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There are two proofs:

One is the short proof that QM/QFT is not locally causal theories. You'll find that under the sections with titles like "Ordinary QM is not locally causal" in Bell's "The theory of local beables" and "La Nouvelle Cuisine". This proof does not assume hidden variables and only makes use of the local beables already present in, and indeed fundamental to, ordinary QM and QFT. Bohr called these the "classical terms".

The second proof shows that it is not possible to "complete" QM or QFT (or change it altogether) with additional hidden variables to avoid the conclusion of non-locality. This proof is where the Bell inequalities are derived and has one additional assumption often referred to as called "statistical independence". It states that it is possible by suitable experimental design to approximately satisfy {\lambda|a,b,c} = {\lambda|c}$\{\lambda|a,b,c\} = \{\lambda|c\}$, i.e. the hidden variables \lambda$\lambda$ relevant for the outcomes does not depend on how the future angles are set. For example, we could use a pseudo-number generator, binary digits of pi, or cosmic radiation, ... to set the angles.

The assumption of statistical independence appears implicitly and ubiquitously throughout scientific experiments. For example, it is assumed in every medical drug test with a placebo control group: the details of a patients medical condition (the equivalent of the \lambdas$\lambda$'s) is assumed not to depend on whether he/she got randomly picked (perhaps using a random number generator) for being part of the placebo control group.

There are two proofs:

One is the short proof that QM/QFT is not locally causal theories. You'll find that under the sections with titles like "Ordinary QM is not locally causal" in Bell's "The theory of local beables" and "La Nouvelle Cuisine". This proof does not assume hidden variables and only makes use of the local beables already present in, and indeed fundamental to, ordinary QM and QFT. Bohr called these the "classical terms".

The second proof shows that it is not possible to "complete" QM or QFT (or change it altogether) with additional hidden variables to avoid the conclusion of non-locality. This proof is where the Bell inequalities are derived and has one additional assumption often referred to as called "statistical independence". It states that it is possible by suitable experimental design to approximately satisfy {\lambda|a,b,c} = {\lambda|c}, i.e. the hidden variables \lambda relevant for the outcomes does not depend on how the future angles are set. For example, we could use a pseudo-number generator, binary digits of pi, or cosmic radiation, ... to set the angles.

The assumption of statistical independence appears implicitly and ubiquitously throughout scientific experiments. For example, it is assumed in every medical drug test with a placebo control group: the details of a patients medical condition (the equivalent of the \lambdas) is assumed not to depend on whether he/she got randomly picked (perhaps using a random number generator) for being part of the placebo control group.

There are two proofs:

One is the short proof that QM/QFT is not locally causal theories. You'll find that under the sections with titles like "Ordinary QM is not locally causal" in Bell's "The theory of local beables" and "La Nouvelle Cuisine". This proof does not assume hidden variables and only makes use of the local beables already present in, and indeed fundamental to, ordinary QM and QFT. Bohr called these the "classical terms".

The second proof shows that it is not possible to "complete" QM or QFT (or change it altogether) with additional hidden variables to avoid the conclusion of non-locality. This proof is where the Bell inequalities are derived and has one additional assumption often referred to as called "statistical independence". It states that it is possible by suitable experimental design to approximately satisfy $\{\lambda|a,b,c\} = \{\lambda|c\}$, i.e. the hidden variables $\lambda$ relevant for the outcomes does not depend on how the future angles are set. For example, we could use a pseudo-number generator, binary digits of pi, or cosmic radiation, ... to set the angles.

The assumption of statistical independence appears implicitly and ubiquitously throughout scientific experiments. For example, it is assumed in every medical drug test with a placebo control group: the details of a patients medical condition (the equivalent of the $\lambda$'s) is assumed not to depend on whether he/she got randomly picked (perhaps using a random number generator) for being part of the placebo control group.

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There are two proofs:

One is the short proof that QM/QFT is not locally causal theories. You'll find that under the sections with titles like "Ordinary QM is not locally causal" in Bell's "The theory of local beables" and "La Nouvelle Cuisine". This proof does not assume hidden variables and only makes use of the local beables already present in, and indeed fundamental to, ordinary QM and QFT. Bohr called these the "classical terms".

The second proof shows that it is not possible to "complete" QM or QFT (or change it altogether) with additional hidden variables to avoid the conclusion of non-locality. This proof is where the Bell inequalities are derived and has one additional assumption often referred to as called "statistical independence". It states that it is possible by suitable experimental design to approximately satisfy {\lambda|a,b,c} = {\lambda|c}, i.e. the hidden variables \lambda relevant for the outcomes does not depend on how the future angles are set. For example, we could use a pseudo-number generator, binary digits of pi, or cosmic radiation, ... to set the angles.

The assumption of statistical independence appears implicitly and ubiquitously throughout scientific experiments. For example, it is assumed in every medical drug test with a placebo control group: the details of a patients medical condition (the equivalent of the \lambdas) is assumed not to depend on whether he/she got randomly picked (perhaps using a random number generator) for being part of the placebo control group.