vegasgeorge said:
I'm still digesting Bell's Theorum and Einstein's 1935 EPR paper, and will get back to you all on all that. In the meantime, as I see this discussion developing in my absence, I have to ask, doesn't Occam's Razor come into this? Wouldn't the assumption that the two entangled particles had opposite properties ab initio be the simplest explanation? Is it possible that the math is leading QM theorists on a wild goose chase?
Let me respond in more common terms.
Normally (but not normal for QM) you would expect that the one photon of the entangled pair were tilted in some specific direction - for example NNE and 20 degrees up, and the other was pointed in exactly the opposite direction (SSW, 20 down). You would also say that those direction were set at the time that the pair became entangled and remained unchanged until they were measure. This "tilt" is the hidden variable and the expectation that it was set when the two were together and remained unchanged while they were apart is what makes it "local".
Finally, the normal expectation is that the measurement made when the photon reaches the filter is simply determined by that tilt of the photon, the angle of the filter, and perhaps other local conditions.
If you always keep the filters opposite of each other, you will discover that you get the same result at both detectors. This is consistent with what you would "normally" expect.
If you hold one detector (detector A) at a constant angle while varying the angle of the other (detector B), then based on "normal" (local hidden variable) assumptions, you can come to certain (inaccurate) conclusions about the distribution of the tilt of those photons. So at this point, you can still hold onto your "normal" view, but you will see that the distribution seems dependent on what angle you picked for the constant angle detector.
Next, you can step detector A through several angles - in each case varying B to determine the new distribution of photon tilts. At this point, your "normal" assumptions are in trouble. First, you will discover that the distribution of results at detector B is dependent on the setting of detector A. Worse yet, Bell worked out the arithmetic to show that that conclusion is unavoidable.
With regards to Occam's Razor: The arithmetic described by Bell is called the "Bell Inequality" and it was published in 1964. I notice that DrChinese has a copy of it here:
http://www.drchinese.com/David/Bell_Compact.pdf. Although, on the face of it, it appears airtight, some loopholes have been described and in most cases closed. Most people who understand the problem that the Bell Inequality presents to "Local Hidden Value" models, do not consider those models to satisfy Occam's Razor.