Sorry this is so long and a diversion from the original question! Ages ago I asked a question here
https://www.physicsforums.com/showthread.php?t=307449
and DrChinese answered very helpfully.
I wanted to find some actual experimental data for what DrC explained was basically calibrating the apparatus. I had thought that if two entangled photons (with the same polarisation) were measured at two distant filters which were orientated the same way then the fact that the first had passed through would mean that its polarisation had been measured and the distant photon would collapse to the same orientation and hence always pass the distant filter. To my mind this would be a dramatic display of action at a distance and would obviate the statistical cunning of John Bell's suggested experiment.
DrC said that it is taken as read that there is a 100% correspondence. Eventually, however, I did find some records of data from a similar experiment (can't remember where) and in fact there isn't 100% correspondence, it's much less. So I then thought a bit more about the experiment and resorted to a larger scale photon (to help my brain). Imagined the entangled photons as radio waves of several metres wavelength and the polarising filters are large grids of aluminium tubes. This is all stuff used in the design of aerials etc. When the electrical field is in line with the tubes then an electrical current is induced which is just enough to create a photon in the opposite direction to the original and destructively interfere with it. i.e. it's reflected (Occasionally the photon is absorbed as heat and the original photon still destructively interfered out of existence). When the electrical field is at right angles to the tubes then no current (too small a current) is produced and the photon passes through the grid unimpeded. At intermediate angles there is a probable outcome depending on Malus' law. All the photons that have passed through the grid have an electrical field orientated at right angles to the tubes even though a vanishingly small percentage (a.k.a. None) of the incident ones did.
So, my thinking went: When the first entangled photon is 'measured' and its wave-function collapses then it must have collapsed before the filter. All we really know is that it had a probable direction of polarisation after collapse that is consistent with Malus' law (we know that a polarised photon has a 50% probability of passing a filter set at 45° etc.) And the same goes for the distant, entangled partner. I could then see that the calibration stage of this experiment was always going to give the same results at photons that just had the same polarisation rather than having quantum properties and this explained the data that I had been able to find.
So I then wondered my way through the following stages:
1. What if the whole Bell's experiment was done with a photon source that guaranteed polarisation of the source photons in a certain direction? Presumably the inequality wouldn't be exceeded. This is the 'null' hypothesis that the experiment sets out to disprove so must be done as a matter of course each time the experiment is performed.
2. What if the experiment was done with a large number of photon sources each set at a different angle. If the timing of each source was know then this would be identical with question 1. So what if the timing was not known but controlled by a computer that randomly switched just one source on at a time. Would it matter how the randomness was generated, i.e. an external 'quantum' random number generator or a pseudo random computer generator? Again I can't believe that the experiment could show a positive result if there was any way of retrospectively finding when each photon source had been running.
3. What if the experimental set-up is the same as in 2. with a large number of photon sources producing polarised photons at different angles but they are all running at the same time with the beams combined so there is no way of telling when a photon leaves each source? So when a photon is counted by either detector there is no way to tell which source it came from and what its polarisation was. But it definitely had some real angle of polarisation, we just don't know which
4. Now we use natural light from the window as a source for our entangle photon generator. We know that the the light has been scattered by dust, clouds, neighbouring buildings etc. and each photon has been polarised in a real direction by a deterministic processes exactly the same as happens in our polarising filters. It has happened as part of a huge complex system that we cannot begin to analyse so we don't know what the direction of polarisation is for a given photon but we know that if a polarising filter is sufficient to collapse a wave-function then all the light that comes in through the window has been collapsed.
I am quite familiar with the ideas of QM (though a unhappy about some of the 'theological, consciousness' interpretations) so I'm not really seeking a theoretical explanation of these ramblings, but is anyone familiar with actual experimental results testing these four stages?
