From the Pure to the Concrete
From the Pure to the Concrete
How Mathematics Yields Physical Information
This chapter addresses the question of whether and how mathematics, in and of itself, is capable of providing genuine physical information, where the latter is characterised as information about phenomena that could not (at the time) be furnished by physical hypotheses or models and emanates solely from a mathematical method or framework. The example considered focuses on the renormalisation group method and how, as a purely mathematical technique, it nevertheless appears able to provide us with information about the behaviour of a system at critical point—information that is simply not available using the resources of the relevant physical theory, often statistical mechanics or thermodynamics. Its explanatory role in treating critical point phenomena is highlighted, and an analysis is provided of what, exactly, is explained using these techniques, in particular the kind of ‘cooperative behaviour’ associated with phase transitions.
Keywords: renormalisation group, quantum field theory, statistical mechanics, mathematical explanation, critical point behaviour
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