Stoney units
In
Units
Quantity | Expression | Value in SI Units |
---|---|---|
Length (L) | 1.3807×10−36 m | |
Mass (M) | 1.8592×10−9 kg | |
Time (T) | 4.6054×10−45 s | |
Electric charge (Q) | 1.6022×10−19 C |
The constants that Stoney used to define his set of units is the following:[1][2]
- c, the speed of light in vacuum,
- G, the gravitational constant,
- ke, the Coulomb constant,
- e, the charge on the electron.
Later authors typically replace the Coulomb constant with 1/4πε0.[3][4]
This means that the numerical values of all these constants, when expressed in coherent Stoney units, is equal to one:
In Stoney units, the numerical value of the
where α is the fine-structure constant.
History
George Stoney was one of the first scientists to understand that electric charge was quantized; from this quantization and three other constants that he perceived as being universal (a speed from electromagnetism, and the coefficients in the electrostatic and gravitational force equations) he derived the units that are now named after him.[5][6] Stoney's derived estimate of the unit of charge, 10−20 ampere-second, was 1⁄16 of the modern value of the charge of the electron[7] due to Stoney using the approximated value of 1018 for the number of molecules presented in one cubic millimetre of gas at standard temperature and pressure. Using the modern values for the Avogadro constant 6.02214×1023 mol−1 and for the volume of a gram-molecule under these conditions of 22.4146×106 mm3, the modern value is 2.687×1016, instead of Stoney's 1018.
Stoney units and Planck units
Stoney's set of base units is similar to the one used in Planck units, proposed independently by Planck thirty years later, in which Planck normalized the Planck constant[a] in place of the elementary charge.[8]
Planck units are more commonly used than Stoney units in modern physics, especially for quantum gravity (including string theory). Rarely, Planck units are referred to as Planck–Stoney units.[8]
The Stoney length and the Stoney energy, collectively called the Stoney scale, are not far from the Planck length and the Planck energy, the Planck scale. The Stoney scale and the
The ratio of Stoney units to Planck units of length, time and mass is , where is the fine-structure constant:[14]
See also
Notes
- reduced Planck constantin place of the Planck constant.
References
- ^ Ray, T. P. "Stoney's fundamental units". Irish Astronomical Journal, Vol. 15, p. 152, 1981 15 (1981): 152.
- ISSN 1941-5982.
- ISBN 978-0-192-82147-8
- ISBN 978-3-540-21967-5
- ^ Stoney, G. (1881), "On The Physical Units of Nature", Phil. Mag., 11: 381–391
- ^ Stoney, G. Johnstone (1883), "On The Physical Units of Nature", The Scientific Proceedings of the Royal Dublin Society, 3: 51–60, retrieved 2010-11-28
- ^ O'Hara, J. G. (1993), George Johnstone Stoney and the Conceptual Discovery of the Electron, Occasional Papers in Science and Technology, vol. 8, Royal Dublin Society, pp. 5–28
- ^ ISBN 978-0-521-82376-0
- ^ Tomilin, K. (2000), "Natural System of Units", Proc. of the XX11 International Workshop on High Energy Physics and Field Theory: 289
- ^ Weyl, H. (1918), "Gravitation und Elekrizitaet", Koniglich Preussische Akademie der Wissenschaften: 465–78
- ^ Weyl, H. (1919), "Eine Neue Erweiterung der Relativitaetstheorie", Annalen der Physik, 59: 101–103
- ^ Gorelik, G. (2002), "Hermann Weyl and Large Numbers in Relativistic Cosmology", in Balashov, Y.; Vizgin, V. (eds.), Einstein Studies in Russia, Birkhaeuser
- PMID 28179829
- S2CID 15806354