Stoney units

Stoney units form a system of natural units named after the Irish physicist George Johnstone Stoney, who first proposed them in 1881. They are constructed using the elementary charge (e), the gravitational constant (G), the speed of light (c), and the Coulomb constant (k_e). This system predates the more widely known Planck units and represents one of the earliest attempts to derive fundamental units from universal constants.

Definition and basis

The system defines base units by setting four fundamental physical constants to unity. The chosen constants are the elementary charge, the gravitational constant, the speed of light in vacuum, and the Coulomb constant. This dimensional analysis yields unique scales for length, mass, time, and electric charge. Unlike the International System of Units, these scales are not anthropocentric but are derived purely from the properties of the universe. The approach is conceptually similar to later systems like Planck units or atomic units, but with a different choice of defining constants.

Relation to Planck units

Stoney units and Planck units are both systems of natural units but differ in their treatment of electric charge. While Planck units set reduced Planck's constant (ħ), G, c, and the Boltzmann constant to unity, Stoney units instead normalize the elementary charge. Consequently, the Stoney mass and length are roughly a factor of the square root of the fine-structure constant smaller than their Planck scale counterparts. This difference highlights the distinct physical perspectives of George Johnstone Stoney and Max Planck, with the former emphasizing electromagnetism and the latter incorporating quantum mechanics.

Physical constants and values

In this system, the Stoney length is approximately 1.38 × 10⁻³⁶ metres, and the Stoney mass is about 1.86 × 10⁻⁹ kilograms. The Stoney time, derived from the length and speed of light, is around 4.61 × 10⁻⁴⁵ seconds. A key feature is that the elementary charge becomes the natural unit of electric charge. These values are calculable from the gravitational constant, the speed of light, and the measured value of the elementary charge, as formalized in the work of physicists like Michael Duff.

Applications and significance

Although largely of historical and pedagogical interest today, Stoney units were pioneering in demonstrating that fundamental units could be derived from constants of nature. They influenced later developments in theoretical physics, including the study of black hole thermodynamics and quantum gravity, where natural scales are essential. The system appears in discussions comparing different schemes of natural units, such as those involving the Dirac constant or the Boltzmann constant. Its legacy persists in modern cosmology and particle physics as a conceptual forerunner to more complete systems.

History and development

The units were first introduced by George Johnstone Stoney in a lecture to the British Association for the Advancement of Science in 1874 and more fully in 1881. Stoney, who also coined the term "electron," sought units independent of human constructs. His work preceded that of Max Planck by over two decades. The system was revisited in the 20th century by figures like Gamow and Landau in the context of large number coincidences and the anthropic principle. Contemporary analysis of Stoney units often references the research of John D. Barrow and Frank J. Tipler on fundamental constants.