On Monday, December 16, 2024 at 10:20:51 PM UTC-7 Bruce Kellett wrote:
On Tue, Dec 17, 2024 at 3:11 PM Alan Grayson <[email protected]> wrote: On Saturday, December 14, 2024 at 5:56:21 AM UTC-7 John Clark wrote: On Sat, Dec 14, 2024 at 4:13 AM Alan Grayson <[email protected]> wrote: *> If local realism is falsified by Bell experiments, does that mean non-locality is affirmed?* *No.* *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* Is this the general consensus in the physics community, or is there none. Is this just your opinion? AG Clark is quite wrong about this. Neither realism nor determinism have anything to do with Bell's theorem. The theorem is entirely and exclusively about locality. This is spelled out fairly clearly in the review paper by Brunner *at al*. (arxiv.org/abs/1303.2849) If we assume locality, Bell's theorem states that certain inequalities must be satisfied. Quantum mechanics violates those inequalities. Therefore, quantum mechanics, in any interpretation, is non-local. The proof is fairly straightforward. Informally, locality means that if we have two disjoint points, A and B, separated by some distance , either spacelike or timelike, then what happens at point A cannot affect what happens at point B, and what happens at point B cannot affect what happens at point A. This informal notion can be formalized by saying that the joint probability for outcomes a at point A , and b at point B, must factorize, so that the joint probability can be written as a product of two terms, one dependent only on factors local to point A, and the other dependent only on factors local to point B: Pr(a,b) = p(a)*p(b), once all common causal factors have been taken into account. We then consider the expression S = <a0b0> + <a0b1> + <a1b0> - <a1b1> for measurement settings 0 and 1 and outcomes a,b in the range (-1, +1). If the joint probabilities all satisfy the factorization condition associated with the locality decomposition, we then have that S = <a0b0> + <a0b1> + <a1b0> - <a1b1> <= 2. This is the Clauser-Horne-Shimony-Holt (CHSH) inequality. The details on the proof of this inequality, under the assumption of locality, is given in the Brunner *et al.* reference above. This inequality depends only on the assumption of locality as implemented in the factorizabitity condition. It is easily shown that quantum mechanical correlations violate this inequality: S = 2sqrt(2) > 2. The conclusion is that quantum mechanics itself, in any interpretation or model, is non-local. This conclusion does not depend on any assumptions about realism or determinism. I see that Russell Standish has a recent post that also states that Bell's theorem depends on assumptions of Realism and Determinism. Russell is just as wrong about this as is John Clark. Bell's theorem depends only on the assumption of locality, as proved above. Bruce Thank you. That's what I thought. AG -- 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/18969d91-c323-464c-a154-02c2a3dc3df6n%40googlegroups.com.
