FrediFizzx wrote: … … There is not all that much significance to the term "marginal". It is just a probability term as opposed to "joint" probability.
Don wrote:… … Regarding the quantum prediction, -a.b is the quantum joint prediction. It cannot be recovered in an experiment with separated measurements, and reduced density matrices must be used instead of the joint distribution. Refer to http://arxiv.org/abs/1309.1153 and the Conclusion of http://arxiv.org/abs/1409.5158 for a full account of this important distinction. ... ...
Ben6993 wrote: Further I have just now had a browse of Don's paper and the word 'marginal' is not even in the paper!
My new model (http://arxiv.org/abs/1507.06231) is a killer for the whole Bell Test program because ....
Don wrote:So you're too stupid to even follow the thread to know what paper we are talking about. Too narcissistic to consider an apology for demeaning me with nonsense. Stupid enough to show that to the world. And stupid enough to think "browsing" scientific works qualifies you to properly criticize them.
C'mon, Fred, get me out of here!
Don wrote:So you're too stupid to even follow the thread to know what paper we are talking about. Too narcissistic to consider an apology for demeaning me with nonsense. Stupid enough to show that to the world. And stupid enough to think "browsing" scientific works qualifies you to properly criticize them.
C'mon, Fred, get me out of here!
minkwe wrote:Therefore the QM joint prediction can never be measured separately.
minkwe wrote:I don't get what all the fuss is about in relation to the word "marginal".
We are interested in measuring the joint conditional probability P(AB|ab). We can do it two ways, we measure AB jointly, or we can measure A and B separately. For example, tossing two coins (a,b) repeatedly and measuring jointly means for each toss, you evaluate if both the A and B events are true. You only need 1 column on your spreadsheet titled "AB" and the rows will be "true", "false" etc. At the end you count the number of "true" and divide by the number of "false" to get your estimate of P(AB|ab) directly. Measuring separately means you toss coin "a" only repeatedly to create a table spreadsheet with one column labeled "A". Then in a separate experiment, you toss coin "b" to create a spreadsheet with one column labeled "B", and then you try to calculate from those two separate experiments.
This is problematic because the separate experiment can only give you P(A|a) and P(B|b), but according to the chain rule of probability theory:
P(AB|ab) = P(A|ab)P(B|Aab) = P(B|ab)P(A|Bab)
and those terms do not appear. You might make the assumption that P(A|Bab) = P(A|ab) = P(A|a), and P(B|Aab) = P(B|ab) = P(B|b). With those additional assumptions, you would then be able to calculate
Although in the usual usage, the marginal probability is P(A) while P(A|ab), P(A|a) are considered conditional, it is correct to say P(A|a) is marginal with respect to the B outcome and settings, compared to P(A|ab) and P(A|Bab).
As far as QM is concerned P(A|a) = P(B|b) = 1/2
But P(AB|ab) = 0.5 cos^2(theta) =/= P(A|a)P(B|b)
Therefore the QM joint prediction can never be measured separately.
Gordon Watson wrote:3. Those "separated measurements", when properly consolidated via proper matching, yield the following pairs: A+B+, A+B-, A-B+, A-B-. In the following beautiful numbers: N(A+B+), N(A+B-), N(A-B+), N(A-B-)! THEN, for any Bellian inequality, it's all down-hill from there.
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minkwe wrote:Gordon Watson wrote:3. Those "separated measurements", when properly consolidated via proper matching, yield the following pairs: A+B+, A+B-, A-B+, A-B-. In the following beautiful numbers: N(A+B+), N(A+B-), N(A-B+), N(A-B-)! THEN, for any Bellian inequality, it's all down-hill from there.
.
The bold text is the glue that joins them. Any calculation which uses terms like N(A+B+), N(A+B-), N(A-B+), N(A-B-) cannot be a separated measurement for those are joint terms. It does not matter how the measurements were actually made. They've been glued already prior to that point. Separated terms should be
N(A+) N(B+), N(A-), N(B-)
minkwe wrote: ...
I aways give the example of the correlation between the heights of husbands and their wives C(HW). A joint measurement means you record both the husband and wife's heights on the same row and use that to jointly calculate C(HW). Separated means you measure all the Husbands only in experiment 1, then measure all the wives only in experiment 2. The only way to recover the joint correlation would be to stitch them using common information. For example if each couple had an index and you recorded the index along side the Husband's or Wife's height, later using the indices to do proper matching. If you do this, the experiment becomes a joint experiment not a separated one. This is the case in all Bell test experiments.
FrediFizzx wrote:A note here; for most EPR experiments the pairing is always done in the analysis after the measurements are done. I guess one could be a little bit pendantic about that saying that the time stamps took care of the pairing during measurements. Anyways, the experiments do attempt to measure in pairs I believe.
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