Abstract
In the nineteenth century (in the process of transition from mechanics to the field theory), the German school of theoretical physics confronted problems similar to the basic problems in the foundations of quantum mechanics (QM). Hertz tried to resolve such problem through analysis of the notion of a scientific theory and interrelation of theory and experiment. This analysis led him to the Bild (image) conception of theory (which was later essentially developed, but also modified by Boltzmann). In this paper, we claim that to resolve the basic foundational problems of QM, one has to use the Bild conception and reject the observational viewpoint on physical theory. As an example of a Bild theory underlying QM (treated as an observational theory), we consider prequantum classical statistical field theory (PCSFT): theory of random subquantum fields.
Highlights
During one hundred years, quantum theory has been suffering of endless debates about its meaning and interpretation
Correspondence Between Prequantum Classical Statistical Field Theory and Quantum Mechanics In quantum mechanics (QM), states are given by density operators acting in complex Hilbert space H and physical variables are represented by Hermitian operators in H
The aim of this paper is to remind to the quantum foundational community studies of Hertz on the Bild conception of physical theory, especially Hertz analysis of connection between theory and experiment
Summary
Quantum theory has been suffering of endless debates about its meaning and interpretation. Or unconsciously, Bohr, Heisenberg, Einstein, Pauli, and other main contributors to foundations of quantum theory (but excluding Schrodinger, see, for example, D’Agostino 1992) ignored the historical lessons of the debate on the interrelation between theory and experiment which was initiated by transition from Newtonian mechanics to Maxwellian electromagnetism (Hertz 1899). In this debate, the problem of hidden variables was enlighten by Hertz—may the first time in history of science (Hertz 1899). I consider the present situation in quantum foundations by appealing to the Herzian Bild conception, section “Hertzian Viewpoint on Foundations of Quantum Mechanics.” In section “Correspondence Between Mathematical Formalisms of Theories of Different Types,” there are formulated rules of correspondence between two theories of different types (especially their mathematical structures). in section “Results: Correspondence Between Prequantum Classical Statistical Field Theory and Quantum Mechanics,” a theory of micro-phenomena based on the Bild conception is presented, prequantum classical statistical field theory (PCSFT); see Khrennikov (2007a, b, 2014, 2017c)
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