Dbar_x said:
Credible, useful physical theories must be clear and unabmigiuous, consistent, and testable by falsification (or refutation) via experimental observation. As, for example, special relativity or quantum electrodynamics. It’s incumbant on those proposing or supporting a theory to meet such criteria, not on the rest of us to try to figure out what in the world they mean.
If quantum erasure means that entanglement between the apparatus and observed system causes an interference pattern to be destroyed, then restored when information is erased, then it must be clear precisely when the two objects are entangled. What unambiguous definition does QE give for entanglement? Is it distinct from the von Neumann measurement correlation between object and apparatus?
Since it is impossible in practice to maintain a macroscopic measuring-apparatus in isolation from its environment and only observe it after enough time has passed that no which-path information would be gained from the observation, we are not dealing with predictions about actual experiments here (in future we might be able to create large isolated multiparticle systems using quantum computers, so this sort of thing is not impossible in principle, just impossible with present technology). But it's routine in theoretical physics to look at what the formalism of a given theory would tell us about an experiment which is impossible in practice for us to do today, like analyzing what would be seen by an observer diving into a black hole in general relativity. In QM, if a system composed of all the particles making up a macroscopic object could be maintained in isolation for some time and then observed, the formalism would say you should set up a giant multiparticle wavefunction for the system and evolve it forward until the moment of observation using the standard rules for wavefunction evolution, and then at the moment of observation you'd use the usual Born rule to figure out the probabilities it will be in different configurations. This is what physicists imagine doing in the Schroedinger's cat thought-experiment for example. It has nothing to do with "quantum erasure" specifically, it's just the universal quantum rules for dealing with
any isolated quantum system composed of multiple interacting particles (and this is exactly what's done for smaller isolated multiparticle systems consisting of just a few particles).
But if Scully didn't include any detailed mathematical analysis to go with the statement you quoted, namely:
...if we put a Welcher Weg detector in place (so we lose interference even if we don’t look at the detector) and then erase the which way information after the particles have passed...such a ‘quantum eraser’ process (would) restore the interference fringes.
...then it seems a little pointless to waste too much time worrying about an offhand remark about an impossible-in-practice thought experiment similar to Schroedinger's cat (aside from pointing out that your notion that his statement assumes 'mixtures evolving from superpositions' is almost certainly a misreading of what he had in mind). Let's focus instead on the actual quantum eraser experiment, which doesn't involve a giant multiparticle wavefunction, but just a 2-particle wavefunction for the signal/idler pair. In that vein, you ask:
Dbar_x said:
How would an experimenter measure the potential to gain which-way information? What’s the equation for such a potential?
"Potential" just means on any given trial, if you choose you can always set up the experiment so that you do gain which-way information on that trial (and if the idler path length is long enough you can make this choice after the signal photon has already been detected). It's similar to saying that on any trial involving a single particle going through the double-slit, prior to the time when the particle reaches the slits there is the potential to gain that particle's which way-information by placing a detector near the slit. You could demonstrate this potential by putting a detector near the slits on 100% of the trials, and in that case for near 100% of particles (allowing for some small amount of experimental error) you would gain the which-way information. Similarly, if you removed the beam-splitters BSA and BSB in Scully's experiment on 100% of trials, for near 100% of signal/idler pairs you could gain the signal photon's which-way information. If you don't like this use of the word "potential", fine, as long as you agree about the basic physical idea that you can set up the experiment so that you gain which-path information on nearly 100% of trials, then this is just a semantic dispute with no real physical content.
I would appreciate it if you'd address my more specific questions about how
you are proposing to demonstrate that the particle does not remain in superposition after passing through the SG device:
That doesn't really make sense to me. If there are two alternative possibilities (in this case, either the atoms are in superposition or aren't after passing through the SG device), then the only way to "falsify" either possibility is to show that they yield different predictions about a given experiment, and then demonstrate one prediction is confirmed while the other isn't. If you don't even know what an advocate of the "atoms do remain in superposition after passing through the SG device" view would predict about your own experiment, how can you possibly say that if the experiment has the results you predict it'd falsify this view? Maybe you're just thinking about it wrong and an advocate of the superposition view would actually predict the same thing you're predicting. And if you do know what they'd predict and it's different from what you predict, then if the actual results matched their prediction but not yours, wouldn't that be a falsification of your own view that they don't remain in superposition?
