Bild Conception of Scientific Theory Structuring in Classical and Quantum Physics: From Hertz and Boltzmann to Schrödinger and De Broglie.

Abstract

We start with a 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 Schrödinger (and reviews of D'Agostino). Following Helmholtz, Hertz established the "Bild conception" 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 a 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 based on the price of acausality. CTM-OM interrelation can be tricky. Schrödinger used the Bild concept to create a 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). QM can be considered as a PCSFT image, but not as straightforward as in Bell's model with hidden variables. 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 the 1970s. The Bild approach is applied to the two-level CTM-OM modeling of Brownian motion: the overdamped regime corresponds to OM. In classical mechanics, CTM=OM; on the one hand, this is very convenient; on the other hand, this exceptional coincidence blurred the general CTM-OM structuring of scientific theories. We briefly discuss ontic-epistemic structuring of scientific theories (Primas-Atmanspacher) and its relation to the Bild concept. Interestingly, Atmanspacher as well as Hertz claim that even classical physical theories should be presented on the basic of two-level structuring.