I believe waveforms must reform, because otherwise you'd have all previously observed particles traveling through space and time being inherently different from unobserved ones.I was clued-in to the Quantum eraser experiment, and followed up...
An interesting experiment would be to recreate the double-slit experiment with a particle detector at one of the slits, but then purposefully ignore or "forget" the output of the detector. In a sense, you'd be putting the results into a "quantum cat box" in a way that it's impossible for you to observe the results. I believe that all "forgotten" observations = "reformed" wave functions, so I believe that the interference pattern would be visible again, if you did it right.
So the expected result is seen ("erasing" the effect of observations restores the photon's probabilistic nature, or whatever). But the real-world consequences displayed by the experiment are still mind-bogglingly unintuitive.... and having information now about events from the past makes those events deterministic in the past. Wikipedia says so, folks!
As for time... "(delaying deciding) whether to measure or destroy the 'which path' information ... appears to have the bizarre effect of determining the outcome of an event after it has already occurred." -- In other words, what you see now depends on what you do later. This is balls as nuts!, but a more intuitive way to put it might be, "The experiment will display probabilistic effects now if there is no way to make 'which path' observations in the future (IE no useable information), and will display deterministic effects now if there is."
It would seem that having deterministic information now about events that occurred in the past, does indeed make those events deterministic in the past. Or perhaps in other words, we can make observations now of events that happened in the past???
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Let's get philosophical about the idea of determining the result of an event in the future. That is, what I see now is apparently the result of what I do tomorrow. I say "determining" instead of deciding, and "apparently", because it might not actually be the case that I'll be causing an effect in the past. It could simply be that I can predict now whether or not there will be information available in the future, to be able to make an observation then about what I'm doing now. The bizarre part is that in the case of the quantum eraser experiment, I can control in the future whether or not there will be information (by measuring or destroying the 'which path' information). So does that mean the experiment predicts what I will do in the future? Or that there is an effect that travels backward through time? Or perhaps the experiment would require such short time periods and such great distances, that "now" and the "future" that I speak of are no longer causally linked (at least in the backward direction), and it is all irrelevant?
I assume the latter option. I assume this fits with the "rules" of causality in a way that makes the time travel of information impossible.
However let's assume that I can tell today from the experiment, whether a measurement will be made tomorrow or sometime in the future (by me or anyone else), or whether the information will be destroyed first. Then I can set up a meta-experiment in which I manipulate how the experiment is done, for example to send a message back in time from the future (lotto numbers, say). I would set up a series of timed experiments or perhaps multiple apparatuses, and code a massage in binary, using the observations of whether or not I see double-slit interference patterns today, to represent the 2 states. Tomorrow I would measure or destroy the 'which-path' information appropriately.
In the end, I would still expect not to be able to send a message back in time. In the meta-experiment, observing the result of the series of experiments constitutes an observation, thus collapsing the probability waveform describing the meta-experiment. This would leave me no way to randomly change what I do tomorrow (whether I measure or destroy). Since it seems impossible that I could lock myself into a particular action, I think the more likely result is that none of the apparatuses would display interference patterns. They would all act as if the information would be measured in the future. In some way, the observation of the meta-experiment would be linked to the 'which-path' information, and observing an outcome of any kind would collapse the waveforms and no interference pattern would be seen.
This still doesn't make sense, so unless I missed something, there is likely some other factor that prevents "impossible" results. It is likely that there is no way to set up the experiment within the scope of causality. For example, say you wanted to destroy the 'which-path' information, and then observed that the interference pattern was visible, so you quickly changed your mind to measure the information instead, creating a paradox -- This could probably never happen because the observation of the interference pattern would likely need to be causally disconnected (via very small time or very large distance), so that you could never "change your mind" fast enough based on the observation, as to whether or not to destroy or measure the information. In other words, you would never be close enough to say for certain that the observation of the interference pattern did in fact happen before the act of measuring or destroying the path information. The very best possible that you could ever say was that they appeared to happen at the same time.
This is all conjecture. Personally I think the second explanation is more likely, unless we can find a direct link between observations in the meta-experiment, and information involved in its apparatuses.
Addendum
After reading about the Delayed choice quantum eraser, a simpler explanation is given for why this could not be used to send a message back in time. Interference patterns are only visible in the "past" portion of the experiment when combined with information from the "future" part. I think basically you could say that multiple possible outcomes that could create a destructive interference pattern in the "past", combine constructively to create no interference pattern at all. You need information from the "future" to be able to filter out the possible interference patterns of the past.
Makes sense.
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