The Natural Units convention file for GNU units.
$ apt-get install units
$ units -V # check that you are running **GNU Units**, not BSD units.
GNU Units version 2.1x
with readline, with utf8, locale en_US
Units data file is '/usr/share/units/definitions.units'
$ units -f natural.units
113 units, 42 prefixes, 0 nonlinear units
You have: 1m
You want: s
1m = 3.335641e-09 s
1m = (1 / 2.9979246e+08) s
$ brew install gnu-units
$ gunits -V # double-check that you are running **GNU Units**, not BSD units.
GNU Units version 2.1x
$ gunits -vf natural.units
113 units, 42 prefixes, 0 nonlinear units
You have: 1 / fm
You want: GeV
1 / fm = 0.19732696 GeV
1 / fm = (1 / 5.0677312) GeV
natural.units
is a definition file of the natural units for GNU units.
This is only for GNU units, not for BSD units pre-installed in macOS.
You can check version by units -v
(for BSD units) or units -V
(for GNU units).
In the natural units, all the units are given in terms of energy (giga electron volt, GeV) with defining c = ℏ = kB = 1, where c, ℏ and kB are respectively the speed of light, the Planck constant and the Boltzmann constant.
For electromagnetism, we use the Lorentz-Heaviside convention, where the vacuum permittivity, ε0, and the vacuum permeability, μ0, are defined by μ0 = c2/ε0 = 1. The fine structure constant is given by α = e^2/4π, where the elementary charge is given by e = 1.60×10-19 C = 0.303.
- Install GNU units.
- Prepare the file
natural.units
. - Run and convert!
You can install GNU Units with apt-get
(Debian/Ubuntu) or via Homebrew (macOS) by
apt-get install units # Debian / Ubuntu
brew install gnu-units # macOS
You should check that you are running GNU units, not BSD units (pre-installed in macOS), by
$ units -V # Debian / Ubuntu + apt-get
$ gunits -V # macOS + Homebrew
GNU Units version 2.1x
Run GNU Units with the file natural.units
, downloaded from this GitHub repository:
units -f natural.units # Debian / Ubuntu + apt-get
gunits -f natural.units # macOS + Homebrew
You will encounter error message below if you are running BSD Units:
units: redefinition of unit '#' on line 2 ignored
units: redefinition of unit '#' on line 3 ignored
units: redefinition of unit '#' on line 3 ignored
units: unexpected end of unit on line 3
units: redefinition of unit '#' on line 4 ignored
...
In this case, you have to recheck that you have installed GNU units and that you are using the correct command.
$ units -f natural.units
You have: 1s
You want: m
* 2.9979246e+08
/ 3.335641e-09
You have: 100 fb
You want: /GeV^2
* 2.5681899e-10
/ 3.893793e+09
You have: 3 pc
You want: m
* 9.2570327e+16
/ 1.0802598e-17
You have: 4.2K
You want:
Definition: 3.6192796e-13 GeV
You have: 200 fm
You want: MeV
* 1.0135462
/ 0.98663482
You have: 200 fm
You want: MeV
reciprocal conversion
* 0.98663482
/ 1.0135462
You have: 1 Mpl
You want: m
reciprocal conversion
* 1.6161943e-35
You have: sqrt(4 pi epsilon0)
You want: C
* 1.8755459e-18
/ 5.331781e+17
$ units -f natural.units
You have: 4pi hbar c / e^2
You want:
Definition: 137.036
You have: 4pi/e^2
You want:
Definition: 137.03599
You have: c
You want:
Definition: 2.99792458e8 m/s = 1
You have: hbar
You want:
Definition: 1.054571726e-34 J s = 1
You have: e
You want:
Definition: 1.602176565e-19 C = 0.30282213
You have: kB
You want:
Definition: 1.3806488e-23 J/K = 1
You have: mu0
You want:
Definition: 4 pi 1e-7 H/m = 1
You have: epsilon0
You want:
Definition: 1/mu0 c^2 = 1
See the Appendix of Peskin's QFT book.
$ units -f natural.units
You have: 1 GeV
You want: g
* 1.7826618e-24
You have: 1/GeV
You want: fm
* 0.19732696
You have: 1/GeV^2
You want: mb
* 0.3893793
You have: 1 e V / m
You want:
Definition: 1.9732696e-25 GeV^2
You have: 1 e tesla
You want:
Definition: 5.9157135e-17 GeV^2
Values are taken from PDG Review of Particle Physics 2014.
Planck mass is symbolized by M_pl
, while reduced Planck mass is by M
.
Light year (ly
) is defined as
c × 365.25day
following NIST publication 811, while yr
denotes tropicalyear
as is in PDG table.
Sho Iwamoto @ http://www.misho-web.com/