Stoney units

Units

The constants that Stoney used to define his set of units is the following:

• c, the speed of light in vacuum,
• G, the gravitational constant,
• ke, the Coulomb constant,
• e, the charge of the electron.

Later authors typically express the Coulomb constant as .

This means that the numerical values of all these constants, when expressed in coherent Stoney units, is equal to one:

\begin{align} c &= 1\ l_\text{S} \cdot t_\text{S}^{-1} \ G &= 1\ l_\text{S}^3 \cdot t_\text{S}^{-2} \cdot m_\text{S}^{-1} \ k_\text{e} &= 1\ l_\text{S}^3 \cdot t_\text{S}^{-2} \cdot m_\text{S} \cdot q_\text{S}^{-2}\ e &= 1\ q_\text{S} \end{align}

In Stoney units, the numerical value of the reduced Planck constant is

\hbar = \frac{1}{\alpha} ~l_\text{S}^2 \cdot t_\text{S}^{-1} \cdot m_\text{S} \approx 137.036 l_\text{S}^2 \cdot t_\text{S}^{-1} \cdot m_\text{S}^{},

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. Stoney's derived estimate of the unit of charge, 10−20 ampere-second, was of the modern value of the charge of the electron 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 and for the volume of a gram-molecule under these conditions of , the modern value is , 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 in place of the elementary charge.

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.

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 Planck scale are the length and energy scales at which quantum processes and gravity occur together. At these scales, a unified theory of physics is thus required. The only notable attempt to construct such a theory from the Stoney scale was that of Hermann Weyl, who associated a gravitational unit of charge with the Stoney length{{citation |author-link=Hermann Weyl |first=H. |last=Weyl |title=Eine Neue Erweiterung der Relativitaetstheorie |journal=Annalen der Physik |volume=59 |year=1919 |issue=10 |pages=101–103|doi=10.1002/andp.19193641002 |bibcode=1919AnP...364..101W }} and who appears to have inspired Dirac's fascination with the large numbers hypothesis. Since then, the Stoney scale has been largely neglected in the development of modern physics, although it is still occasionally discussed.

The ratio of Stoney units to Planck units of length, time and mass is \sqrt{\alpha}, where \alpha is the fine-structure constant: l_\text{S} = \sqrt{\alpha},l_\text{P}; m_\text{S} = \sqrt{\alpha},m_\text{P}; t_\text{S} = \sqrt{\alpha},t_\text{P}; q_\text{S} = \sqrt{\alpha},q_\text{P}.

Notes

References

References

1. Ray, T. P.. (1981). "Stoney's fundamental units". Irish Astronomical Journal.
2. Stoney, G. Johnstone. (May 1881). "LII. On the physical units of nature". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science.
3. (1988). "The anthropic cosmological principle". Oxford University Press.
4. (2004). "Astrophysics, clocks and fundamental constants". Springer.
5. Stoney, G.. (1881). "On The Physical Units of Nature". Phil. Mag..
6. Stoney, G. Johnstone. (1883). "On The Physical Units of Nature". The Scientific Proceedings of the Royal Dublin Society.
7. Barrow, John D.. (2004). "Space: in science, art and society". Cambridge University Press.
8. Weyl, H.. (1918). "Gravitation und Elekrizitaet". Koniglich Preussische Akademie der Wissenschaften.
9. Uzan, Jean-Philippe. (2011). "Varying Constants, Gravitation and Cosmology". Living Rev. Relativ..
10. (2002-03-09). "Trialogue on the number of fundamental constants". Journal of High Energy Physics.