Delayed Choice Quantum Eraser: Am I missing something here? 
Hello everyone,
I actually have three questions:


*

*Am I missing an important detail in my understanding of how the delayed choice quantum eraser experiment is done?

*How does one account for what takes place in the experiment without using the concept of "retrocausality" (effect before cause)?

*If the photon passes through both slits, wouldn't the BBO crystal produce 4 photons? If it does, what happens in that case, and if it doesn't, then why?


Okay so here is my understanding of the experiment. A laser fires a photon at a double slit. It can either go through slit A (red), slit B (blue), or both. After the double slit, there's a nonlinear optical crystal (BBO) that converts the photon into two entangled photons. A Glan-Thompson prism diverges these two entangled photons. One of them (called the signal photon) goes towards the detector D0 while the other (idler photon) goes towards a prism PS and is deflected depending on whether it follows path A or path B. An idler photon following path A passes through a beam splitter BSb where it can either reflect and go to D4 or transmit, reflect off of mirror Mb and then either reflect off of BSc and enter D2 or transmit and enter D1 (sorry about the run-on sentences, trying to keep this short). An idler photon following path B will either reflect off of BSa or transmit and reflect off Ma and arrive at BSc where it will either go to D2 or D1. Detectors D1 and D2 always give interference patterns, while D3 and D4 only show diffraction without interference. If the idler photon enters D4, then we know that it passed through slit A, if D3, then slit B. What ends up happening though is that whether or not the signal photon displays interference at D0 depends on whether the idler photon enters D1/D2 or D3/D4. If the idler photon enters D1/D2, there will be an interference pattern at D0. If the idler photon enters D3/D4, there will not be an interference pattern at D0.
I'm not studying this for a class or anything, I've just been having a discussion with someone about the role of consciousness within these double-slit experiments. They used this as an example of how consciousness can effect matter. I, however, have a very hard time accepting this. There just has to be another explanation that does not involve retrocausality. If there isn't, then my friend would have to be right; somehow the signal photon knows whether or not we will have the path information (it is "erased" at D1/D2). I know some people believe consciousness plays a role in the original double-slit experiment, but I know that it doesn't. In that experiment, the reason why the photon acts like a particle is not because it knows a physicist is attempting to measure it, but because of the way it physically interacts with the detector. The delayed time version can't be explained this way. I'm not really too familiar with entangled particles, I only understand the main concept. All 5 detectors are the same kind of detector correct? The only difference between the last 4 is that we the observers know that D3/D4 will let us know the path information, while D1/D2 will not. How in the world would a photon "know" this??? There just has to be something I'm missing here. I would really like to know what the explanations that don't involve retrocausality (Ex. of explanation using retrocausality: if the idler photon arrives at say D3/D4, then it will "go back in time" and make sure that the original photon only passes through one slit, even if it originally passed through both) are. Wikipedia says that this paper provides such an explanation, however, I'm having some trouble understanding it http://arxiv.org/abs/1103.0117.
Thank you for taking the time to read all of this.
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These comments are for @Timaeus. I have so many, that if I try posting them in the comments section of their answer, I'll end up having to post nearly a dozen of them and I've already got that warning that comments should not involve discussions yesterday. I don't know if posting too many comments might redflag me as a spammer or someone who's not following the rules, but I don't want to take that chance.
Thank you very much for taking the time to help me with this, I appreciate it. I’d just like to comment on a few of your responses. 

“This question doesn't make sense”

Why do you think my second question doesn’t make sense? Dont you see how someone who does not have an established background in QM can understand why the results of this experiment happened the way it did by considering retrocausality? I am by no means saying that I believe retrocausality is possible. All I’m saying is that without the necessary knowledge, someone may not be able to conceptualize why this experiment had these results without considering retrocausality.  

“Passing through both slits is one of your misunderstandings.”

In your response to my 3rd question, are you saying that a single photon cannot pass through two slits? What are the “sectors” you mention? By “single state”, are you’re implying that the wave function of the photon has collapsed before going through the double slit right? Doesn’t the photon need to interact with something, like a some kind of measuring device, in order for that to happen? This is why I asked about what you meant by sectors. From the original paper that published the results of this experiment: “This reflects the wave property (both-path) of photon 1.” “The which-path or both-path information of a quantum can be erased or marked by its entangled twin even after the registration of the quantum.” If the photons never pass through both slits, then what did the authors mean by “both-path”. Here is the link to the paper: http://arxiv.org/abs/quant-ph/9903047 

“so if you had a state that only made a detector outside one slit fire then this crystal would make two photons.”

You also kept mentioning detectors outside each slit. In the descriptions of the setup of this experiment and even in the original paper, though, detectors placed before the slits are never mentioned. This is what I meant when I said “the delayed time version can't be explained this way.” In the original double slit experiment, there is a detector placed before the slits and that’s what causes the photon’s wave function to collapse into a single state. In the delayed time version though, there is no mention of anything being placed between the laser and the slits that the light can interact with and take on a single state.  

“And thinking it is following. a blue path or a red path is as wrong as thinking a vector in the 2d plane has to be on the x axis or the y axis. It's that totally wrong.”

I’m also confused about why you were saying that we cannot get the path (you call it red/blue state) information from D3 or D4. If you’re right, then why does everyone, even the original paper that published the results of this experiment say that we can? I thought that was one of the most important details of this experiment. From the original paper: “The registration of D 3 or D 4 provides which-path information (path A or path B) of photon 2 and in turn provides which-path information of photon 1 because of the entanglement nature of the two-photon state of atomic cascade decay.” http://arxiv.org/abs/quant-ph/9903047

“Totally totally totally wrong.”

Why was I that wrong about saying “the only difference between the last 4 is that we the observers know that D3/D4 will let us know the path information,…”, this is supposed to be the whole point of this experiment. D1 and D2 “erases” the path information. The quote I previously mentioned: “The registration of D 3 or D 4 provides which-path information (path A or path B) of photon 2…”. Here’s another: “The triggering of detectors D 1 or D 2 erases the which-path information.” http://arxiv.org/abs/quant-ph/9903047

“Yes there is. But its absolutely everything.”

How can I have “absolutely everything” wrong? Honestly, all I did was summarize Wikipedia and the original paper. If I explained absolutely everything wrong, then the paper is absolutely wrong as well. 

“Its like you learned quantum mechanics from someone that wanted to make it seem mysterious.”

Why do you say that? I never said that I believe retrocausality is taking place. In fact I explicitly stated that I don’t. And actually, since when is QM not mysterious? You make it seem as if the results of this experiment are intuitive. After enough time passes, we notice that an interference pattern forms at D0 only when the idler photons entangled with the signal photons, that generate that pattern, hit D1 or D2. We also notice that an interference pattern is not formed at D0 only when the idler photons entangled with the signal photons, that do not form the pattern, hit D3 or D4. This is why some people resort to retrocauslity. Original paper: “It was predicted that the “joint detection” counting rate R01 (joint detection rate between D0 and D1) and R02 will show interference pattern when detector D0 is scanned along its x-axis. This reflects the wave property (both-path) of photon 1. However, no interference will be observed in the “joint detection” counting rate R03 and R04 when detector D0 is scanned along its x-axis. This is clearly expected because we now have indicated the particle property (which-path) of photon 1.” To make the results of this experiment even less intuitive, the signal photon reaches D0 before the idler photon reaches any of the other detectors. “The experiment is designed in such a way that L0, the optical distance between atoms A, B and detector D0, is much shorter than Li , which is the optical distance between atoms A, B and detectors D1, D2, D3, and D4, respectively. So that D0 will be triggered much earlier by photon 1.” This is the precise reason why people think that the idler photon “travels back in time” to make sure the signal photon demonstrates wave properties if it hits D1/D2 or particle properties if it hits D3/4. http://arxiv.org/abs/quant-ph/9903047

“and in your entire post I never say evidence that you know a single tiniest bit of quantum mechanics (you might, bit you didn't show it).”

I disagree. I’d say that a statement like this, “in that experiment, the reason why the photon acts like a particle is not because it knows a physicist is attempting to measure it, but because of the way it physically interacts with the detector”, would indicate that someone does know at least a tiny bit about QM. I don’t see the point of making statements like that or the one about who’s been teaching me quantum mechanics. How are those statements relevant? All I was doing here was trying to gather information and terms that I am not yet aware of so that I can use them as guidelines in knowing what to look up in order for me to gain a better understanding of this experiment. You can’t expect someone learning QM to understand everything perfectly the first time around. It may not have been your intention, but I got the impression that you were criticizing me. Nonetheless, thanks again.
 A: 
  
*
  
*Am I missing an important detail in my understanding of how the delayed choice quantum eraser experiment is done?
  

Yes. I'll respond to your list of your understanding.


  
*How does one account for what takes place in the experiment without using the concept of "retrocausality" (effect before cause)?
  

This question doesn't make sense, if someone tried to claim you need retrocausality, they were tricking you. But also you need to be clear which experiment you ate talking about. The one pictured above or the one in the paper you cite with a quantum controller? You can always have a sorting, a sorting that depends on the controller, all the particles involved, and detectors. But this sorting doesn't mean that certain properties are fixed, some properties are created through interactions rather than existing already. But this isn't retrocausailty, this is just interactions that change things into states that have particular properties when in general only some states have those properties.


  
*If the photon passes through both slits, wouldn't the BBO crystal produce 4 photons? If it does, what happens in that case, and if it doesn't, then why?
  

Passing through both slits is one of your misunderstandings.

A laser fires a photon at a double slit. It can either go through slit A (red), slit B (blue), or both. 

This is already a misunderstanding caused by really poor explanations of quantum mechanics. There is a single state going through the double slit. It is the kind if state that would cause sectors placed right in front of slit A or right in front of slit B to fire. But only one would fire. But it isn't a statistical mixture of a state that make just one fire and a state that makes just the other fire and we can't experimentally distinguish the two through further possible experiments. It's this last possibility that makes people say it goes through both. But that's a wild mischaracterization.  Since Quantum mechanics is linear you can analyze what happens if it were a state that only made one fire and then analyze what happens if it were a state that only made the other one fire and compute the complex results both ways and the result will be the complex sum of the results. If it were a statistical mixture you would just add the frequencies of results.

After the double slit, there's a nonlinear optical crystal (BBO) that converts the photon into two entangled photons. 

So if you had a state that only made a detector outside one slit fire then this crystal would make two photons.

A Glan-Thompson prism diverges these two entangled photons. One of them (called the signal photon) goes towards the detector D0 while the other (idler photon) goes towards a prism PS and is deflected depending on whether it follows path A or path B. 

And these two photons could be in states that make detectors in two different directions go off. And each of these states can interact with the prism to make a new state that can make a detector in a new direction go off. 

An idler photon following path A passes through a beam splitter BSb where it can either reflect and go to D4 or transmit, reflect off of mirror Mb and then either reflect off of BSc and enter D2 or transmit and enter D1

And here is a problem. Again each time it interacts is doesn't go in some direction it changes into a state that would make detectors in that direction go off. This might sound like a pointless distinction, but it comes up right here in D1 and D2. 
What we've done is say that a state that could only make a detector outside the red slit go off would interact with stuff and become a state with two photons, one of which could make detectors D4, D1, or D2 go off.
Later we'll see that a state that could only make a detector outside the blue slit go off would interact with stuff and become a state with two photons, one of which could make detectors D3, D2, or D1 go off.
Since both states (the one that could only make red go off and the one that could only make blue go off) both are capable of by themselves making D1 and D2 go off all by themselves find out that when you have a state that is a superposition of those two states the superposition makes detectors D1 and D2 go off differently.
Let's be a bit more precise. If you had a red state that wasnt part of a pair then D4 goes off half the time and D1 and D2 go off 25% of the time. And if you had a red state that wasn't part of a pair then D3 goes off half the time and D1 and D2 go off 25% of the time. Assuming half silvered mirrors everywhere for the beamsplitters.
But when you make a state that could make detectors by the red or blue slits go off there are multiple ways to do that. Firstly you can make states that make the detectors go off at different rates and you can do it by flipping a spin and then making one state or the other state or you can make a new state that really is a new thing that can make either detector go off. And if you make that new state then you find out a note detailed thing about what is going in to detectors D1 and D2 and it is possible to make experiments where a red state makes it fire and a blue state makes it fire but a new state makes it not fire.
In the classic double slit experiment that is exactly how a dark fringe happens. So if you didn't realize this, then you never understood the original quantum double slit experiment.
So to be clear it isn't that you have a photon going along one path or the other and it isn't a photon going along each. It is a state that could make detectors placed along any of those blue or red paths go off. And in the places where you see a red line and a blue line you can just expect your detector to go off 25% of the time because the exact placement could allow destructive interference.

Detectors D1 and D2 always give interference patterns, 

Here you need to be clear where and what pattern you are talking about. Are you talking about coincidence with a moving screen on the other photons of the pair? Adjusting where detectors D1 and D2 are? Or do you just mean not getting 25% of the hits?

while D3 and D4 only show diffraction without interference.

Same deal. What diffraction? It's a detector, it goes off or it doesn't. Are you moving it? Are you post selecting to sort through it and look at coincidences with something else?

If the idler photon enters D4, then we know that it passed through slit A, 

No. If we made a statistical mixture of red states and blue states (like flipped a coin and then made a red state if heads or a blue state if tails) and then D4 went off we'd know which state the coin was in (heads). But we didn't do that. So it wasn't in red or blue back then (it was in a new state, one that could make either red or blue detectors go off) and so saying that doing something bow could tell us if was red or blue back then is just wrong, since it provably was in neither a red state nor a red state but was in a totally new type of state.

if D3, then slit B. 

Also wrong. Think of being red as like a vector being on the x axis and being blue as like a vector being on the y axis. These are perfectly possible. But there are way way more possibilities. In additional to being on the x axis or on the y axis or having someone flip and and be secretly placed on one and we don't know which, there are other possibilities the vector could be anywhere in the whole 2d plane. And later if it gets forced onto the the x axis or the y axis that in no way means it was one those axis originally. And in fact we know it wasn't.
That's not just an analogy, and that is indeed how truly wrong you are. We represent the red state mathematically with a vector. And we represent the value state mathematically with an orthogonal vector. And we represent the new states with linear combinations. And if probably you can detect that it isn't on either of those axis originally then no result can tell you it was.
It wasn't there. And thinking it is following. a blue path or a red path is as wrong as thinking a vector in the 2d plane has to be on the x axis or the y axis. It's that totally wrong.

What ends up happening though is that whether or not the signal photon displays interference at D0 depends on whether the idler photon enters D1/D2 or D3/D4. 

The spirit of the idea might be there. But this is a post selection coincidence sorting. You sort all the results at D0 based on whether D0 went off when D1/D2 went off and you see that that collection has a wavy distribution (being higher or lower depending on where you place D0). Whereas when you take all the times D0 went off and sort them based on whether D0 went off when D3/D4 went off and you see that that collection doesnt have a wavy distribution (it get higher or lower depending on where you place D0 but it just has a central peak that gets smaller away from the center and doesn't get smaller than larger again in a wavy way). 

If the idler photon enters D1/D2, there will be an interference pattern at D0.

The detectors either go off or they don't. The pattern is based on doing the experiment many times and varying where D0 is placed and seeing if D0 goes off more often in one location for D0 when D1/D2 goes off compared to other locations for D0.

If the idler photon enters D3/D4, there will not be an interference pattern at D0.

The pattern is based on doing the experiment many times and varying where D0 is placed and seeing if D0 goes off more often in one location for D0 when D3/D4 goes off compared to other locations for D0.

the role of consciousness within these double-slit experiments.

Zero role for consciousness. Notice no brains were in the setup or the description or the analysis.

They used this as an example of how consciousness can effect matter.

There is literally no way they can do that since it literally doesn't come up at all, anywhere. That would be like saying they used this as an example of how they like coffee, or any other unrelated non sequitur.
Here is a simple way to deal with an argument that wants to bring up consciousness. When the argument says a person matters, just remove the person from the experimental setup and the analysis. Now there are no people. If they try to bring up animals remove the animals. None of the math changes and then you see the brains were irrelevant.
So don't let them bring them up brains in the first place.

I, however, have a very hard time accepting this.

You let them bring in brains for no reason. That would be like if you were trying to compute how quickly a battery discharges or how to add 3+5 and you somehow for some reason let someone bring brains into the conversation. You already failed. No accepting or allowance is required. You didn't bring it up. If you were adding 3+5 and someone else wanted to bring brains into it you shouldn't have to accept at all, it's their problem that they can't avoid bringing up irrelevant issues when discussing other issues.

There just has to be another explanation that does not involve retrocausality.

Neither consciousness nor retrocausality were mentioned as explanations for anything. Ever.

If there isn't, then my friend would have to be right; 

Again. No. Your friend doesn't have an explanation any more than. Conscious explains 3+5=8 and if for some reason you could remember for to explain why 3+5=8  doesn't mean your so called friend's no explanation wins by default.
A win by default is a dirty tactic, something you might expect from someone that brings up brains in a conversation that didn't need them.

somehow the signal photon knows whether or not we will have the path information (it is "erased" at D1/D2).

There is a state for the whole system. If you think the individual parts have their own states that is like thinking points in the plane have to be on one of the two axis. And this isn't an analogy. The states with the parts having their own separate states are subsets of all possible states just like the x axis and y axis are subsets of the plane.
The state for the whole system tells you everything. The rate at which you get every result and the correlations and everything.

I know some people believe consciousness plays a role in the original double-slit experiment, but I know that it doesn't.

Why are we even discussing beliefs? We can discuss models and predictions and a results instead.

In that experiment, the reason why the photon acts like a particle

That isn't a word with much meaning. There are particle states and was e states and little brain attached to stuff choosing to be one or the other. There are states. And they evolve to new states.

the way it physically interacts with the detector. 

It depends on how the whole experiment is set up and on the original state

The delayed time version can't be explained this way. 

Says nobody. We do explain it by saying there is a state for the whole system and the state for the whole system evolves and produces results with frequencies and correlations as determined by the state of the whole system and the interactions given by the actual experimental setup.
The explanation never changes because this is just another setup.
The one sign of bad science is when you have to make different explanations for different setups. In quantum mechanics we figured out how to make one explanation that works for all set ups. If your explanation isn't working for all setups then you've been learning a hack instead of the correct  explanation.

I'm not really too familiar with entangled particles, I only understand the main concept.

That's like saying you aren't familiar with 2d space and yet want to analyze motion in 2d, that's fine as a starting point but if you think you can understand what's going on even the tiniest bit while not learning 2d then you are hopelessly wrong.
The very first fact you need is that there is a state of the whole system (that's the vector in 2d) and that it is allowed to be a complex linear combination of special states corresponding to each part having its own states (those are the unentangled states and they are the x and y axis).

All 5 detectors are the same kind of detector correct? 

Sure. They go off or they don't. They can be translated or rotated.

The only difference between the last 4 is that we the observers know that D3/D4 will let us know the path information, 

Totally totally totally wrong. The state wasn't going on one path or the other (those states are like the x axis or the y axis it was a complex linear combination of the two). And these detectors aren't hooked up to brains and their is no impact. The detectors interact with the state of the whole system.

How in the world would a photon "know" this???

How would a vector know it is on the x axis or the y axis when it isn't on either? It won't, it doesn't, and it can't because it isn't even a thing to know it is a lie.

There just has to be something I'm missing here. 

Yes there is. But its absolutely everything. Its like you learned quantum mechanics from someone that wanted to make it seem mysterious. If that was supposed to motivate you to sit down and learn it, then it failed if you didn't sit down and learn it.
All the talk about which way was supposed to show you that classical methods don't work (no interference if it just went one way or the other). It was supposed to motivate you to learn quantum mechanics and in your entire post I never say evidence that you know a single tiniest bit of quantum mechanics (you might, bit you didn't show it).

I would really like to know what the explanations that don't involve retrocausality

Quantum mechanics itself. Having a state of the system, having it evolve, having it give results with the predicted frequencies and correlations.

Ex. of explanation using retrocausality: if the idler photon arrives at say D3/D4, 

That's not an explanation. The photon doesn't travel and it doesn't arrive. The state of the system allows some detectors to go off and sometimes they do.

then it will "go back in time" and make sure that the original photon only passes through one slit, 

No, that doesn't happen and again isn't an explanation. There aren't photons going along paths, there is a state.

Wikipedia says that this paper provides such an explanation, however, I'm having some trouble understanding it http://arxiv.org/abs/1103.0117.

That paper is about a different topic.
A: This question was cross-posted to physics forums word for word. I'll give the same basic answer I gave there.

Consciousness is never part of any quantum mechanical explanation. Every experiment runs the same whether or not a person is in the room.
Retrocausality is also not required here. For example, the Copenhagen interpretation explains the delayed choice eraser with instantaneous non-local partial collapse and the many worlds interpretation explains it with worlds staying coherent and interfering. Those are the two most popular interpretations.
Thinking of the delayed choice eraser in terms of an optical experiment muddles the issue, in my opinion. We can create the same basic effect with a much simpler system, involving three qubits.
Analogous Simpler Situation
Suppose you have the state $\psi = \frac{1}{2} \left|000\right\rangle + \frac{1}{2} \left|110\right\rangle + \frac{1}{2} \left|011\right\rangle + \frac{1}{2} \left|101\right\rangle$. That is to say: you have three qubits, the first two qubits are each initialized into the half-and-half state $\frac{1}{\sqrt{2}} \left|0\right\rangle + \frac{1}{\sqrt{2}} \left|1\right\rangle$, and then the third qubit is conditionally toggled so that its value tells you whether the first two qubits differ or not.
Now, run some bell tests with the first two qubits. You'll find that they don't violate any bell inequalities, and fail any other test of entanglement. They aren't entangled.
But, if you later measure the third qubit, and split the tests you did on the other two qubits into a "third qubit was 0" group and a "third qubit was 1" group, you'll see that within each group there are bell inequalities being violated! So the first two qubits were entangled all along.
BUT, if you measure the third qubit along the X axis instead of the Z axis we've been working with, then you'll never be able to split the two groups apart and see the entangled sub-cases. The distinguishing information becomes permanently inaccessible, unrecoverable due to thermodynamics stopping you from reverting the measurement.
So which is it? Were they entangled? Not entangled? Only entangled when we made the right measurement? I would say that they are entangled, but in an unusual way that's harder to detect. The third qubit tells you what type of entanglement exists between the first two qubits (entangled to agree, or entangled to disagree). Each subcase is entangled, but  the cases are complementary in a way that hides any signal of entanglement if you count them together instead of individually.
Whether or not we choose to measure the correct axis of the third qubit doesn't determine whether the original two qubits are entangled or not, it determines whether we have the information needed to split the results into the two complementary sub-cases. If you try to simplify the situation into just "two-particles-maximally-entangled" vs "not-entangled", or into "is-just-a-particle" vs "is-just-a-wave", you're throwing away the context needed to understand what's going on.
Mapping Back
The exact same logic applies to the delayed choice quantum eraser experiment, except there's an extra value involved and you're looking for interference patterns instead of passing bell tests. No consciousness. No retrocausality. Just "did we get and use the distinguishing information needed to group the lack-of-interference pattern into two complementary interference patterns"
A: I'll add this as your question seems to be almost the inverse of this one of my own:
Delayed Choice Quantum Eraser without retrocausality?
Regarding the need for retrocausality (or lack thereof), consider this:
Remember that a single detection in a node for D1 is also compatible with a single detection location for the general bell-shaped no-interference distribution associated with D3/D4. It's only by correlating either D1 or D2 with their paired D0 hits that interference can be recovered. Coordinate (x,y) on D0 can be compatible with either D1, D3, or D4 (assuming it's at a trough for D2).
In all scenarios forward causality is preserved regardless of the choice. If a D0(x,y) is recorded, the future options for which detectors can light up for its entangled sister are reduced to the subset of detectors with which-path info (whose D0 distributions overlap), or the detector without which-path info for which D0(x,y) corresponds to a node. The choice to detect which-way info (or not) further reduces the available subset of detectors in the same manner.   
