2025/06/30 by Poletti, Marcello
#FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2507.00098
This work explores the connection between logical independence and the algebraic structure of quantum mechanics. Building on results by Brukner et al., it introduces the notion of onto-epistemic ignorance: situations in which the truth of a proposition is not deducible due to an objective breakdown in the phenomenal chain that transmits information from a system A to a system B, rather than to any subjective lack of knowledge. It is shown that, under such conditions, the probabilities accessible to a real observer are necessarily conditioned by decidability and obey a non-commutative algebra, formally equivalent to the fundamental postulates of quantum mechanics.