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Nonlocality or Local Retrocausality? – The Non-signalling Theorem in Ontological Quantum Mechanics

Jan Walleczek Related
Physics 28/10/2017

How to interpret the non-signalling theorem in time-symmetric quantum ontologies, including those that posit retrocausal influences from the future? To answer that question, I will first explain how the non-signalling theorem is to be interpreted in strictly nonlocal quantum ontologies, including in de Broglie-Bohm (dBB) theory. The non-signalling theorem is thought to ensure the compatibility of quantum theory with special relativity by preventing the possibility of causal paradox. Crucially, for ontological quantum mechanics, any thorough analysis of the non-signalling constraint needs to distinguish between these three concepts: (1) causality and causal influence, (2) information and information transfer, and (3) signalling and message communication (see Walleczek and Grössing, 2016). Unfortunately, the standard literature on quantum foundations often conflates these concepts leading to false conclusions about the impossibility of dBB-theory and of quantum-causal ontologies in general. For example, the standard (axiomatic) interpretation of the non-signalling theorem is wholly incompatible with dBB-theory (e.g., Walleczek and Grössing, 2014, 2016). That is, the AXIOMATIC position on non-signalling denies the existence of any (local or nonlocal) causal influences, i.e., an axiomatic non-signalling theorem represents a general “NO-INFLUENCE” theorem (Walleczek and Grössing, 2014). Therefore, an EFFECTIVE non-signalling theorem must be adopted in the context of ontological quantum theories, including for dBB-theory. Importantly, EFFECTIVE non-signalling denies only the superluminal transmission of Shannon signals, while – at the same time – enables the transmission of non-Shannon signals between spacelike-separated locations in EPR-type experiments. For the definition of SHANNON SIGNALLING see Walleczek and Grössing (2016).

Furthermore, when assuming the FREE CHOICE of the experimenter agent, an axiomatic non-signalling theorem has often been employed in orthodox quantum interpretations as an argument against the possibility of determinism and realism in quantum mechanics, including dBB-theory. However, I have recently shown that this often-repeated argument is logically incoherent due to the fallacy of circular reasoning which is captured in the notion of SUPER-INDETERMINISM (see Walleczek, 2016).

Finally, is there any advantage of the (local) RETROCAUSAL interpretation over the strictly NONLOCAL interpretation in view of the compatibility issue between quantum and relativity theories? This presentation will apply insights from the prior analysis of the EFFECTIVE non-signalling theorem to recent proposals of retrocausal quantum ontologies, for which must be prohibited the possibility of RETRO-SIGNALLING (i.e., of message transfers from the future to the past) in order to prevent causal paradox.

Walleczek, J. and Grössing, G. (2016) Nonlocal Quantum Information Transfer Without Superluminal Signalling and Communication. Found. Phys. 46, 1208–1228.
Walleczek, J. and Grössing, G. (2014) The Non-signalling Theorem in Generalizations of Bell’s Theorem. J. Phys.: Conf. Ser. 504, 012001.
Walleczek, J. (2016) The Super-indeterminism in Orthodox Quantum Mechanics Does Not Implicate the Reality of Experimenter Free Will. J. Phys.: Conf. Ser. 701, 012005.

Funded in part by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.