In physics the Stoney units form a system of units named after the Irish physicist George Johnstone Stoney, who first proposed them in 1881. They are the first historical example of natural units, i.e. units of measurement designed so that certain fundamental physical constants serve as base 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 set of the constants that Stoney used as base units is the following:^{[1]}^{[2]}
This means that, in terms of Stoney units, the numerical values of all these constants equal one:
Stoney's set of base units is similar to the one used in Planck units, proposed independently by Planck thirty years later, but Planck normalized the Planck constant in place of the elementary charge.^{[3]} (In modern usage, Planck units are understood to normalize the reduced Planck constant in place of the Planck constant.) In Stoney units, the numerical value of the reduced Planck constant is
where α is the fine-structure constant. Planck units are more commonly used than Stoney units in modern physics, especially quantum gravity (including string theory). Rarely, Planck units are referred to as Planck–Stoney units.^{[3]}
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.^{[4]}^{[5]} James G. O’Hara^{[6]} pointed out in 1974 that 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. The reason is that Stoney used the approximated value of 10^{18} 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 6.02214×10^{23} mol^{−1} and for the volume of a gram-molecule (at s.t.p.) of 22.4146×10^{6} mm^{3}, the modern value is 2.687×10^{16}, instead of Stoney's 10^{18}.
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 H. Weyl, who associated a gravitational unit of charge with the Stoney length^{[7]}^{[8]}^{[9]} and who appears to have inspired Dirac's fascination with the large numbers hypothesis.^{[10]} Since then, the Stoney scale has been largely neglected in the development of modern physics, although it is still occasionally discussed.^{[11]}^{[12]}