This experimental Question is a result of reading a particular article on Bell violations. I addressed the e-mail below to the corresponding authors —because who knows, they might reply— but it is not specific to them, it's just that their article crystallized the Question, and perhaps someone on Physics SE can tell me what the results of the experiment would be without doing it (although I think these time-dependent properties are not part of the usual data sheets for off the shelf components).
There is a subsidiary question: have such experiments been done, and I haven't seen them in the literature?
Dear Johannes and Anton,
I've read your PNAS article "Violation of local realism with freedom of choice" as a result of a blog posting by Sabine Hossenfelder at http://backreaction.blogspot.com/2011/06/nonlocal-correlations-between-canary.html [Physics SE readers can find PNAS and arXiv links there]. I was impressed by your three key remarks on the second page, which seem to me nicely balanced.
Reading your article I wondered as I have many times whether Bell inequality violations appear instantly when the source is turned on, or to what extent they increase over time. I am partly led to the questions below because it seems that Bell violating experiments run continuously, whereas it seems that technological applications may well be intermittent.
I imagine, specifically, an experiment based on an experiment in which we observe Bell violations routinely (presumably in CHSH form). The crucial physical modification is to block both paths from the source to the two detectors physically, at a point near the source, on a time scale of, say, about a second, so that light travels from the source only for half a second at a time. A steady state condition of the source, the quantized electromagnetic field, and the detectors will presumably not be instantly established, but, I suppose, would be established in half a second, so that if we considered data only from the last quarter second of the on-phase we would see the usual violation of Bell inequalities.
The crucial modification of the analysis is to consider the way Bell violation changes over time, microsecond by microsecond (or more or less finely time-sliced as experience indicates), after the moment that the physical block is removed. Clearly this is a statistical analysis, since we would expect to see approximately one photon pair every four microseconds (at a local production rate comparable to the 250,000 photon pairs per second that you report in your PNAS article).
I suppose that a number of questions emerge, some of which may be characteristics of the source and detectors; others might be characteristic of the experimental apparatus more generally considered. Firstly, most elementarily, how does the rate of single photon detections change over time in the microseconds after the physical block is removed? We would expect that there would be a rapid approach to the steady state, but not instantaneous.
Secondly, how does the rate of photon pair detections change over time in the microseconds after the physical block is removed? Does the approach to the steady state have the same relaxation rate as the relaxation rate for the single photon approach to the steady state?
Thirdly, how does the violation of Bell inequalities vary over time in the microseconds after the physical block is removed? Again, does this have the same relaxation rate for the approach to the steady state?
It seems a matter of technological interest as well as of foundational interest whether relaxation of Bell inequality violations towards the steady state immediately after a light source is exposed is the same as the relaxation rates of single photon detections and/or double photon detections, or whether we have to wait longer for usable Bell violations to emerge.
Because I suppose these questions to be of general interest, I have also posted them at http://physics.stackexchange.com. I don't imagine the results of such an experiment will go against quantum theoretical expectations, but I'm curious whether characterizing these time-dependent properties of the sources and detectors might give some surprises.