Employing NTC and NSC theorems, we report that effective, instead of axiomatic, non-signalling is entirely sufficient for prohibiting nonlocal communication. We find that an effective non-signalling theorem represents two sub-theorems: (1) Non-transfer-control (NTC) theorem, and (2) Non-signification-control (NSC) theorem. In search of a decisive communication-theoretic criterion for differentiating between “axiomatic” and “effective” non-signalling, we employ the operational framework offered by Shannon’s mathematical theory of communication, whereby we distinguish between Shannon signals and non-Shannon signals. By contrast, associated with orthodox quantum mechanics is the foundational position referred to here as “axiomatic non-signalling”. This position we refer to as “effective non-signalling”. Concerning Bell’s theorem, we argue that Bell employed both interpretations, and that he finally adopted the operational position which is associated often with ontological quantum theory, e.g., de Broglie–Bohm theory.
However, as a ‘no-go’ theorem there exist two opposing interpretations of the non-signalling constraint: foundational and operational.
However, does the presence of hidden superluminal influences automatically imply superluminal signalling and communication? The non-signalling theorem mediates the apparent conflict between quantum mechanics and the theory of special relativity. It is a frequent assumption that-via superluminal information transfers-superluminal signals capable of enabling communication are necessarily exchanged in any quantum theory that posits hidden superluminal influences.
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