment. If there is anything in a double slit experiment that has the potential to provide such information, then the interference pattern on the back screen is reduced accordingly. (Note that it is not either-or, it is variable.)

Consequently the position of such detector has no relevance. If you want to better understand the quantum issues involved in an actual experiment, I recommend studying the following paper on the DSE using photons:

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

https://www.researchgate.net/publication/261011417_Young's_double-slit_experiment_with_single_photons_and_quantum_eraser
(Scroll down a bit to see full paper)

I'm missing something here. I understand that when the orthoginal (to each other) filters are placed in front of the place the interference pattern disappears. The resulting waves cannot add/subtract from one another because their amplitudes are in different orientations.

But what I'm not following is why the 45 degree polarizer doesn't simply block the rest of the light since the light entering this polarizer is at an angle of 45 degrees to the first two polarizers? Or does lights continually "twist" (rotate) as it propigates? But this would mean for the first two polarizers to function they would have be the exact same distance from the detector in order for phase angle between the two to be maintained to the screen, which seems very hard to do considering the distance to the detector vs. the tiny wavelength of the source.

Barring that rather mundane misunderstaning on my part the result of this one brings me to another "Norman coordinate" moment.

In the first part of the experiment it seems clear that for the interference pattern to disappear one of two things is happening. 1. Either the decoherence occurs upon interaction with the first polarizers, or 2. the wave function itself is polarized, thus preventing decoherence and superposition (classical sense of adding/subtracting amplitudes) until hitting the detector screen.

#1 is problematic because it would imply that the particle nature of the light is somehow converted back to wave nature upon interaction with the 45 degree polarizer.

#2 kind of solves the previous problem because the light would technically still be a wave of probability at it interacts with the 45 degree polarizer. Now all probably waves would be coherent with no which-way information so interference occurs.

#2 is strange because it would seem to indicate that the wave function is not simply a model but a good representation of reality right down to the fact that probability waves can not only interfere with themselves, but also can be polarized!

I love this one. Thanks for sharing!

 

[PeroK]

I'm missing something here.

It's called Quantum Mechanics!

I understand that when the orthoginal (to each other) filters are placed in front of the place the interference pattern disappears. The resulting waves cannot add/subtract from one another because their amplitudes are in different orientations.

Exactly.

But what I'm not following is why the 45 degree polarizer doesn't simply block the rest of the light since the light entering this polarizer is at an angle of 45 degrees to the first two polarizers? Or does lights continually "twist" (rotate) as it propigates? But this would mean for the first two polarizers to function they would have be the exact same distance from the detector in order for phase angle between the two to be maintained to the screen, which seems very hard to do considering the distance to the detector vs. the tiny wavelength of the source.

I'm not sure I understand the point here. Light is typically in a superposition of polarized states. Light polarized in one direction is equivalent to an equally weighted superposition of light polarized in the two orthogonal directions. If the light passes through one polarizing filter, it doesn't need to "twist" or change to pass through a different polarizing filter: this happens with a defined probability amplitude based on the rules of superposition. That's the fundemental concept at the heart of QM. Until you understand the superposition of states, all QM phenomena will be inexplicable.

Barring that rather mundane misunderstaning on my part the result of this one brings me to another "Norman coordinate" moment.

In the first part of the experiment it seems clear that for the interference pattern to disappear one of two things is happening. 1. Either the decoherence occurs upon interaction with the first polarizers, or 2. the wave function itself is polarized, thus preventing decoherence and superposition (classical sense of adding/subtracting amplitudes) until hitting the detector screen.

The wavefunction represents the polarized state. QM depends on the concept of one state being a superposition of two (or more) different states. It's both definitely one thing and partly the other. A non-QM example is a vertical force like gravity. It's both definitely a vertical force, but also the vectorial sum of normal and tangential forces relative to any inclined angle.

#1 is problematic because it would imply that the particle nature of the light is somehow converted back to wave nature upon interaction with the 45 degree polarizer.

It's all wavefunction mechanics. Wave-particle duality is at best an experimental heuristic. There is no wave-particle duality in the mathematics of QM.

#2 kind of solves the previous problem because the light would technically still be a wave of probability at it interacts with the 45 degree polarizer. Now all probably waves would be coherent with no which-way information so interference occurs.

Again, you are missing the fundamentals of QM: wavefunctions and superposition.

#2 is strange because it would seem to indicate that the wave function is not simply a model but a good representation of reality right down to the fact that probability waves can not only interfere with themselves, but also can be polarized!

Again, the wavefunction in this case represents polarized light.

 

[PhysicsIsReallyFun]

Okay thank you for taking the time to reply. I have re-read the paper and have a better understanding of the experiment.

Unfortunately outside of math I don't think I'm going to be able to find an explanation for this that I can wrap my head around. When it comes to the last part of the experiment here's what I believe is happening. Please let me know where I'm going wrong.

The photon starts as an unpolarized state, or I suppose a superposition of polarized states?

After passing through one of the first two slits, the photons state becomes entangled with the slit. Since the slits have different polarizations (hor or vert) "which-way" information is known from polarization and no interference occurs.

Upon exiting the third slit both photons are "re-encoded" with new and identical which-way information, thus erasing the previous which-way information so the interference pattern is restored.

Is this essentially correct?

If so I get it and I hate it. It is deeply unsatisfying to me!

The fact that this happens as photons are emitted one-at-a time is baffling. I realize the photons "don't know" anything, they are just following the math, but there is so much probability in it. It's almost like the universe is trying to save on data storage by not putting "numbers" on events until absolutely necessary!

 

[PeroK]

Okay thank you for taking the time to reply. I have re-read the paper and have a better understanding of the experiment.

Unfortunately outside of math I don't think I'm going to be able to find an explanation for this that I can wrap my head around. When it comes to the last part of the experiment here's what I believe is happening. Please let me know where I'm going wrong.

The photon starts as an unpolarized state, or I suppose a superposition of polarized states?

After passing through one of the first two slits, the photons state becomes entangled with the slit. Since the slits have different polarizations (hor or vert) "which-way" information is known from polarization and no interference occurs.

Upon exiting the third slit both photons are "re-encoded" with new and identical which-way information, thus erasing the previous which-way information so the interference pattern is restored.

Is this essentially correct?

I think so.

If so I get it and I hate it. It is deeply unsatisfying to me!

It's how nature works. Modern Quantum Mechanics by J.J. Sakurai starts with analagous experiments for electron spin, and uses this as the motivation for (the mathematical formalism of) QM. Physicists are bound to explore and explain the natural phenomena they are presented with. Note that all of chemistry depends on QM. If the universe were nice and classical and satisfying to you, there would be no atoms, chemistry, life and you wouldn't be here to enjoy its Newtonian simplicity!

The fact that this happens as photons are emitted one-at-a time is baffling. I realize the photons "don't know" anything, they are just following the math, but there is so much probability in it. It's almost like the universe is trying to save on data storage by not putting "numbers" on events until absolutely necessary!

The fundamental difference between Classical Mechanics (CM) and Quantum Mechanics (QM) is this:

In CM a particle is described kinematically by its position in space at all times. This is sometimes called a classical trajectory. For these double split experiments I suspect you are thinking in terms of these classical trajectories for photons.

In QM a particle is described kinematically by an abstract state vector (also known as a wavefunction). This conceptual hurdle is reached before you delve into the mathematical formalism of QM - i.e. the mathematics of state vectors (or of wave mechanics). First, you have to rid yourself of classical notions of what a particle is, or must be.

This was all worked out in the 1920s and 1930s. And is the basis of all modern physics (except perhaps Cosmology).

I'm sceptical that you can understand QM at any level without understanding how the mathematics works. It's a bit like trying to understand chess without ever learning how the pieces move. You can talk about it in broad, general terms and can memorise an explanation for any particular experiment. But, you won't be able to work out for yourself how an experiment will turn out and really understand what's going on.

 

[PhysicsIsReallyFun]

Again thank you for taking the time to reply. I am by no means advanced in my educations but I did take 5 semesters of calculus in college, ending with partial differential equations so the math while difficult to "get back into" is not foreign to me.

I love math. Don't get me wrong, but it's nice to be able to put some intuitive "feel" to the equations and operators. For example, Maxwells equations can be thought of in an intuitive way. QM is much more, it is what it is and that's what it is.

As a musician it's almost like the difference between playing a song by ear or just having chords and improvising as opposed to reading music. QM is like reading music, there is no intuitive feel for what should come next, you have to go to the music (math) for every note forward. With classical physics, where we have a feel for how reality works from our every day perspective, you can "think things" through to (generally) a correct result without needing to go directly to the maths. It is a little unsettling to know the path but not to know why. It's like driving to a destination without a map but only using a compass (classical physics) vs. needing to look at Google maps for every single turn (QM).

This is is a monumental change in world view and it doesn't occur over night I'm realizing. This is a journey to a new way of thinking about things. More of a how things happen rather than why from a classical viewpoint.

As I mentioned I used to teach AP Physics and Chemistry but the focus, as least then in physics was on classical mechanics with a bit of QM, which is why I'm re-investigating now. Chemistry is/was almost entirely taught at the high school level based on valence shell electron pair repulsion theory. Of course it is ALL based on physics, which comes down to QM when the kids start asking questions like why the electron doesn't spiral into the nucleus. Which is what the guys who figured this all out started asking when they thought all of physics was pretty much a done deal, we've done it! Not so fast.

The standard model and the frontiers of QM are facinating and I have been enjoying the study.

Moving forward I will make sure I formulate my questions/posts with more care and research.

When I learned about the double slit experiment many years ago in high school I was told light was both a wave and a particle. Now I'm thinking light and everything is a wave but the effects on reality are particle-like as we understand them.

 

[PeroK]

The standard model and the frontiers of QM are facinating and I have been enjoying the study.

Moving forward I will make sure I formulate my questions/posts with more care and research.

With your background, you could try this:

https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

It's the most accessible, but genuinely undergraduate level treatment of QM. And full of wonderful insights.

 

[PhysicsIsReallyFun]

With your background, you could try this:

https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

It's the most accessible, but genuinely undergraduate level treatment of QM. And full of wonderful insights.

Thank you!!! This is exactly the type of brain exercise I need each night for an hour or so before bed.

With a little review here and there I think I can follow the math. This is good as it puts some "meat on the bones" of the theory that words alone cannot manage.

 

[phinds]

This is is a monumental change in world view and it doesn't occur over night I'm realizing.

Exactly. I remember when I first started learning about QM, outside of pop-science presentations, which had misinformed me about almost everything, I would joke to friends that it was making me pace around my room screaming "THAT CAN'T BE RIGHT !!!" and pulling my hair out.

In the world in which humans evolved, there was no knowledge of QM and thus zero survival value in it so it is not part of our "intuition", "common sense" and so forth.