Why doesn't delayed choice quantum eraser experiment imply retrocausality? WRT: https://www.youtube.com/watch?v=0ui9ovrQuKE&ab_channel=ArvinAsh

Now I found a paper "Why Delayed Choice Experiments do NOT imply Retrocausality by David Ellerman" on the internet but as a layman, I couldn't understand the paper but everyone on youtube is saying that this experiment shows retrocausality, can someone explain in simple terms why this experiment does not imply retrocausality?
 A: This experiment implies retrocausality if you assume a classical way of thinking.  The point of these experiments is to demonstrate that either retrocausality is real or the physics of the world are not precisely classical.  The QM community, of course, would prefer to argue that their causal model is better than accepting retrocausality.
The tradeoff is interesting.  Classical mechanics ensures every object has a simple state.  A photon either went through slit A or slit B.  However, to make this model describe the results of this real experiment, we need retrocausality.  Quantum mechanics, on the other hand, gives each object a much more complicated concept of state.  In QM, we assume a much weaker assumption about how the world works.  We assume that the world can be modeled using linear operators.  In the quantum way of thinking, photon goes through all paths at once (through both slit A and slit B), and has to have a complicated enough state to deal with that.  We add the results of these two possible paths (something we can do because linear operators have a property called superposition).
In this QM interpretation, where the photon goes through slit A and slit B, we have to grapple with the intuition that most objects we know of go through one slit or another.  It is the interpretations of QM that grapple with this, the most common being the Copenhagen Interpretation.  The idea here is that if you design a sensor to react in a way which becomes increasingly classical after a detection (i.e. after the detection occurs, its state is well described classically), you have a "measurement."  The interpretations explain exactly what this measurement means. You and I are both much more comfortable with thinking classically, so the sooner we can get into thinking in terms of measurements of the quantum system, the sooner we can get back to handling the rest of the system (like the data collection computer) in a classical way!
I mention there are multiple interpretations.  They all yield the same results of the measurements, statistically, but they all justify it differently.  Each has its own quirks.  Copenhagen has a random draw associated with measurement, which is easy to understand but suggests the measurement "did" something important.  Others, like Pilot Wave avoid this random draw, but bring in other fun quirks.  Copenhagen is the most popular, so I'm using that.
So in the QM world, the detectors on the bottom do not tell you what path the photon took.  That would be meaningless, as the photon took all paths.  What they do provide is a measurement that is heavily correlated to path information.  If the system were thought of as a classical system, they would provide you which path the photon took, but we're not thinking of it that way.  It just provided a measurement providing path information.
Likewise, the gridded detector at the top does not tell you where the photon struck.  That would be meaningless, at the photon "struck" everywhere.  What it provides is a measurement that is related to the photons evolution.
Neither of these sensors provide anything unusual on their own.  If you looked at the top part of the circuit, you could handwave away the quantumness and say that it told you where the photon struck classically.  If you looked at the bottom part of the circuit, you could handwave away the quantumness and say it told you which path the photon took.
The oddity comes when you try to combine the measurements.  Now quantum mechanics says this is two measurements of a singe photon with its complex state that took all paths.  Now we can do a statistical correlation of them.  This is where it gets interesting because the information here is not which-path, but a measurement related to paths.  If the photon is detected by one of the sensors which provided path information in the classical sense, and we look at only those measurements taken by the grid, we see no interference pattern.  The result of integrating all paths that lead the photon to a path-sensing sensor yields those measurements on the top sensor which are consistent with the photon taking one one path or the other.
If the photon is detected by the "path erasing" sensor in a classical sense, and we select only the grid detections associated with those, we see the interference patterns associated with the double slit.  This is because, if we integrate all paths that lead the photon to the path-erasing sensor, they yield measurements on the top sensor that have fringes.
So what does this all mean?  Well, it means the QM scientists came up with a complicated set of equations which modeled this one experiment better than classical mechanics did, without having to resort to retrocausality.  Whooptie-doo.  However, what is more interesting is to realize that this experiment is just one of many.  Indeed, there are many quantum erasers experiments.  If you are trying to model their results with classical mechanics, you have to come up with a retrocausality structure to explain each and every one of them.  This leads to a long string of "what if I do this..." "what if I do that..." which exhausts time and resources!  What if Bill and Ted come back from the future and tweak the path of my photon 29 years after they went to hell?  The reformulation of classical mechanics to support this retrocausality is daunting!
The QM argument is that, rather than having to model everything with some retrocausality variant of classical mechanics, you can treat the "quantum" part of the system with one set of rules, and treat the entire rest of the world as a causal classical system.  Now all of those ugly "What if" questions are answerable with "It will be the same as-if the rest (non-quantum) of the system was classical... go calculate what happens classically."  These more difficult equations and strange quantum concepts let us scope down the part of the system that is complicated (the one with all the beam splitters and brifringic crystals).  And then, when Death comes to ask for best 5 out of 7, you know the odds, because the strange quantum behavior has been simplified into a random interaction with the larger classical system.
A: Suppose you have a bowl containing two red slips and two black slips. You draw a slip. If it's red, you draw another one. The second one will be black in about 2/3 of the trials, because there are two black slips and one red one left in the bowl when you draw it.
Now consider a variation of this experiment with the draws reversed. You draw a slip and set it aside. Then you draw a second one . If the second one is red, you look at the first one. Even though there were equally many red and black slips in the bowl when you made the first draw, if you actually try this experiment, you'll find that the first slip will be black in about 2/3 of the trials.
Is this an example of retrocausality in classical physics? No, it's an example of the inherent atemporality of probabilistic reasoning, whether classical or quantum. If A is correlated with B, then B is correlated with A; it makes no difference which one happens first.

The emphasis in delayed-choice experiments on the order in which the measurements happen shows that most people don't understand the above point. The delay doesn't make the outcome of the delayed-choice experiment any more surprising. The result of the experiment is not that the later measurement influences the earlier one; it's only that the outcomes are correlated, and this only shows up in later analysis.
I don't mean to imply that the delayed-choice quantum eraser experiment is classical. It's not; it's essentially a variant of the EPR/Bell experiment, with the following two differences:

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*The measurements are timelike separated, instead of spacelike separated.


*The experimenter only chooses a measurement basis "on the fly" for one of the two measurements (the later one).
Both of these changes violate the assumptions of Bell's theorem, meaning that his argument that the experimental outcome can't be explained by a local, causal hidden variable theory doesn't go through. And, in fact, the outcome of the DCQE experiment can be explained by a local, causal hidden variable theory. So it's nothing but a strictly less interesting version of Bell's experiment.

To make this more concrete, here's a version of Bell's experiment. You have two people who are allowed to agree on a strategy, then separated. Each one is asked one of three questions, say A, B, or C, and must give one of two answers, say yes or no. The rules are that if they are asked the same question they must give the same answer, and they win a prize each time they're asked different questions and give different answers.
You can make the following argument: since they must agree on their answers to the same questions, the only possible strategies involve pre-agreeing on what those answers will be. There are eight possibilities: NNN, NNY, NYN, ..., YYY. Two of those (NNN and YYY) never win them a prize. The other six win them a prize 2/3 of the time that they're asked different questions. And that's the best they can do. That's Bell's theorem.
It turns out, though, that if the players live in a quantum world, and generate a pair of entangled particles, and base their answers on measurements of those particles, they can win 3/4 of the time. That's the fundamental nonclassicality result.
In the standard Bell experiment, the questions are randomly chosen, and asked, at spacelike separated locations, so there's no chance of surreptitous communication between the players. In the "delayed choice" version, we make the following changes:

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*One player is asked before the other, so a radio signal could be surreptitiously sent from the first one to the second one.


*One of the players (the first one) is allowed to choose the question as well as the answer.
Either of these changes alone makes it possible for the players to win 100% of the time.
