FrediFizzx wrote:Hmm... Well, unlike Gill's version of CHSH that NOTHING can violate, not even QM, the QRC can show violation if there is a connection between the a and b vectors. Do you have Mathematica? I have programmed the QRC with your parameters and the notebook file is here.
I am just trying to find what the exact mathematical flaw might be but I hear what you are saying.
Bell wrote:Of course the explanation is well known: A measurement of a sum of non-commuting observables cannot be made by combining trivially the results of separate observations on the two terms -- it requires a quite distinct experiment.
...
But this explanation of the non-additivity of allowed values also establishes the non-triviality of the additivity of expectation values.
All EPR-type experiments (and QM) are calculating expressions of the type <A1B1> + <A2B2'> + <A3'B3> - <A4'B4'>, and comparing the results with the CHSH which is an expression of the type <A1B1> + <A1B1'> + <A1'B1> - <A1'B1'>. The correct upper bound for the former expression is 4 not 2. Gills proof is deriving an expression of the latter type (upper-bound 2) not the former type (upper-bound 4).
The QRC and similar challenges ask you to produce A1, A1', B1, B1' which will violate the CHSH. This is an invalid challenge because QM and experiments do not produce that, they produce A1, B1, A2, B2', A3', B3, A4', B4'!
FrediFizzx wrote:We are going around in circles here and the discussion of Gill's version of CHSH is off topic for this thread. This thread is about the QRC.
FrediFizzx wrote:Take a look at the CHSH calculation in this PDF file.
FrediFizzx wrote:That is not what you were talking about. Please stay focused. You will see a real calculation of CHSH. That is how it is done. Not the way you express it.
FrediFizzx wrote:Ok sorry, looked at your quote again and that is right if you are just using the primes to indicate where a' and b' are used. What you have wrong is the following quote.The QRC and similar challenges ask you to produce A1, A1', B1, B1' which will violate the CHSH. This is an invalid challenge because QM and experiments do not produce that, they produce A1, B1, A2, B2', A3', B3, A4', B4'!
The QRC does not do that. Only Gill does that. QRC does the correct calculation of CHSH I believe. Take a look at the CHSH calculation in this PDF file.
FrediFizzx wrote:We were talking about the difference between your CHSH expression and how it is done in the QRC.
FrediFizzx wrote:No. There are "If" conditions there so it is only adding up the 1's for if the condition is met. If the condition is not met, a 0 is put in the summation. Take for example E_0 = 2N_E0/N_0 -1. Which we could say represents the E(a, b) part of CHSH. For that sum it is only adding up if a = b, etc. Of course that only happens when a and b are at 0 degrees. Then E_1 is taking a different set of when the angles are at a certain value. And so forth.
minkwe wrote:It is similar to claiming that the expression "women are shorter than men" is not true, by using height data from one set of randomly selected people without regard for gender, and gender data from a disjoint set of randomly selected people without regard for height. Its bad statistics.
minkwe wrote: I see, so the sets used to calculate each term is disjoint from each other. Which means they are calculating an expression of the form <A1B1> + <A2B2'> + <A3'B3> - <A4'B4'>, for which the upper bound is 4. In that case it is a fair representation of what is possible in experiments but it is not calculating the true CHSH, which requires a single spreadsheet (that is, an expression of the type <A1B1> + <A1B1'> + <A1'B1> - <A1'B1'>.). That is why it can violate it.
The main point I'm making is that all the paradoxes originate from confusing The results from <A1B1> + <A2B2'> + <A3'B3> - <A4'B4'> with a condition based on <A1B1> + <A1B1'> + <A1'B1> - <A1'B1'>. The QRC does it by comparing the former expression based on 4 disjoint sets, with 2, which is the upper bound for the latter expression derived from a single set.
FrediFizzx wrote:Something is not quite right with your analysis for the "true CHSH" as it has been mathematically proven that the upper bound on
E(a, b) + E(a', b) + E(a, b') - E(a', b') is 2sqrt(2).
But I think I did notice that sometimes when QRC's CHSH is violated, it was like 3.9 so I think you are right about it is doing <A1B1> + <A2B2'> + <A3'B3> - <A4'B4'>. If that is the case then that is a mistake in the QRC. But perhaps not a serious mistake. I will check this out further. Thanks.
FrediFizzx wrote:"Is it valid?" just means is it really a true Bell model tester? Nothing really perplexing about that. So far, it seems pretty limited since you can only have 3 different angles for a, a', b, and b'. Actually that is not quite right; you can have two angles for a and a' and two angles for b and b'. Is that sufficient for a true test?
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