“Astonishing successes” and “bitter disappointment”: The specific heat of hydrogen in quantum theory

The specific heat of hydrogen gas at low temperatures was first measured in 1912 by Arnold Eucken in Walther Nernst’s laboratory in Berlin, and provided one of the earliest experimental supports for the new quantum theory. Even earlier, Nernst had developed a quantum theory of rotating diatomic gas molecules that figured in the discussions at the first Solvay conference in late 1911. Between 1913 and 1925, Albert Einstein, Paul Ehrenfest, Max Planck, Fritz Reiche, and Erwin Schrödinger, among many others, attempted theoretical descriptions of the rotational specific heat of hydrogen, with only limited success. Quantum theory also was central to the study of molecular spectra, where initially it was more successful. Moreover, the two problems interacted in sometimes surprising ways. Not until 1927, following Werner Heisenberg’s discovery of the behavior of indistinguishable particles in modern quantum mechanics, did American theorist David Dennison find a successful theory of the specific heat of hydrogen

Hierarchical Growth: Basic and Applied Research

We develop a model that incorporates salient features of growth in modern economies. We combine the expanding-variety growth model through horizontal innovations with a hierarchy of basic and applied research. The former extends the knowledge base, while the latter commercializes it. Two-way spillovers reinforce the productivity of research in each sector. We establish the existence of balanced growth paths. Along such paths the stock of ideas and the stock of commercialized blueprints for intermediate goods grow with the same rate. Basic research is a necessary and sufficient condition for economic growth. We show that there can be two different facets of growth in the economy. First, growth may be entirely shaped by investments in basic research if applied research operates at the knowledge frontier. Second, long-run growth may be shaped by both basic and applied research and growth can be further stimulated by research subsidies. We illustrate different types of growth processes by examples and polar cases when only upward or downward spillovers between basic and applied research are present