gill1109 wrote:This is the letter I am thinking of sending to the adjudicators:
Nice letter, but in the mean time a new argument has emerged that "b" may be fixed in my simulation. I would like to investigate that further before we proceed.
gill1109 wrote:This is the letter I am thinking of sending to the adjudicators:
Joy Christian wrote:minkwe wrote:Heinera wrote:First the code loops on i (the alpha angles), and then on j (the beta angles).
But the assignment to the correlations corrs[i] within the j-loop only has one index i. So for each new value of j, the previous assignment to corrs[i] is simply forgotten and overwritten. So at the end of the loop, we end up with corrs[i] dependent only on angles[K-1] (the last assignment to beta). All other values of beta are irrelevant. Agree?
That is a fair criticism.
How is this equivalent to "b" being fixed? It seems to me that the last assignment of beta can take any value.
Joy Christian wrote:gill1109 wrote:This is the letter I am thinking of sending to the adjudicators:
Nice letter, but in the mean time a new argument has emerged that "b" may be fixed in my simulation. I would like to investigate that further before we proceed.
minkwe wrote:1) Is Joy's simulation local-realistic or not? If not state precisely where in the code.
2) Does any of the correlations E(a,b) deviate from the QM prediction by more than 0.2 or not? (Simply look at the plot. or point out precisely why you believe the calculation of the plot is in error, the code is public).
Joy Christian wrote:Nice!
Now we are making progress. I see these images as both good news and bad news. Note that my LHV surface is a massive improvement over the traditional LHV surface (or Bell-CHSH surface). But the images also reveal that the surfaces do not match perfectly.
Heinera wrote:Joy Christian wrote:Nice!
Now we are making progress. I see these images as both good news and bad news. Note that my LHV surface is a massive improvement over the traditional LHV surface (or Bell-CHSH surface). But the images also reveal that the surfaces do not match perfectly.
Actually not. For some pints it is an improvement, for orher points it performs worse. If you take the average absolute difference between your surface and the QM surface, it persforms as bad as the picewice linear Bell surface.
Joy Christian wrote:Heinera wrote:Joy Christian wrote:Nice!
Now we are making progress. I see these images as both good news and bad news. Note that my LHV surface is a massive improvement over the traditional LHV surface (or Bell-CHSH surface). But the images also reveal that the surfaces do not match perfectly.
Actually not. For some pints it is an improvement, for orher points it performs worse. If you take the average absolute difference between your surface and the QM surface, it persforms as bad as the picewice linear Bell surface.
I disagree. I have run the R script for 10^6 and 10^7 trials, and the wrinkles in the LHV surface smooth out considerably for these larger number of trials. They do not go away, however, and so there are indeed specific points where my (current) LHV model does worse than the Bell-CHSH model.
Heinera wrote:I have published an R script where average performance is computed:
http://rpubs.com/heinera/16559
gill1109 wrote:Tsirelson's theorem shows that this is not only optimal *given* the singlet state and just optimizing over von Neumann measurements, but also optimal over all possible joint states, of whatever dimension Hilbert spaces you like, and over generalised as well as von Neumann measurements; in other words, over the largest possible class of states and measurements allowed within conventional QM. That's quite some theorem...
Joy Christian wrote:gill1109 wrote:Tsirelson's theorem shows that this is not only optimal *given* the singlet state and just optimizing over von Neumann measurements, but also optimal over all possible joint states, of whatever dimension Hilbert spaces you like, and over generalised as well as von Neumann measurements; in other words, over the largest possible class of states and measurements allowed within conventional QM. That's quite some theorem...
Tsirelson's theorem is easy to understand. It is a consequence of the topological structure of S^7, which is of course deeply connected to the four possible division algebras: http://arxiv.org/abs/1101.1958. See especially the concluding section of this paper for the physical significance of the theorem.
gill1109 wrote:Are you saying that all of conventional quantum theory, including all the Hilbert spaces, the POVM's, etc etc can be *derived* from a mathematical structure grounded on division algebras? If that were true, it would be a very exciting theorem.
Joy Christian wrote:gill1109 wrote:Are you saying that all of conventional quantum theory, including all the Hilbert spaces, the POVM's, etc etc can be *derived* from a mathematical structure grounded on division algebras? If that were true, it would be a very exciting theorem.
See the "exciting" theorem on the page 12 of this paper: http://arxiv.org/abs/1201.0775.
gill1109 wrote:I did not yet see Atiyah, Penrose and so on getting wildly excited about it.
Joy Christian wrote:gill1109 wrote:I did not yet see Atiyah, Penrose and so on getting wildly excited about it.
That is thanks to you and your friends. You have been spooking them all (and indeed the whole community) out about anything I have to say.
gill1109 wrote:I do communicate occasionally with Klaas Landsman. He always thought I was crazy to have any interest whatsoever in your work. So we never discussed in further, together.
So apparently he had noticed it about the same time I had, drawn his own conclusions, and forgotten about it again.
Joy Christian wrote:I have published a 2D surface simulation of my 3-sphere model for the EPR-Bohm correlation: http://rpubs.com/jjc/16567.
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