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.