by gill1109 » Sun May 09, 2021 6:49 am
FrediFizzx wrote:gill1109 wrote:Sorry Fred, that was an illegitimate substitution which you just did. ...
How could it be illegitimate? Don't make nonsensical claims like that without backing it up. Are A and B equal to +1 or -1 or not? Of course they are. So their product is always going to be +1 or -1. The formulation produces nonsense just like I said. You have to figure out a way to keep the vectors a and b in the calculation while producing the +/-1's.
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Dear Fred
A and B are not identically equal to -1 or identically equal to +1. For given a and b their product still depends on lambda. As lambda varies, their product can take both values. Not at the same time. But for some lambda, their product can be +1. For other lambda, their product can be -1. There are no other possibilities.
For each a, b and lambda, A(a, lambda) equals +1 or it equals -1, and B(b, lambda) equals +1 or it equals -1.
Joy Christian does not have a counterexample to Bell’s theorem … because Bell’s theorem is a simple, true, theorem of elementary pure mathematics. Which can be proved in a myriad of different ways.
If you use the CHSH inequality to prove the theorem you don’t even need any calculus. Since there are only two a’s in the game and only two b’s, everything depends on a single list of 16 probabilities adding up to +1. Because (in obvious notation) there only 16 possible values of the quadruple (A1, A2, B1, B2). As lambda varies it takes values in the set {-1, +1}^4. That’s a set of 16 elements. It’s easy to show that A1 B1 - A1 B2 - A2 B1 - A2 B2 always equals -2 or +2. Its mean value therefore lies between -2 and +2 (inclusive).
Bell wrote that Bohr would not have been impressed by Bell’s theorem. Bohr did not subscribe to local realism.
[quote="FrediFizzx"][quote="gill1109"]
Sorry Fred, that was an illegitimate substitution which you just did. ...[/quote]
How could it be illegitimate? Don't make nonsensical claims like that without backing it up. Are A and B equal to +1 or -1 or not? Of course they are. So their product is always going to be +1 or -1. The formulation produces nonsense just like I said. You have to figure out a way to keep the vectors a and b in the calculation while producing the +/-1's.
.[/quote]
Dear Fred
A and B are not identically equal to -1 or identically equal to +1. For given a and b their product still depends on lambda. As lambda varies, their product can take both values. Not at the same time. But for some lambda, their product can be +1. For other lambda, their product can be -1. There are no other possibilities.
For each a, b and lambda, A(a, lambda) equals +1 or it equals -1, and B(b, lambda) equals +1 or it equals -1.
Joy Christian does not have a counterexample to Bell’s theorem … because Bell’s theorem is a simple, true, theorem of elementary pure mathematics. Which can be proved in a myriad of different ways.
If you use the CHSH inequality to prove the theorem you don’t even need any calculus. Since there are only two a’s in the game and only two b’s, everything depends on a single list of 16 probabilities adding up to +1. Because (in obvious notation) there only 16 possible values of the quadruple (A1, A2, B1, B2). As lambda varies it takes values in the set {-1, +1}^4. That’s a set of 16 elements. It’s easy to show that A1 B1 - A1 B2 - A2 B1 - A2 B2 always equals -2 or +2. Its mean value therefore lies between -2 and +2 (inclusive).
Bell wrote that Bohr would not have been impressed by Bell’s theorem. Bohr did not subscribe to local realism.
