The Bild-conception for Scientific Theory Structuring in Classical and Quantum Physics: from Hertz and Boltzmann to Schr\"odinger and De Broglie

Abstract

We start with methodological analysis of the notion of scientific theory and its interrelation with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and Schr\"odinger (and reviews of D' Agostino). Following Helmholtz, Hertz established the "Bild concept" for scientific theories. Here "Bild" ("picture") carries the meaning "model" (mathematical). The main aim of natural sciences is construction of the causal theoretical models (CTMs) of natural phenomena. Hertz claimed that CTM cannot be designed solely on the basis of observational data; it typically contains hidden quantities. Experimental data can be described by an observational model (OM), often on the price of acausality. CTM-OM interrelation can be tricky. Schr\"odinger used the Bild concept to create CTM for quantum mechanics (QM) and QM was treated as OM. We follow him and suggest a special CTM for QM, so-called prequantum classical statistical field theory (PCSFT). The common interpretation of the violation of the Bell inequality is criticized from the perspective of the two level structuring of scientific theories. Such critical analysis of von Neumann and Bell no-go theorems for hidden variables was performed already by De Broglie (and Lochak) in 1970s. The Bild-approach is applied to the two level CTM-OM modeling of Brownian motion: the overdamped regime corresponds to OM. We briefly discuss ontic-epistemic structuring of scientific theories (Primas-Atmanspacher) and its relation to the Bild concept.