Can someone sketch me the Many-Worlds version of what happens in the delayed choice quantum eraser experiment? Does a last-minute choice to preserve or erase the which-path information affect which “worlds” decohere “away from” the experimenter? If so, how does that go, in broad outline? If not, what?
The key to understand this kind of experiment under the MWI is to remember that if you erase (or never register) information specific to one of the branches of the super-position, then you can effectively merge two branches just as easily as you had split them.
The delayed quantum erasure is too complex for me to analyze now (it has a lot of branches), but the point is that when you make two branches interact, if those branches have not acquired information on their path, then they can be constructively re-merged.
Even though it’s been quite a few years since I attended any quantum mechanics courses, I did do a talk as an undergraduate on this very experiment, so I’m hoping that what I write below will not be complete rubbish. I’ll quickly go through the double slit experiment, and then try to explain what’s happening in the delayed choice quantum eraser and why it happens. Disclaimer: I know (or knew) the maths, but our professors did not go to great lengths explaining what ‘really’ happens, let alone what happens according to the MWI, so my explanation comes from my understanding of the maths and my admittedly more shoddy understanding of the MWI. So take the following with a grain of salt, and I would welcome comments and corrections from better informed people! (Also, the names for the different detectors in the delayed choice explanation are taken from the wikipedia article)
In the normal double slit experiment, letting through one photon at a time, the slit through which the photon went cannot be determined, as the world-state when the photon has landed could have come from either trajectory (so it’s still within the same Everett branch), and so both paths of the photon were able to interfere, affecting where it landed. As more photons are sent through, we see evidence of this through the interference pattern created.
However, if we measure which slit the photon goes through, the world states when the photon lands are different for each slit the photon went through (in one branch, a measurement exists which says it went through slit A, and in the other, through slit B). Because the end world states are different, the two branch-versions of the photon did not interfere with each other.
I think of it like this: starting at a world state at point A, and ending at a world state at point B, if multiple paths of a photon could have led from A to B, then the different paths could interfere with each other. In the case where the slit the photon went through is known, the different paths could not both lead to the same world state (B), and so existed in separate Everett branches, unable to interfere with each other.
Now, with the delayed choice: the key is to resist the temptation to take the state “signal photon has landed, but idler photon has yet to land” as point B in my above analogy. If you did, you’d see that the world state can be reached by the photon going through either slit, and so interference inside this single branch must have occurred. But time doesn’t work that way, it turns out: the true final world states are those that take into account where the idler photon went. And so we see that in the world state where the idler photon landed in D1 or D2, this could have occurred whether the photon went through either slit, and so both on D0 (for those photons) and D1/D2, we end up seeing interference patterns, as we’re still within a single branch, so to speak (when it comes to this limited interaction, that is).
Whereas in the case where the idler photon reaches D3, that world state could not have been reached by the photon going through either slit, and so the trajectory of the photon did not interfere with any other trajectory (since the other trajectory led to a world state where the idler photon was detected at D4, so a separate branch).
So going back to my point A/B analogy, imagine three world states A, B and C as points on a page, and STRAIGHT lines represent different hypothetical paths a photon could take, you can see that if two paths lead from point A to point B, the lines would be on top of each other, meaning a single branch, and the paths would interfere. But if one of the paths led to point A and the other to point B, they would not be on top of each other, they go into different branches, and so the paths would not interfere.
Can someone sketch me the Many-Worlds version of what happens in the delayed choice quantum eraser experiment? Does a last-minute choice to preserve or erase the which-path information affect which “worlds” decohere “away from” the experimenter? If so, how does that go, in broad outline? If not, what?
The key to understand this kind of experiment under the MWI is to remember that if you erase (or never register) information specific to one of the branches of the super-position, then you can effectively merge two branches just as easily as you had split them.
The delayed quantum erasure is too complex for me to analyze now (it has a lot of branches), but the point is that when you make two branches interact, if those branches have not acquired information on their path, then they can be constructively re-merged.
Even though it’s been quite a few years since I attended any quantum mechanics courses, I did do a talk as an undergraduate on this very experiment, so I’m hoping that what I write below will not be complete rubbish. I’ll quickly go through the double slit experiment, and then try to explain what’s happening in the delayed choice quantum eraser and why it happens. Disclaimer: I know (or knew) the maths, but our professors did not go to great lengths explaining what ‘really’ happens, let alone what happens according to the MWI, so my explanation comes from my understanding of the maths and my admittedly more shoddy understanding of the MWI. So take the following with a grain of salt, and I would welcome comments and corrections from better informed people! (Also, the names for the different detectors in the delayed choice explanation are taken from the wikipedia article)
In the normal double slit experiment, letting through one photon at a time, the slit through which the photon went cannot be determined, as the world-state when the photon has landed could have come from either trajectory (so it’s still within the same Everett branch), and so both paths of the photon were able to interfere, affecting where it landed. As more photons are sent through, we see evidence of this through the interference pattern created. However, if we measure which slit the photon goes through, the world states when the photon lands are different for each slit the photon went through (in one branch, a measurement exists which says it went through slit A, and in the other, through slit B). Because the end world states are different, the two branch-versions of the photon did not interfere with each other. I think of it like this: starting at a world state at point A, and ending at a world state at point B, if multiple paths of a photon could have led from A to B, then the different paths could interfere with each other. In the case where the slit the photon went through is known, the different paths could not both lead to the same world state (B), and so existed in separate Everett branches, unable to interfere with each other.
Now, with the delayed choice: the key is to resist the temptation to take the state “signal photon has landed, but idler photon has yet to land” as point B in my above analogy. If you did, you’d see that the world state can be reached by the photon going through either slit, and so interference inside this single branch must have occurred. But time doesn’t work that way, it turns out: the true final world states are those that take into account where the idler photon went. And so we see that in the world state where the idler photon landed in D1 or D2, this could have occurred whether the photon went through either slit, and so both on D0 (for those photons) and D1/D2, we end up seeing interference patterns, as we’re still within a single branch, so to speak (when it comes to this limited interaction, that is). Whereas in the case where the idler photon reaches D3, that world state could not have been reached by the photon going through either slit, and so the trajectory of the photon did not interfere with any other trajectory (since the other trajectory led to a world state where the idler photon was detected at D4, so a separate branch).
So going back to my point A/B analogy, imagine three world states A, B and C as points on a page, and STRAIGHT lines represent different hypothetical paths a photon could take, you can see that if two paths lead from point A to point B, the lines would be on top of each other, meaning a single branch, and the paths would interfere. But if one of the paths led to point A and the other to point B, they would not be on top of each other, they go into different branches, and so the paths would not interfere.
Belated thanks to you and MrMind, these answers were very helpful.