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Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics

Time in quantum mechanics: a story of confusion

Jan Hilgevoord

Published Feb 4, 2005• 69 citations
Publisher
DOI
10.1016/j.shpsb.2004.10.002

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It is widely accepted that the papers by Bose in 1924 and by Einstein in 1924-1925 definitely opened the path to the quantum concept of ‘indistinguishability’. Since then, distinction in physics between ‘identity’ and ‘indistinguishability’ of particles has come to be required. However, even before the rise of quantum physics, Maxwell, Boltzmann and Gibbs, among others, had to tackle the difficulties and paradoxes that appear when counting identical particles. Later, after Sackur’s and Tetrode’s first quantum derivation of the canonical partition function of an ideal gas, much confusion arose around its dependence on the number of molecules in the system. Many other physicists, such as Planck, Lorentz or Schrodinger took part in those debates. In 1921, Ehrenfest and Trkal devoted a whole paper to this subject. Clearly, in the days before Bose’s seminal work, embroiling and misunderstanding were commonplace. In considering the emergence of the distinction between ‘identical’ and ‘indistinguishable’ particles, we will go through the so-called statistical route to quantum mechanics. The first developments in statistical mechanics became immediately confused and entangled with the irruption of quantum physics. In the first quarter of the twentieth century the mutual influence between both disciplines was profuse. We will pay special attention to the story of the so-called ‘Gibbs Paradox.’ We will argue that what is now often known by this name in some textbooks of statistical mechanics did not exist as such in those foundational days.

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It is widely accepted that the papers by Bose in 1924 and by Einstein in 1924-1925 definitely opened the path to the quantum concept of ‘indistinguishability’. Since then, distinction in physics between ‘identity’ and ‘indistinguishability’ of particles has come to be required. However, even before the rise of quantum physics, Maxwell, Boltzmann and Gibbs, among others, had to tackle the difficulties and paradoxes that appear when counting identical particles. Later, after Sackur’s and Tetrode’s first quantum derivation of the canonical partition function of an ideal gas, much confusion arose around its dependence on the number of molecules in the system. Many other physicists, such as Planck, Lorentz or Schrodinger took part in those debates. In 1921, Ehrenfest and Trkal devoted a whole paper to this subject. Clearly, in the days before Bose’s seminal work, embroiling and misunderstanding were commonplace. In considering the emergence of the distinction between ‘identical’ and ‘indistinguishable’ particles, we will go through the so-called statistical route to quantum mechanics. The first developments in statistical mechanics became immediately confused and entangled with the irruption of quantum physics. In the first quarter of the twentieth century the mutual influence between both disciplines was profuse. We will pay special attention to the story of the so-called ‘Gibbs Paradox.’ We will argue that what is now often known by this name in some textbooks of statistical mechanics did not exist as such in those foundational days.
Quantum mechanics is one of the great success stories of modern physics, making sense of the very small just as Einstein's theory of relativity made sense of the very large. But, for most students, the ideas that make quantum mechanics powerful can be confusing and counterintuitive. This volume in the Greenwood Guides to Great Ideas in Science series provides a history of quantum mechanics from the early breakthroughs of Planck and Einstein, at the beginning of the 20th century, to the present frontiers of quantum computing and quantum gravity. The approach is entirely non-technical, and is aimed at the general reader who may not have much mathematical background but who has a strong curiosity about some of the most important developments in modern science. Quantum Mechanics: A Historical Perspectivetraces the history of this powerful theory, including: ; The early discoveries by Max Planck and Albert Einstein regarding the quantization of radiation ; The early quantum theory, including Neils Bohr's theory of the atom ; The birth of modern quantum mechanics through the work of Heisenberg, Schrodinger, Born, Dirac and others ; Applications of quantum mechanics in chemistry, nuclear physics, electronics, and many other areas ; Recent work in quantum computation and quantum information theory The book emphasizes the fact that despite the great success of quantum mechanics, many exciting intellectual frontiers remain open for further researchers to explore. It includes a glossary, a timeline, and a bibliography of accessible resources for further research.