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The Physics of Scale

In the early 1970's two fields of physics intersected in a set of techniques that have since been used to explore both the connections between the "fundamental" forces and to gain insight into character of "critical phenomena." These techniques entailed working out the relationship between phenomena at different scales. What follows is a thumb-nail sketch that will evolve through the collaborations hosted on the Physics of Scale web site.

One thread begins in the early 1930's. By then physicists were in no doubt about the need for theories that applied to quantum mechanical phenomena while obeying the constraints of special relativity. By the late 1940's it seemed that no such theory was mathematically tractable. Exact solutions were out of the question, and all attempts to achieve good approximations for phenomena involving photons and electrons led to equations involving infinities. Reformulating these approximations in such a way that the infinities could be isolated in a few parameters - a controversial trick - made calculations tractable and empirically verifiable. Many such reformulations proved to be possible. By the mid 1950's physicists had begun to exploit the resulting ambiguity to derive equations relating quantities such as the charge of the electron, measured at a given momentum, to its value as measured at another momentum, and - consequently - at another distance scale.

The second thread examines the attempts of physicists working in statistical mechanics in the late 1940's to collect examples of theoretical systems that they could solve by approximation or exactly, and the solutions of which differed in surprising ways from those derived with well established "classical" averaging techniques. These developments stimulated a wave of precise experiments and further theoretical work. By the mid 1960's it seemed that the collection of "non-classical" examples fell into distinct classes. Roughly speaking, the examples within each class had similar properties which were largely independent of the details of the short-range forces at work. That remained a mystery until the early 1970's when an explanation was offered using methods that related physical quantities at one scale to those at another scale.

Our goal for this project is to understand these two developments and their historical and conceptual relationship.