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Register a new userA Quantum Godelian Hunch
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Authors
Hippolyte Dourdent
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What if the paradoxical nature of quantum theory could find its source in some undecidability analog to that of Godels incompleteness theorem ? This essay aims at arguing for such Godelian hunch via two case studies. Firstly, using a narrative based on the Newcomb problem, the theological motivational origin of quantum contextuality is introduced in order to show how this result might be related to a Liar-like undecidability. A topological generalization of contextuality by Abramsky et al. in which the logical structure of quantum contextuality is compared with Liar cycles is also presented. Secondly, the measurement problem is analyzed as emerging from a logical error. A personal analysis of the related Wigners friend thought experiment and and a recent paradox by Frauchiger and Renner is presented, by introducing the notion of meta-contextuality as a Liar-like feature underlying the neo-Copenhagen interpretations of quantum theory. Finally, this quantum Godelian hunch opens a discussion of the paradoxical nature of quantum physics and the emergence of time itself from self-contradiction.
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Quantum weirdness has been in the news recently, thanks to an ingenious new experiment by a team led by Roland Hanson, at the Delft University of Technology. Much of the coverage presents the experiment as good (even conclusive) news for spooky action-at-a-distance, and bad news for local realism. We point out that this interpretation ignores an alternative, namely that the quantum world is retrocausal. We conjecture that this loophole is missed because it is confused for superdeterminism on one side, or action-at-a-distance itself on the other. We explain why it is different from these options, and why it has clear advantages, in both cases.
It is argued that the traditional realist methodology of physics, according to which human concepts, laws and theories can grasp the essence of reality, is incompatible with the most fruitful interpretation of quantum formalism. The proof rests on the violation by quantum mechanics of the foundational principles of that methodology. An alternative methodology, in which the construction of sciences finishes at the level of human experience, as standard quantum theory strongly suggests, is then conjectured.
In a recent paper, Rovelli responds to our critical assessment of Relational Quantum Mechanics (RQM). His main argument is that our assessment lacks merit, because we fail to understand, or cope with, the premises of his theory; instead, he argues, we judge his proposal, blinded by the preconceptions inherent to ``our camp. Here, we explicitly show that our assessment judges RQM on its own terms, together with the basic requirements of precision, clarity, logical soundness and empirical suitability. Under those circumstances, we prove false Rovellis claim that RQM provides a satisfactory, realistic, non-solipsistic description of the world. Moreover, his reply serves us to further exhibit the serious problems of the RQM proposal, as well as the failures of its author to understanding the basic conceptual difficulties of quantum theory.
In this letter, we point to three widely accepted challenges that the quantum theory, quantum information, and quantum foundations communities are currently facing: indeterminism, the semantics of conditional probabilities, and the spooky action at a distance. We argue that these issues are fundamentally rooted in conflations commonly made between causal dependencies, counterfactual dependencies, and statistical dependencies. We argue that a simple, albeit somewhat uncomfortable shift of viewpoint leads to a way out of the impossibility to extend the theory beyond indeterminism, and towards the possibility that sound extensions of quantum theory, possibly even deterministic yet not super-deterministic, will emerge in the future. The paradigm shift, which we present here, involves a non-trivial relaxation of the commonly accepted mathematical definition of free choice, leading to non-Nashian free choice, more care with the choice of probabilistic notations, and more rigorous use of vocabulary related to causality, counterfactuals, and correlations, which are three concepts of a fundamentally different nature.
I give a scientific perspective, with a personal emphasis, on the seminal 1992 paper, The quantum-state diffusion model applied to open systems, by Gisin and Percival.
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