According to John Bell, if A is one of the two wings of a typical Bell apparatus, i the observable to be measured in A and x its possible value, and if B is the other of the two wings, j is the observable to be measured in B and y its possible value, and if Lambda is the hidden-variable joint state description of the composite (entangled) quantum system, we can write the following Bell factorisability condition p_A,B,Lambda (x,y|i,j) = p_A,Lambda (x|i) p_B,Lambda (y|j) which just means that the joint probability of outcomes x and y, for measurements of observables i and j, in the A and B wings, is equal to the product of the the separate probabilities. We know that so many experiments have shown the expression above is far from reality. In other words it is well known that this factorisability condition is violated by quantum mechanics (QM). Following Jarrett (and also Shimony, Howard, Cushing, Suppes, van Fraassen, and others) the Bell factorisability condition is equivalent to two independent conditions, Locality Condition p_A,Lambda (x|i,j) = p_A,Lambda (x|i) p_B,Lambda (y|i,j) = p_B,Lambda (y|j) Separability Condition p_A,Lambda (x|i,j,y) = p_A,Lambda (x|i,j) p_B,Lambda (y|i,j,x) = P_B,Lambda (y|i,j) where Locality is defined as: Given two systems A and B, space-like separated, the state of A cannot be influenced by events (measurements) on B, and viceversa. where Separability is defined as: Two systems, separated by some spatio-temporal interval, possess their own separate states, regardless of their previous history, and the joint state is completely determined by their own separate states. Eberhard, Page, Shimony, Ghirardi (et al.) have shown that QM only implies the violation of the Separability condition (the world is non-separable, there is wholeness, there is some tao in physics) . In other words it is possible to show (following Jarrett, Shimony, Ghirardi, Howard, Cushing, Eberhard, maybe van Fraassen, maybe Fine, etc.) that QM violates the Separability condition but does not violate the Locality condition. In physical terms the above means that QM does not allow faster than light (FTL) signaling (Eberhard, Nuovo Cimento, 46B, 1978, 392; Ghirardi et al., Found. Phys., 23, 1993, 341). It is possible to show (following Jarrett, Shimony, Ghirardi, Howard, Eberhard, Cushing, maybe van Fraassen, maybe Fine, etc.) that a “deterministic” theory (i.e. one in which the range of any probability distribution of outcomes is the set: 0 or 1) reproducing all the predictions of QM, does not violate the Separability Condition, but must violate the Locality Condition. In fact the Separability Condition means that ... p_A,Lambda (x|i,j,y) = p_A,Lambda (x|i,j) p_B,Lambda (y|i,j,x) = P_B,Lambda (y|i,j) so, if the specification of Lambda, i, j, in principle determines completely the outcomes x, y, then any additional conditioning on x or y is superfluous, having x and y just one value allowed, so they cannot affect the probability, which (in a deterministic theory) can take just the values 0 or 1. Thus a *deterministic* QM can not violate the Separability Condition and must violate the Locality Condition, which means ... faster than light (FTL) signaling.
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