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Published online by Cambridge University Press: 30 December 2016
Physical Constants
Speed of light in vacuum: c = 299 792 458 ms −1
Gravitational constant: GN = 6. 67428(67) × 10 −11 m3 kg −1s−2
= 6. 70881(67) × 10 −39 ħc (GeVc−2) −2
Planck's constant: h = 6. 62606896(33) × 10 −34 J s
(Planck's constant)/2π: ħ = 1. 054571628(53) × 10 −34 J s
= 6. 58211899(16) × 10 −22 MeV s
Reduced Planck mass: MPl = (8πGN/ħc) −1/2
= 2. 43 × 1018GeVc2
Fine structure constant: α = e2/ħc = 1/137. 035
Fermi constant: GF/(ħc)3 = 1. 16637(1) × 10 −5 GeV −2
Boltzmann constant: kB = 1. 3806504(24) × 10 −23 JK −1
= 8. 617343(15) × 10 −5 eVK −1
Electron mass: me = 0. 51099 MeV
Proton mass: mp = 938. 2720 MeV
W−boson mass: MW = (80. 399 ± 0. 023) GeV
Z − boson mass: MZ = (91. 1876 ± 0. 0021) GeV
Strong coupling constant: αs (MZ) = 0. 1184(7)
Electron electric dipole moment: de < (7 ± 7) × 10 −28 ecm
Neutron electric dipole moment: dn < 0. 29 × 10 −25 ecm,
confidence limit (CL) = 90%
Some useful conversions are
The values of the physical constants listed are from K. A. Olive et al. (Particle Data Group), “Review of Particle Physics,” Chin. Phys. C 38, 090001 (2014).
Natural Units
Often, it is convenient to use units where the natural physical constants assume unit values. For instance, if we assume units so that
then in these units energy can be expressed as inverse length since L = ħc/E = 1/E, which gives
One may also assume as fundamental units the Boltzmann constant and Newton's constant so that
Equations (23.1) and (23.2) taken together are often referred to as Planck natural units.
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