On Fri, Nov 29, 2024 at 10:55 PM smitra <[email protected]> wrote: > On 27-11-2024 04:48, Bruce Kellett wrote: > > >> So, basically the standard local hidden variables framework. > > > > Read a little more carefully. "Once all such factors have been taken > > into account .... > > the probabilities for a and b should factorize." > > They take into account hidden variables and then it should factorize. > They only generalize a bit, the theory does not need to be > deterministic, you have a probability distribution that then expresses > the correlations as an integral over the hidden variables, which is eq, > (3). > > > > If it were a hidden variable theory, then the probabilities for a and > > b would depend on those hidden variables, and that is what is > > explicitly ruled out. > > No, it's not ruled out, it expicitely depends on the probability > distribution over huidden variables. >
The inclusion of the factor lambda and integrating over it in the factorization of eqn. (3) is merely to take account of the possibility of hidden variables -- it does not imply that this is a hidden variable theory. > > > So Brunner is not using a hidden variable > > theory. > > It's a hidden variable theory, but not necessarily a classical > deterministic theory. > > The main point is that, even taking unknown joint causal > > factors into account, the probabilities at the remote ends factorize. > > In other words, what happens at A does not affect what happens at B, > > and vice versa. This is the notion of locality that they use to derive > > the CHSH inequality -- nothing to do with hidden variables. > Exactly. The fact that hidden variables and other unknowns are taken into account shows that the main result applies to any theory -- hidden variables or not. The main result is that any theory that satisfies the factorizability condition (3) cannot reproduce the quantum correlations. Since factorizability (3) is the condition for locality, it means that no local theory can reproduce the quantum correlations. The contrapositive of this is that any theory that gives the quantum correlations cannot satisfy the factorization condition, and hence must be non-local. In particular, it means that quantum mechanics itself is intrinsically non-local, since it gives the quantum correlations, but does not satisfy the factorizability condition. It's a hidden variable theory that's not equivalent to QM (when the > correlations factorize). Locality in these theories does not correspond > to locality in QM. > > > QM is what it is, it's a manifestly local theory when we use a local > Hamiltonian, but the theory is of a different structure than the class > of theories that correspond to our intuitions. Imposing locality in > those theories makes them unable account for correlations within QM, we > need to invoke non-local behaviors in these theories to be able to > reproduce QM. Does that mean that QM is non-local. No, because what we > did here was to replace QM by a different theory and then interpret QM > using that different theory. I don't think you have understood the basic logic of the contrapositive above. Quantum mechanics gives certain correlations. It has been proved that no theory satisfying the locality condition can reproduce those correlations. Therefore, QM is non-local. The proper conclusion should be that QM is > a fundamentally different theory than the class of theories in that > paper, so stochastic vatriants of classical deterministic theories don't > fit the bill either. > Rubbish. Bell's theorem applies to all theories, including quantum mechanics. At the end of the day entanglement is a real phenomenon that QM has no > problems describing via only local interactions. Unfortunately, you have routinely been unable to provide a local account of the quantum correlations. All you have ever done is repeat the claim that is in dispute, without providing any evidence that can undermine the proof provided by Bell's theorem. This then naturally > leads to a Many Worlds picture, because when measuring z-components of a > singlet state, if everything is manifestly local and Alice finds spin > up, how can Bob's result now been determined to be spin down, given than > if Bob's outcome is not pre-determined before Alcie found spin up (we > know this from Bell's theorem, you don't need a violation of a Bell's > inequality in a particular experiment to conclude this for any > particular experiment), unless the two possible outcomes for Bob both > physically exist? > That is what many-worlds theories maintain. Whenever Bob measures his particle from the entangled pair, he must get both possible outcomes, albeit in different branches. The problem many-worlds faces is coping with the copy of Bob that gets spin-up when Alice gets spin-up when they are both measuring particles from a singlet spin state. In fact, if you take this result further to the case where Alice and Bob both measure a sequence of N entangled pairs. Many-worlds states that there will be 2^N copies of Alice with all possible sequences of results, and also, 2^N copies of Bob with the same set of all possible result sequences. Many-worlds theory then has the problem of resolving how , when Alice and Bob meet (or exchange data sets), the correct correlations result every time. People who have faced this question have either resorted to magic (as Wallace does in his book), or invoke another interaction between Alice and Bob when they meet. The nature of this final interaction is never specified, nor is it clarified how this supposed interaction can account for the situation in which Alice and Bob never actually meet, but only email their respective results to some third party, who then calculates the correlation. The upshot, as far as I can see, is that many worlds cannot account for any correlation, much less correlations that violate the Bell inequalities. If you dispute that QM is local, then you still have a big problem, > because when measuring z-components of a singlet state, Alice measuring > spin up still means that Bob will find spin down, and you cannot point > to any known non-local interactions capable of explaining how Alice's > measurement instantaneously makes Bob's result physically determined. > So, your general opposition to a many worlds picture is far more your > own problem than it is for the proponents of such theories. The > proponents of MWI do face other problems, but non-locality isn't one of > them. > Non-local does not mean that there are specifiable interactions between the remote observers. If there were such interactions (FTL , say), then the theory would involve only local interactions. FTL interactions are just as local as any other interactions. Non-local means that the system depends on both x_1 and x_2, when x_1 and x_2 are at different locations (say, spacelike separated). Bruce -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRLoMkokUMzJd84XcOfYfdLSvWdEnOFhq0FZATaXnuVHg%40mail.gmail.com.
