From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory

From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory explores the critical role of classical analogies in the development of quantum theory, examining how key figures such as Planck, Bohr, Heisenberg, and Dirac employed these analogies to bridge the gap between classical and quantum mechanics. At the heart of the book is the idea that quantum mechanics, while radically different from classical theories, still relies heavily on formal structures and mathematical procedures inherited from classical physics. By analyzing three major stages in quantum theory―Planck's radiation theory, Bohr's atomic theory, and Dirac's quantum mechanics―the book reveals how analogies with classical theories not only facilitated the formation of quantum ideas but also provided a framework that allowed quantum mechanics to evolve from classical roots.

The book identifies four distinct types of classical analogies: Planck's horizontal analogy, which merely extended classical methods; Bohr's vertical analogies, which involved more direct, though incomplete, translations of classical laws; Heisenberg's and Dirac's analogies, which mathematically aligned classical and quantum mechanics; and Dirac's use of relativistic strategies for theory-building. These analogies were essential in navigating the intellectual challenges of quantum mechanics, especially in the absence of complete theories. The study underscores the continuity between classical and quantum physics, illustrating how quantum theory, through its innovative use of mathematical formalisms, preserved the elegance of classical mechanics while embracing new, non-intuitive principles. This approach shows that the construction of quantum theory was deeply intertwined with classical precedents, allowing quantum mechanics to mature while maintaining connections to earlier frameworks of understanding.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1992.