[Paper Review] Reply to Norsen's paper "Are there really two different Bell's theorems?"

Howard M. Wiseman, Eleanor Rieffel|arXiv (Cornell University)|Mar 24, 2015

Quantum Mechanics and Applications14 references3 citations

TL;DR

This paper defends the existence of two distinct Bell's theorems: Bell’s 1964 theorem, which assumes locality and determinism, and his 1976 theorem, which assumes local causality. The authors argue that operationalists and realists legitimately use 'Bell’s theorem' to refer to different results, and they refute Norsen’s claim that the 1964 theorem is merely a precursor to the 1976 version, emphasizing that the 1964 formulation remains valid and meaningful for quantum foundations and quantum information science.

ABSTRACT

Yes. That is my polemical reply to the titular question in Travis Norsen's self-styled "polemical response to Howard Wiseman's recent paper." Less polemically, I am pleased to see that on two of my positions --- that Bell's 1964 theorem is different from Bell's 1976 theorem, and that the former does not include Bell's one-paragraph heuristic presentation of the EPR argument --- Norsen has made significant concessions. In his response, Norsen admits that "Bell's recapitulation of the EPR argument in [the relevant] paragraph leaves something to be desired," that it "disappoints" and is "problematic". Moreover, Norsen makes other statements that imply, on the face of it, that he should have no objections to the title of my recent paper ("The Two Bell's Theorems of John Bell"). My principle aim in writing that paper was to try to bridge the gap between two interpretational camps, whom I call 'operationalists' and 'realists', by pointing out that they use the phrase "Bell's theorem" to mean different things: his 1964 theorem (assuming locality and determinism) and his 1976 theorem (assuming local causality), respectively. Thus, it is heartening that at least one person from one side has taken one step on my bridge. That said, there are several issues of contention with Norsen, which we (the two authors) address after discussing the extent of our agreement with Norsen. The most significant issues are: the indefiniteness of the word 'locality' prior to 1964; and the assumptions Einstein made in the paper quoted by Bell in 1964 and their relation to Bell's theorem.

Motivation & Objective

• To resolve a longstanding interpretational divide between operationalists and realists in quantum foundations by clarifying that 'Bell’s theorem' refers to two distinct results.
• To challenge Norsen’s claim that Bell’s 1964 paper derives determinism from locality, arguing instead that the EPR paragraph in Bell’s 1964 paper is flawed and insufficient to support such a derivation.
• To demonstrate that the term 'locality' was not unambiguously defined before 1964, and that Einstein’s 1949 notion of 'no-telepathy' differs from Bell’s later 'local causality'.
• To show that operationalists can reasonably accept Bell’s 1964 theorem as a meaningful result, even if it does not assume local causality, by preserving a notion of locality compatible with relativity.
• To argue that redefining Bell’s 1964 result as equivalent to the 1976 theorem would diminish its significance for operationalist quantum information theory and wrongly obscure its foundational value.

Proposed method

• Analyzes Bell’s 1964 paper, particularly the 'Formulation' section and the EPR paragraph, to show that it does not logically derive determinism from locality.
• Contrasts Bell’s 1964 notion of 'locality' with his 1976 concept of 'local causality', arguing that they are not equivalent and were not intended as such by Bell.
• Examines Einstein’s 1949 scientific autobiographical notes to clarify his 'no-telepathy' principle and show it is distinct from Bell’s later assumptions.
• Reviews the historical usage of 'locality' in physics literature to argue that its meaning was ambiguous before 1964, undermining Norsen’s claim of a single, consistent definition.
• Engages in a comparative analysis of operationalist and realist interpretations of quantum mechanics, showing that both camps have coherent reasons to prefer different formulations of Bell’s theorem.
• Uses rhetorical and logical critique to challenge Norsen’s interpretation of Bell’s later statements, arguing that Bell’s later self-revision does not invalidate the 1964 theorem as a standalone result.

Experimental results

Research questions

• RQ1 Are Bell’s 1964 and 1976 theorems logically and conceptually distinct, or is the 1964 result merely a precursor to the 1976 theorem?
• RQ2 Does Bell’s EPR paragraph in the 1964 paper successfully derive determinism from locality, as Norsen claims?
• RQ3 What is the historical and conceptual status of the term 'locality' before 1964, and does it support Norsen’s claim that it is synonymous with 'local causality'?
• RQ4 How do Einstein’s 1949 views on 'no-telepathy' relate to Bell’s 1964 and 1976 notions of locality, and are they compatible with the operationalist interpretation?
• RQ5 Would redefining Bell’s 1964 theorem as equivalent to the 1976 theorem diminish its relevance for operationalist quantum information theory and foundational physics?

Key findings

• The EPR paragraph in Bell’s 1964 paper fails to derive determinism from locality, as Norsen claims, and is instead 'problematic' and 'disappointing' in its logical structure.
• Bell’s 1964 notion of 'locality' is not equivalent to his 1976 concept of 'local causality', and the term 'locality' was not unambiguously defined before 1964.
• Einstein’s 1949 'no-telepathy' principle is distinct from Bell’s later assumptions and does not imply the same constraints as local causality.
• Operationalists can reasonably accept Bell’s 1964 theorem as a valid and meaningful result, even without assuming determinism, because it preserves a notion of locality compatible with relativity.
• The claim that Bell’s 1964 theorem rests on a single assumption (locality) is incorrect; it actually relies on two independent assumptions: locality and determinism.
• Redefining the 1964 theorem as equivalent to the 1976 theorem would obscure its foundational significance for operationalist quantum foundations and quantum information theory, potentially denying Bell proper credit for a result widely accepted in that community.