SMuK 2023 – wissenschaftliches Programm

Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 10: Quantum Foundations Poster Session

AGPhil 10.1: Poster

Donnerstag, 23. März 2023, 16:15–16:45, JAN/0027

The Limits of the ℏ-Limit — •Renzo Kapust — Institute of Philosophy, KU Leuven

It is often thought that the limit of ℏ → 0 is a classical limit, meaning that it retrieves classical mechanics from quantum mechanics. Against this common belief, we argue that the ℏ-limit does not fully instantiate the relation between classical and quantum mechanics on its own and mostly serves anecdotal purposes.

Importantly, the conceptual analysis shows that "ℏ → 0" expresses two different limits, which also has practical consequences. Firstly, the "classical idealization" tries to map the set of quantum formulas to the set of classical formulas by changing the constant ℏ; pictorially imagining other possible worlds with different ℏ-values. Secondly, the "classical approximation" remains in this actual world and tries to map quantum explanations to classical phenomena by letting a variable grow relative to the actual value of ℏ.

The problems of the classical approximation include the failure to be a limit in any proper sense and to necessarily neglect important effects of quantum composition. Moreover, it does not fully include other parameters necessary to wholly retrieve classical mechanics. The problems of the classical idealization include implausible convergences, the danger of divergences, the failure to tackle ℏ-independent quantum phenomena as well as the failure to apply to all required equations. Consequently, although the investigation of the ℏ-limit bears great insight into the quantum-classical relation, neither of its senses fully instantiates it.