Time and setting dependent instrument parameters and proofs of Bell-type inequalities

We have criticized in previous work [1]-[4] the various proofs of Bell-type inequalities as given in [5], [6]. Other authors have put forward related criticism of which we quote only some of the latest publications [7]-[9]. A very interesting discussion has developed during the last year [10]-[14]. In the present paper we concatenate our arguments into what we call “row” and “column” arguments. These arguments contain reasoning that is essential to any Bell-type proof. As we show, these arguments can not be completed when setting and time dependent instrument parameters are involved. This conclusion is obtained independently of our previous paper where we derive the quantum result [3]. We first review the parameter space introduced by Bell and our extension of this parameter space. We use a notation that is close to our previous papers [1]-[4]. However, for reasons of clarity we capitalize here all random variables and use the lower case for the values these random variables can assume. Bell’s [5] parameter random variables are essentially given by the functions Aa(Λ) = ±1, Bb(Λ) = ±1 that are related to the possible outcomes of spin measurements, with Λ being a parameter random variable that is related to information carried by the correlated particle pair that is sent out from a common source to two stations S1 and S2. We assume with Bell and others that the way Einstein-Podolsky-Rosen (EPR)experiments are performed guarantees that Λ is independent of the instrument settings a,b. The form of the experiment was proposed originally by Bohm and Hiley [15]. We extend this parameter space [1]-[4] by adding setting and time dependent instrument parameter random variables Λ∗ a,t specific to station S1 and Λ ∗∗ b,t to station S2. These variables may be stochastically independent of Λ. As an illustration, these variables Λ∗ a,t, Λ ∗∗ b,t can be