Once Before Time - Martin Bojowald [48]
Rovelli and Smolin’s work was possible only thanks to a reformulation of general relativity undertaken by Abhay Ashtekar in 1986. Ashtekar is a mathematical physicist, an analyst equipped with technical brilliance and unparalleled mastery of the dark art of scientific power play. Senior to Rovelli and Smolin, he quite naturally saw the leadership role fall into his hands. And he seized it. It helped that his earlier work in mathematical relativity had endowed him with significant stature in the field (as well as personal force). Now he summoned a powerful gang of several younger postdocs to work out the required mathematics in all its details.3 The result was a form of geometry similar to what underlies general relativity, but suitable for discrete and atomic space-times: a new type of mathematics combining that of general relativity and quantum mechanics. In just a few years a beautiful, striking framework was forged, a beacon that later attracted many researchers and students entering their research careers (including me).
The postdocs moved on to form their own projects in different coalitions. Especially important for the development of the field was the work by Thomas Thiemann, a mathematical physicist like Ashtekar, but a constructive rather than an analytic one. His specialty is not the detailed analysis of existing mathematics, but contrived constructions of new objects. He was still a student in Aachen, Germany, at the time when loops were introduced, graduating in 1993 (a student of Hans Kastrup, who would later become my Ph.D. adviser). After his initial collaboration with Ashtekar, Thiemann started to work on “transforms on spaces of connections.” It is not important to explain here exactly what that means; suffice it to say that it can warm the heart only of a true mathematician. But for Thiemann, this was the way to destiny. In the process, he discovered several identities that, as he realized in 1996, could be used to make the dynamic laws formulated by Rovelli and Smolin much more solid and specific.4 With this contribution, loop quantum gravity had achieved its characteristic, though still unfinished, shape.
It is interesting that the early years of loop quantum gravity were shaped by representatives of the four main types of theoretical physicists, realized in almost pure forms: The thrill-seeking phenomenal physicist who dares the wildest suggestions; he wanders through nature with powerful strides, and wears the label “crazy” with pride; by virtue more often mistaken than right, he must be constrained by all the other types. The philosopher-physicist who, focusing on the concepts, provides a solid footing for a physical theory, but may have a tendency to be impractical. The mathematical analyst who at his humble best advances and crystallizes the laws underlying a physical theory, but at his greedy worst may take known results and resell them refurbished as his own. And the mathematical constructor who endures long and tedious advances but can also indulge in convoluted detours on which he can lose track of the physics involved.
All these different types are needed to develop intuitive insights from the physical side and subject them to strict mathematical analysis for checks and balances. Despite the small number of researchers, loop quantum gravity’s early