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[According to the received view of the development of particle physics, mathematics, and more specifically group theory, provided the key which, between the late 1950s and the early 1960s, allowed scientists to achieve both a deeper physical understanding and an empirically successful modeling of particle phenomena. Indeed, a posteriori it has even been suggested that just by looking at diagrams of observed particle properties (see Fig. 1) one could have recognized in them the structures of specific groups (see Fig. 2). However, a closer look at theoretical practices of the 1950s and early 1960s reveals a tension between the employment of advanced mathematical tools and the “modeling” of observation, if the term “model” is understood as a construction allowing for the fitting and predicting of phenomena. As we shall see, the most empirically successful schemes, such as the “Gell-Mann and Nishijima model” or the “eightfold way”, were mathematically very simple, made no use of group-theoretical notions and for quite a time resisted all attempts to transform them into more refined mathematical constructs. Indeed, the theorists who proposed them had little or no interest in abstract approaches to mathematical practice. On the other hand, there were a number of particle theorists who did care about and employ group-theoretical notions, yet not primarily as tools to fit phenomena, but rather as a guide to uncover the fundamental principles of particle interactions. Moreover, these theorists did not regard all groups as epistemically equivalent, and instead clearly preferred those transformations related to space-time invariances over all others. These authors also often made a distinction between purely descriptive “models” and the “theories” they were (unsuccessfully) trying to build and which in their opinion would provide a deeper understanding of nature. Nonetheless, they expected their “theories”, too, to be empirically successful in describing observation, and thus to also function as “models”. In this sense, like their less mathematically-inclined colleagues, they also saw no clear-cut distinction between “modeling” and “theorizing” particle phenomena. In my paper I will discuss the development of these theoretical practices between the 1950s and the early 1960s as examples of the complex relationship between mathematics and the conceptualization of physical phenomena, arguing that, at least in this case, no general statements are possible on the relationship of mathematics and models. At that time, very different mathematical practices coexisted and the epistemic attitudes of physicists towards theoretical constructs could depend both on the assumptions and goals of the individual authors and on the specific mathematical methods and concepts linked to the constructs.]
Published: Aug 9, 2022
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