The answer is in a question no one dares to ask.
So it seems. Here's some additional information for y'all:
THE FIRST ENTANGLEMENT OF THREE PHOTONS has been experimentally demonstrated by researchers at the University of Innsbruck (contact Harald Weinfurter, harald.weinfurter@uibk.ac.at, 011-43-512-507-6316). Individually, an entangled particle has properties (such as momentum) that are indeterminate and undefined until the particle is measured or otherwise disturbed. Measuring one entangled particle, however, defines its properties and seems to influence the properties of its partner or partners instantaneously, even if they are light years apart. In the present experiment, sending individual photons through a special crystal sometimes converted a photon into two pairs of entangled photons. After detecting a "trigger" photon, and interfering two of the three others in a beamsplitter, it became impossible to determine which photon came from which entangled pair. As a result, the respective properties of the three remaining photons were indeterminate, which is one way of saying that they were entangled (the first such observation for three physically separated particles).
The researchers deduced that this entangled state is the long-coveted GHZ state proposed by physicists Daniel Greenberger, Michael Horne, and Anton Zeilinger in the late 1980s. In addition to facilitating more advanced forms of quantum cryptography, the GHZ state will help provide a nonstatistical test of the foundations of quantum mechanics. Albert Einstein, troubled by some implications of quantum science, believed that any rational description of nature is incomplete unless it is both a local and realistic theory: "realism" refers to the idea that a particle has properties that exist even before they are measured, and "locality" means that measuring one particle cannot affect the properties of another, physically separated particle faster than the speed of light.
But quantum mechanics states that realism, locality--or both--must be violated. Previous experiments have provided highly convincing evidence against local realism, but these "Bell's inequalities" tests require the measurement of many pairs of entangled photons to build up a body of statistical evidence against the idea. In contrast, studying a single set of properties in the GHZ particles (not yet reported) could verify the predictions of quantum mechanics while contradicting those of local realism. (Bouwmeester et al., Physical Review Letters, 15 Feb.)
Bell's Inqualities and Kolmogorov's Axioms (pdf)
New Loophole for the Einstein-Podolsky-Rosen Paradox
So it seems. Here's some additional information for y'all:
I've alluded to this before. This paradox is analogous to those that confronted physics before the turn of the last century, when everyone was sure they had everything wrapped up in a tidy little box except for a few 'loose ends.' And then Einstein came along and blew up the box!
This is an interesting paradox. Einstein's theories give rise to QM which is the foundation of Bell's Theorem which then in turn, violates Einstein's theories. I like the last line of the second paper you referenced here:
"This proves that quantum mechanical theory is logically consistent with relativity."
They are trying to keep the whole thing from falling down, which they can see is a real possibility with QM. There IS something wrong here. But where?
You might know of, or run across, since you are clearly deep into this, much more than I am, (if I only had the time!) so let me ask you about something I've seen other writers allude to a couple times (years ago when I was really trying to understand this stuff, so I can't remember where to go back and look it up) that:
QM is a house of cards built upon Planke's Constant and that Planke's Constant is bad math, not derived from any actual observation but by working backwards and plugging in a certain figure because that is the only figure that works but no one knows the how or why of that figure. Nobody wants to question it because if they find a fault here then the whole house of cards comes tumbling down.
You ever run across something like this? It may have been superceded since then and I wouldn't know about it.
Thanks again (I think, you are tempting me and arousing an interest that is hugely time consuming to just follow, let alone understand, and that I really don't have the time for. Good job!)