Joy Christian wrote:.
Are you trying to spam the forum? You already started a thread on this paper just a few days ago. Or are you becoming forgetful in your old age?
gill1109 wrote:Joy Christian wrote:.
Are you trying to spam the forum? You already started a thread on this paper just a few days ago. Or are you becoming forgetful in your old age?
I forget lots of things. It means I can keep re-watching old movies.
I wanted to discuss this paper again since I’m beginning to understand what these folk are doing. There was a lot of discussion about it on FaceBook today and quite a few people got pretty upset. It’s intriguing. I’m hoping someone here can explain “invariant set theory” for me. But I also think there is a fundamental misunderstanding of Bell’s theorem in the paper. So I do have some new “news” on the subject. Maybe tomorrow.
Justo wrote:gill1109 wrote:Joy Christian wrote:.
Are you trying to spam the forum? You already started a thread on this paper just a few days ago. Or are you becoming forgetful in your old age?
I forget lots of things. It means I can keep re-watching old movies.
I wanted to discuss this paper again since I’m beginning to understand what these folk are doing. There was a lot of discussion about it on FaceBook today and quite a few people got pretty upset. It’s intriguing. I’m hoping someone here can explain “invariant set theory” for me. But I also think there is a fundamental misunderstanding of Bell’s theorem in the paper. So I do have some new “news” on the subject. Maybe tomorrow.
Richard, I know you have made important contributions to the field. That is really surprising given that you do not understand the very easy physical principles underlying the inequality. I guess that shows the power of mathematics.
I am sure you can still contribute to the field if you just recognize you were mistaken about those physical principles instead of stubbornly insisting on nonsense. I guess that is the c***pot side of you that is betraying you.
gill1109 wrote:Their text is fascinating: "Measure theory is not usually discussed in physics textbooks. However, a variety of measures make their appearance in physics nevertheless. The most widely used one is the Lebesgue measure on R^n and (pseudo-)Riemannian manifolds. On fractals it can be generalised to the Hausdorff measure. In the context of Hamiltonian dynamical systems, a non-trivial measure on state-space arises in the theory of symplectic manifolds (leading, for example, to the Gromov non-squeezing theorem). In Section IV A, we discuss non-trivial invariant measures associated with chaotic attractors. The measure of "script S_math" appears in the calculation of any expectation value and therefore should enter the derivation of Bell’s theorem together with the probability-distribution ρ. Since these two functions always appear together, it is tempting to simply combine them into one ρ_Bell(λ, X) := ρ(λ, X)µ(λ, X), where we use the index “Bell” to emphasise that this is the quantity that really enters Bell’s theorem."
Yes! It is indeed te quantity that really enters into Bell's theorem. It is not only tempting, but it is also necessary!!!! Bell even said himself that really they should be combined, he was just using lazy physicists' (who don't know measure theory) common notation!!!! Bell allows any fancy state-space too. Explicitly. "lambda" doesn't have to be localized anywhere. It can be as weird and abstract as you like. Bell has said all these things 40 years ago but it seems that many contrary minds only read his first one or two papers and then stop reading, because they are already sure he is wrong, because they did not understand what they read, because they are entrapped in old-fashioned ways of thinking and using inadequate notations and unaware of the progress of mathematics in the last one hundred years. Kolmogorov made probability into a serious part of mainstream hard-core mathematics in 1933. He needed Western catch to renovate his dacha so he published his little book in German thereby answering one of Hilbert's problems. He could do this thanks to the Radon-Nikodym theorem which allowed him to put conditional probability firmly into mathematics, too. Borel and Lebesgue and others had already done a great deal, thirty years before that, but the Radon-Nikodym theorem allowed Kolmogorov's breakthrough.
Notice that their terminology Is wrong. Bell's rho is not a probability distribution, it is a probability density.
gill1109 wrote:Perhaps you have a different notion of “random variable” to me. For me, it is a measurable function from a probability space (Omega, F, P) to the real line endowed with the Borel sigma algebra. It’s a mathematical object in a mathematical model.
I think physicists confuse mathematical models of reality with reality itself, since they already use mathematics to describe reality. Statisticians know “all models are wrong, some are useful”. Poor physicists… Then there are the poor philisophers who are mostly discussing words.
Justo wrote:There is no way out of the irrelevance of the CFD assumption because even assuming it makes sense, you can completely ignore it and derive the inequality from physically meaningful assumptions, i.e., Local Causality(LC) and Statistical Independence(SI). The issue is so simple that even someone like me who does not know probability theory can do it. All you need to know is the intuitive meaning of probability as a relative frequency.
Since Bell left all these trivialities implicit because he concentrated on the important points, I give a detailed explanation of how LC and SI naturally describe the Bell experiment without introducing metaphysics.
All you need is to count events, record them, and evaluate relative frequencies. That explains why the results of four different sets of experiments can be reduced under the same sum with equal hidden variables.
If you say I am wrong then I guess you would agree with @minkwe. Basically, he says that I am wrong about the following: let us assume we have a great number of cards with 16 different values 1,2,...16 (for the sake of simplicity let us say the number of cards with different values is the same) My claim is that when you extract (with replacement) one card more than 16 times the values you choose will necessarily start to repeat and if you calculate the relative frequency of each extracted value after a great number of trials, the relative frequency of each extracted number should be approximately 1/16.
Austin Fearnley wrote:Hi Justo
No, I do not claim to have a counter example to Bell's Theorem (though the use of 'counter example' seems vague to me). If I had, I would have tried to claim Richard's prize money (the forum thread for that prize money is now on the second page of this site). I discussed my retrocausal method with Richard on that 'prize' thread. I never intended to make a claim and only used that thread as it was convenient for me at the time. I can get the 0.707 correlation using retrocausality but my model bypasses the Bell Inequalities and does not break them. Clearly the use of retrocausality is, quite understandably, not likely to persuade Richard to empty his pockets ... even of loose change. But IMO retrocausality is what is happening in real experiments.
Likewise I do not believe that superdeterminism can break the Bell inequalities. It may be able to get the 0.707 correlation, though I have not seen evidence of that. But IMO it will need to bypass the Bell Inequalities by using unfair sampling of particle LHVs. On the other hand the universe should determine what a fair sampling is, and if the universe is not providing a random allocation of possible LHV values, then who can say that a simulation is not using a fair sample? AFAIK there are no computer simulations offered for superdeterminism?
The paper by Eugen (aka Esail) is discussed on a nearby thread and I have already made comments there although not on the recent pages. I also have the opinion that Esail uses non-local formulae.
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