On foundational thinking in fundamental physics, from Riemann to Einstein to Heisenberg

Abstract

This paper considers the nature of foundational thinking in fundamental physics, most especially in quantum mechanics. By “fundamental physics” I mean those areas of experimental and theoretical physics that deal with the ultimate constitution of nature, for example, as defined by the so-called elementary particles in the case of quantum physics. By “foundational thinking” I mean thinking that concerns fundamental physics itself. First, I argue, following Riemann, that our foundational thinking is based on hypotheses that we form and test. Second, I argue that foundational thinking in physics is defined by concepts, and that in modern physics foundational concepts always contains physical, mathematical, and philosophical components. Third, finally, I argue that the relationships between these components and, hence, our foundational thinking, are different in quantum mechanics than they are in classical physics and relativity. In these theories mathematics describes, by way of idealized models, physical reality, and predictions made by them are derived from these descriptions. By contrast, in quantum mechanics, mathematics only serves to predict the outcome of quantum experiments in the absence of any description, however idealized, of quantum objects and their behavior. At least such is the case in certain interpretations of quantum mechanics, which follow and develop Heisenberg's approach in his paper introducing quantum mechanics, as does, for example, Bohr's interpretation, known as complementarity.