Logical reformulation of quantum mechanics. III. Classical limit and irreversibility

Roland Omn�s

Mario Castagnino, Edgard Gunzig, Roberto Laura

G. C. Ghirardi

Raoul Bianchetti

Hilbert’s Sixth Problem asks for an axiomatization of physics, especially the probabilistic foundations of mechanics and the passage from microscopic dynamics to macroscopic laws. Despite foundational progress in probability theory and statistical mechanics, a persistent conceptual gap remains: probability appears as a primitive or as an epistemic tool, rather than as a quantity derived from the structure of physical evolution itself. This paper proposes a Viscous Time Theory (VTT) reformulation of Hilbert 6: physics is axiomatized by admissibility (what transformations can occur while preserving identity), coherence (the measurable structure of informational organization), and recoverability (which collapses are irreversible independent of observer perspective). We present a minimal axiomatic system in which (i) time emerges as informational viscosity, (ii) probability emerges as an induced measure over admissible trajectories, and (iii) the micro→macro transition becomes a geometric scaling limit of coherence fields rather than an ad hoc coarse-graining step. We do not claim a completed proof of Hilbert 6 in the classical sense. Instead, we provide a coherent, falsifiable program that reframes the target: the objective is not “derive probability from mechanics,” but “derive probability from the geometry of admissible informational evolution,” with classical mechanics and statistical mechanics emerging as distinct regime limits.

N. V. Lunin, Vladimir I Kogan

N. David Mermin

These are volumes II and III of Sir Karl Popper's hitherto unpublished Postscript to the Logic of Scientific Discovery. In addition to the Postscript itself, which was largely completed twenty years after L.S.D. in 1954, about a third of each volume is devoted to more recent writings. Volume II, The Open Universe , subtitled “An argument for Indeterminism”, has three “addenda”: a reprint of Popper's 1973 essay, “Indeterminism is not enough”, a revised version of his 1974 “Scientific Reduction and the essential incompleteness of all science”, and a brief essay, “Further remarks on reduction”, written in 1981. Volume III, Quantum Theory and the Schism in Physics , has a lengthy 1982 preface, and contains a revised and expanded version of Popper's 1967 “Quantum mechanics without the observer”. It was not Popper's original intent that the work should appear in separate volumes. Volume II, though primarily about classical physics, bears importantly on his views of the quantum theory, and further discussions of classical concepts (notably entropy and irreversibility) are in Volume III. I shall therefore discuss the two books as a single coherent work. (Volume I, Realism and the Aim of Science , was unavailable at the time this review was written.) Popper argues with wit, ingenuity, and passion, that the prevailing “Copenhagen” interpretation of the quantum theory is a mistake. Heisenberg, he says, “led a generation of physicists to accept the absurd view that one can learn from quantum mechanics that ‘objective reality has evaporated’” (III p. 9). According to Popper, there really are particles out there, not “wavicles”, and each particle has both a position and a momentum.