Joy Christian wrote:Let R, S, T, and U be Hermitian operators whose eigenvalues are r = AB, s = AB', t = A'B, and u = A'B', where A, B, A', and B' = +1 or -1 are the measurement results observed by Alice and Bob. Now, in the proof of Bell's "theorem," it is assumed that the sum of the individual eigenvalues, (r + s + t - u), is an eigenvalue of the sum (R + S + T - U) of the corresponding operators. Without this assumption, the stringent bounds of -2 and +2 on the CHSH correlator cannot be derived. But this assumption is simply false. No such correspondence between the Hermitian operator (R + S + T - U) and the sum (r + s + t - u) of individual eigenvalues exists mathematically.
gill1109 wrote:Joy Christian wrote:Let R, S, T, and U be Hermitian operators whose eigenvalues are r = AB, s = AB', t = A'B, and u = A'B', where A, B, A', and B' = +1 or -1 are the measurement results observed by Alice and Bob. Now, in the proof of Bell's "theorem," it is assumed that the sum of the individual eigenvalues, (r + s + t - u), is an eigenvalue of the sum (R + S + T - U) of the corresponding operators. Without this assumption, the stringent bounds of -2 and +2 on the CHSH correlator cannot be derived. But this assumption is simply false. No such correspondence between the Hermitian operator (R + S + T - U) and the sum (r + s + t - u) of individual eigenvalues exists mathematically.
Bell, working within a mathematical framework satisfying a property called Local Realism, does *not* assume any correspondence between measurements and Hermitian operators. Quantum mechanics *does* make such an assumption. You are explaining, correctly, why QM can violate Bell inequalities.
Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.
In the real world, Bell's inequalities can be violated. So QM is a viable description of the real world, LR isn't.
gill1109 wrote:
Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.
Joy Christian wrote:gill1109 wrote:
Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.
But that assumption is manifestly wrong for any EPR-Bohm type experiment. The observables R, S, T, and U do not commute in such experiments. That is the Achilles heel of Bell's theorem.
Joy Christian wrote:Joy Christian wrote:gill1109 wrote:Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.
But that assumption is manifestly wrong for any EPR-Bohm type experiment. The observables R, S, T, and U do not commute in such experiments. That is the Achilles heel of Bell's theorem.
The spin operators R, S, T, and U do not commute in the EPRB experiments. This is a fact. But suppose one denies this fact. Suppose one insists --- just to be difficult --- that R, S, T, and U are commuting operators in the EPRB experiments. But in that case, even quantum mechanics predicts the bounds of -2 and +2 on the CHSH correlator: By definition, we have R = AB, S = AB', T = A'B, and U = A'B'. Then the CHSH operator is simply CHSH = \sqrt{ 4 + [ A, A' ] [ B', B ] }, which reduces to +\-2 if R, S, T, and U are commuting.
gill1109 wrote:
Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.
gill1109 wrote:
The spin operators R, S, T, and U do not commute in EPR-B experiments, *if* you assume Bohm's conventional QM model of those experiments. If you start by assuming the absolute reality of the QM description of the world, then the case of commuting operators is a special case, and within that special case, you can use QM to derive the CHSH inequality.
gill1109 wrote:
By the way, Jeffrey Bub has published a paper entitled "Is Von Neumann’s “No Hidden Variables” Proof Silly?"
He argues very carefully (and takes 15 pages to do this) that Bell (and others) misunderstood von Neumann's argument, which, he argues, is a whole lot more subtle than superficially appears.
Bub, J. (2011). Is Von Neumann's “No Hidden Variables” Proof Silly? In H. Halvorson (Ed.), Deep Beauty: Understanding the Quantum World through Mathematical Innovation (pp. 393-408). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511976971.012
Joy Christian wrote:gill1109 wrote:By the way, Jeffrey Bub has published a paper entitled "Is Von Neumann’s “No Hidden Variables” Proof Silly?"He argues very carefully (and takes 15 pages to do this) that Bell (and others) misunderstood von Neumann's argument, which, he argues, is a whole lot more subtle than superficially appears.
Bub, J. (2011). Is Von Neumann's “No Hidden Variables” Proof Silly? In H. Halvorson (Ed.), Deep Beauty: Understanding the Quantum World through Mathematical Innovation (pp. 393-408). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511976971.012
I know Jeff Bub very well. A student of David Bohm. We were together at the Perimeter Institute and I also visited him at the University of Western Ontario when he was a professor there. Unfortunately, in recent years Jeff has become a firm believer in quantum information theory and also a firm believer in Bell's fallacious theorem. So he has his own reasons for arguing what he is arguing in the paper you have linked. No one in the foundations of quantum mechanics is persuaded by his argument. In fact, it has been thoroughly debunked by David Mermin and Rudiger Schack in this fine paper: https://link.springer.com/article/10.10 ... 018-0197-5. So, nice try, but you will not be able to save Bell's "theorem" by invoking Jeff Bub's argument.
SOME LOCAL MODELS FOR CORRELATION EXPERIMENTS
ABSTRACT. This paper constructs two classes of models for the quantum correlation experiments used to test the Bell-type inequalities, synchronization models and prism models. Both classes employ deterministic hidden variables, satisfy the causal requirements of physical locality, and yield precisely the quantum mechanical statistics. In the synchronization models, the joint probabilities, for each emission, do not factor in the manner of stochastic independence, showing that such factorizability is not required for locality. In the prism models, the observables are not random variables over a common space; hence these models throw into question the entire random variables idiom of the literature. Both classes of models appear to be testable.
Joy Christian wrote:gill1109 wrote:
Bell's assumption of local realism (LR) corresponds to the assumption that the operators R, S, T and U commute. In that case, the correspondence you just mentioned would hold true, and Bell's inequalities would hold.gill1109 wrote:
The spin operators R, S, T, and U do not commute in EPR-B experiments, *if* you assume Bohm's conventional QM model of those experiments. If you start by assuming the absolute reality of the QM description of the world, then the case of commuting operators is a special case, and within that special case, you can use QM to derive the CHSH inequality.
You are not going to escape the inescapable by making contradictory statements. Bohm's conventional quantum model is the only model for the EPRB experiment universally accepted by the physics community. So we agree that R, S, T, and U do not commute in those experiments. It is then inescapable that (r + s + t - u) is not an eigenvalue of the operator (R + S + T - U). But assuming that (r + s + t - u) is an eigenvalue of the operator (R + S + T - U) is necessary for deriving the bounds of -2 and +2 on the CHSH correlator. In other words, assuming something patently wrong is necessary for deriving the conclusion of Bell's theorem.
Reviewer # 2 wrote:
This paper attempts to disprove Bell’s theorem, one of the fundamental results of quantum mechanics. Bell’s theorem cannot be disproved, just like, e.g., Pythagorean theorem. In fact, the proof of Bell’s theorem is simple and straightforward. The theorem imposes restrictions (inequalities) on the correlations functions under assumptions of local realism and the existence of hidden variables. Numerous experiments done in the past thirty or so years show clearly that quantum systems violate Bell’s inequalities, thus violating at least one of the assumptions of Bell's theorem. Therefore, I cannot recommend this paper for publication.
Joy Christian wrote:You are not going to escape the inescapable by making contradictory statements.
Joy Christian wrote:Bohm's conventional quantum model is the only model for the EPRB experiment universally accepted by the physics community. So we agree that R, S, T, and U do not commute in those experiments. It is then inescapable that (r + s + t - u) is not an eigenvalue of the operator (R + S + T - U).
Joy Christian wrote:But assuming that (r + s + t - u) is an eigenvalue of the operator (R + S + T - U) is necessary for deriving the bounds of -2 and +2 on the CHSH correlator. In other words, assuming something patently wrong is necessary for deriving the conclusion of Bell's theorem.
Joy Christian wrote:I hear that John S. Bell has been beatified by the church of Quantum Fraudation and it is only a matter of time before he will be declared a saint --- Saint John of nonlocality and nonreality.
Joy Christian wrote:***
[...]
But in the Bell-test experiments the operators R, S, T, and U do not commute with each other because they correspond to different detections made at mutually exclusive measurement directions. [...]
Heinera wrote:Joy Christian wrote:***
[...]
But in the Bell-test experiments the operators R, S, T, and U do not commute with each other because they correspond to different detections made at mutually exclusive measurement directions. [...]
Well, they do commute in a macroscopic experiment with colorful exploding balls.
Joy Christian wrote:Heinera wrote:Joy Christian wrote:***
[...]
But in the Bell-test experiments the operators R, S, T, and U do not commute with each other because they correspond to different detections made at mutually exclusive measurement directions. [...]
Well, they do commute in a macroscopic experiment with colorful exploding balls.
That kind of deflection is not going to help the Bell-believers. It would be much more honest and dignified to recognize the silly mistake Bell and his followers have made and apologize to the physics community for misleading them for over fifty years.
***
Return to Sci.Physics.Foundations
Users browsing this forum: No registered users and 90 guests