Physical
Constants| Physical
Constants |
Boltzmann Constant
* Idea: The
constant relating the microscopic (rms) kinetic energy of particles in an equilibrium
ensemble and thermodynamic, macroscopic quantities such as temperature and
pressure in kinetic
theory; An accurate value is important for the definition of the K.
* Measurement methods:
2007, So far only one technique – measuring the speed of sound in
argon
gas – can determine kB to an
accuracy of about 2 parts-per-million (ppm) (other techniques include measuring
noise in a resistor, determining the dielectric constant of a gas, and measuring
the radiation emitted
from a black body, but none of these techniques has yet reached ppm accuracy).
* Value: kB =
1.380658(12) × 10–23 J/K = 1.380658(12) ×
10–16 erg/K.
@ References: Daussy et al PRL(07)
+ pw(07)jun
[new measurement method].
Mechanical Equivalent of Heat
* Value: 1 cal = 4.186 J.
Planck's Constant and Units
* Value: 1998, h =
6.62606891(58) × 10–34 J
· s or × 10–27
erg · s; 
=
1.05457266(63)
× 10–34 J
· s, or × 10–27 erg ·
s.
* Length: lP =
(G/c3)1/2 =
1.6 × 10–33 cm.
* Time: tP =
lP / c = 5.4 × 10–44 s.
* Energy: EP =
lP c4/G = 2 × 1016 erg
= 1.3 × 1019 GeV = 2.2 ×
10–5 g.
@ General references: Planck SBAW(1899);
Fischbach et al PRL(91)
[quantum mechanics with different ];
Cooperstock & Faraoni
MPLA(03)ht,
IJMPD(03)gq [including e and s];
Wilczek PT(05)oct
[absolute units].
@ Related topics: Zeilinger AJP(90)
[Planck stroll]; Casher & Nussinov ht/97 [pP unattainable];
Williams et al PRL(98)
+ pn(98)sep
+ pw(98)sep
[measurement]; Sivaram a0707 [Planck
mass].
Particle Properties > s.a. charge; particle
types.
* Electron: Charge e =
1.60217733(49) ×
10–19 C; Mass me =
10–27 g = 511 keV/c2.
* Nucleon: Mass mN =
1.7 ×
10–24 g.
Avogadro's Number
* Determination: 1908, Perrin's
experiment, using the
mean square displacement of small particles undergoing Brownian motion.
* Value: NA =
6.0221 × 1023.
@ References: Mana & Zosi RNC(95); Pesic EJP(05)
[estimate from skylight and airlight]; Straumann phy/05 [Einstein's
doctoral thesis]; Newburgh et al AJP(06)
[history]; Fox & Hill AS(07)
[proposed def].
Molar Gas Constant
* Value: R = 8.314510(70) J/(mol · K).
Stefan-Boltzmann Constant
* Value: 
=
5.67051(19) × 10–5 erg/(cm2 ·
s).
* Quantum mechanics prediction:
Using G = k = c =
1 units,
= 
2/153.
Rydberg Constant
* Value: Rinfty =
109 737.315 34(13) cm–1.
@ References: Zhao et al PRL(87)
[most precise value].
Speed of Light (or "Einstein's constant"); > s.a. special
relativity [including tests];
cosmological constant; light;
variation of constants.
* Value: c =
2.99792458 × 108 m/s (exact – def
of m) 
1.86 ×
105 mi/s 500,000,000
furlongs/fortnight 1
ft/ns.
@ References: Terrien Met(74) [international agreement]; Bates AJP(88);
Antonini PRA(05)
[test of isotropy]; Mendelson AJP(06)
[story of symbol c].
Other Constants and Topics > s.a. multiverse [cosmic natural
selection]; units; variation
of constants.
* Combinations: Josephson constant, KJ = 2e/h;
von Klitzing constant, RK = h/e2.
@ Theoretical arguments for values: Desloge AJP(94)
[setting them to unity];
Gambini & Pullin IJMPD(03)gq [discrete
quantum gravity]; Efremov & Mitskievich gq/03 [topology];
Page ht/03 [e and mp,
anthropic]; Tegmark et al PRD(06)ap/05 [particle
physics and cosmology].
@ Combinations: Sloggett et al PRL(86) [2e/h and h/e2].
@ Relationships: in Harrison 81; Sidharth IJMPA(98)qp;
Wignall IJMPA(00) [number]; Kafatos et al APPB(05)ap/03.
@ Related topics: Taylor et al 69 [and QED]; Hsu & Zee MPLA(05)ht/04 [Mcc (MP MU)1/2];
Press AJP(80)
[our size ito fundamental constants]; Crease pw(08)feb
[improving the definitions].
> Other constants:
see Bohr Magneton; cosmological, fine
structure and gravitational constant; Coupling
Constants.
Other References > s.a. Large
Numbers Hypothesis; Number [mathematical
constants]; summary of values.
@ Updates on values: Cohen & Taylor RMP(87);
Barnett et al (PDG) PRD(96), RMP(96);
Mohr & Taylor PT(01)mar, RMP(05)
[2002 values]; Particle Data Group PLB(04);
Mohr et al PT(07)jul,
RMP(08) [new sets of recommended values]; > s.a. Particle
Data Group.
@ General: Okun SPU(91); Barrow 02; NIST
reference site;
Matsas et al a0711 [two
dimensional fundamental constants]; Fritsch 08.
@ Conceptual: Lévy-Leblond RNC(77);
Desloge AJP(84),
AJP(94) [suppression
and restoration in physical equations]; Duff et al JHEP(02)phy/01 [number
of fundamental constants]; Wilczek a0708 ["fundamental
constants"].
@ Theoretical: Condon AJP(34);
Taylor et al Rech(70);
issue PTRS(83)#1512;
Grabe PLA(96)
[adjusting values].
"In a few years, all the great physical constants will
have been approximately estimated, and...
The only occupation which will then
be left to the men of science will be to carry these measurements
to another
place of decimals." – James Clerk Maxwell, 1871 University of Cambridge
inaugural lecture
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
22 jul 2008