Spare the Rod: Relativity as Pure Chronometry

At the dawn of general relativity's golden age in the 1950s, Irish mathematician and physicist John Synge proposed to reduce spatial concepts to temporal concepts.

Synge argued that the structure of the spacetime metric allows one to define length in terms of time, a reduction of chronogeometry to what he calls pure chronometry. Synge's arresting proposal nevertheless has two problems. First, he retains an inadequate operationalist definition of durations in terms of "standard clocks." Second, his technical argument only defines infinitesimal length in terms of infinitesimal durations. In light of these criticisms, I defend a more moderate version of Synge's thesis and sketch a mathematical argument to establish it.