Physical Constants |

**In General** > s.a. Large-Numbers Hypothesis;
Mathematical Constants; summary of values.

* __Fundamental constants__: Following Lévy-Leblond,
there are three types — constants of objects (e.g., masses), constants of phenomena (coupling
constants, such as α and *G*), and "universal constants" (such as the speed
of light *c* and the Planck constant \(\hbar\)); Future theories may allow us to derive the
values of some of them, as well as that of a possible fundamental length/energy scale for quantum
gravity (already proposed by Heisenberg).

@ __General references__: Okun SPU(91); Barrow 02;
NIST reference site;
Matsas et al a0711 [two-dimensional fundamental constants];
Fritzsch 09;
Mohr & Newell AJP(10)apr [physics].

@ __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),
PLB(08);
Mohr et al PT(07)jul,
RMP(08) [new sets of recommended values];
> s.a. Particle Data Group.

@ __Conceptual aspects__: Lévy-Leblond RNC(77);
Desloge AJP(84)apr,
AJP(94)mar [suppression and restoration in physical equations];
Duff et al JHEP(02)phy/01 [number of fundamental constants];
Wilczek a0708 ["fundamental constants"];
Cohen-Tannoudji EPJST(09)-a0905 [and fundamental metrology];
Sheykin a2103.

@ __Theoretical aspects__: Condon AJP(34)may;
Taylor et al Rech(70);
issue PTRS(83)#1512;
Desloge AJP(94)mar [setting them to unity];
Grabe PLA(96) [adjusting values];
Gambini & Pullin IJMPD(03)gq [discrete quantum gravity];
Efremov & Mitskievich gq/03 [topology];
Page PLB(09)ht/03 [*e* and *m*_{p}, anthropic];
Tegmark et al PRD(06)ap/05 [particle physics and cosmology];
Page a1101
[evidence against fine tuning by a biophilic principle];
Vilela Mendes a1111
[as deformation parameters that stabilize algebraic structures];
Husain & Singh IJMPD(19)-a1807 [and the Wheeler-DeWitt equation];
Barrow & Magueijo PRD(19)-a1809 [as quantum observables];
Sheykin & Manida a2005 [and units].

@ __Relationships__: Zágoni IJTP(80);
in Harrison 81;
Sidharth IJMPA(98)qp;
Wignall IJMPA(00) [number];
Kafatos et al APPB(05)ap/03.

**Boltzmann Constant**
> s.a. Wikipedia page.

* __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 *k*_{B} 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__: 2013, \(k^~_{\rm B}\)
= 1.380 651 56 (98) × \(10^{-23}\) J/K = 1.380 651 56 (98) ×
\(10^{-16}\) erg/K; 2018, Defined to be 1.380649 × \(10^{-23}\) J/K.

@ __Measurement__: Daussy et al PRL(07)
+ pw(07)jun [new method];
Rodríguez-Luna & de Urquijo EJP(10) [simple circuit];
Tyukodi EJP(12) [from evaporation experiments];
de Podesta et al Metr(13)
+ news sa(13)jul [from measurements of the speed of sound in argon gas];
Moretti et al PRL(13);
Krishnatreya et al AJP(14)jan [holographic video microscopy of a single colloidal sphere];
Ehnholm & Krusius a2010
[*T* scale and the Boltzmann constant].

**Avogadro's Number**

* __Determination__: 1908, Perrin's
experiment, using the mean square displacement of small particles undergoing Brownian motion.

* __Value__: 2011,
*N*_{A} = 6.02214078(18) × 10^{23}
(with a relative uncertainty of 3.0 × 10^{−8}).

@ __References__: Mana & Zosi RNC(95);
Pešić EJP(05) [estimate from skylight and airlight];
Straumann phy/05-talk [Einstein's doctoral thesis];
Newburgh et al AJP(06)jun [history];
Fox & Hill AS(07) [proposed def];
Andreas et al PRL(11) [counting the atoms in 1-kg single-crystal spheres].

**Stefan-Boltzmann Constant**

* __Idea and value__: The constant
appearing in the expression *E* = *σT*^{ 4}
for the total energy emitted per unit surface and unit time by a black body at
temperature *T*; Its value is *σ* = 5.67051(19) ×
10^{−5} erg/(cm^{2}
· s).

* __Quantum mechanics prediction__:
It is not a fundamental constant, and its value can be derived using the quantum
statistical mechanics of black-body electromagnetic radiation; Using *G*
= *k* = *c* = 1 units, *σ*
= π^{2}/15\(\hbar\)^{3}.

> __Online resources__:
see Wikipedia page.

**Speed of Light** (or "Einstein's constant");
> s.a. special relativity [including tests]; cosmological constant;
light [including special propagation effects].

* __History__: Most
scientists before the 17th century, including Kepler and Descartes, thought
that it was infinite; Galileo was among the first who thought it was finite,
and attempted to measure it in a very crude way; The first serious measurement
was made by Ole Rømer in 1676; 1949, Armand Fizeau publishes his results,
giving 313,300 km/s.

* __Value__: *c* =
2.99792458 × \(10^8\) m/s (exact – def of m) ≈ 1.86 ×
\(10^5\) mi/s ≈ 500,000,000 furlongs/fortnight ≈ 1 ft/ns.

@ __General references__:
Terrien Met(74) [international agreement];
Bates AJP(88)aug;
Mendelson AJP(06)nov [story of the symbol *c*];
Viennot & Vigoureux IJTP(09)-a0905 [new interpretation, and cosmological expansion];
Anber & Donoghue PRD(11)-a1102 [emergence of a universal limiting speed];
Mareš et al PS(12)-a1606 [consequences of the speed of light having an exact value];
Braun et al CQG(17)-a1502 [limits to experimental precision].

@ __Student lab measurements__:
Carlson TPT(96)mar [using a laser pointer];
Stauffer TPT(97)mar [using marshmallows in a microwave oven];
Mak TPT(03)jan [along a coaxial cable];
Brody TPT(03)may
[using a laser, reflector, two photodetectors and an oscilloscope];
Keeports TPT(06)oct [from Earth-Moon communication];
Doran et al TPT(14)sep [using an LC circuit].

@ __One-way__: Pérez EJP(11)-a1102 [experimental determination];
Philip CS-a1212 [circular-track experiment];
Nissim-Sabat a2004 [measurement without synchronized clocks?].

@ __Isotropy__: Antonini PRA(05) [test of isotropy];
Nagel et al nComm(15)-a1412 [direct terrestrial measurement];
> s.a. Anisotropy.

@ __The c equivalence principle__:
Heras AJP(10)oct;
Choy a1108 [and the weak equivalence principle];
> s.a. formulations of electromagnetic theory.

>

**Other Constants and Topics**

* __Mechanical equivalent of heat__:
It sets the correspondence between thermodynamic heat and mechanical energy,
1 cal = 4.186 J.

* __Molar gas constant__:
Its value is *R* = 8.314510(70) J/(mol · K); > s.a.
Wikipedia page.

* __Rydberg constant__: Its value
is *R*_{∞} = 109 737.315 34(13)
cm^{−1}.

* __Combinations__: Josephson
constant, *K*_{J} = 2*e*/*h*;
von Klitzing constant, *R*_{K}
= *h*/*e*^{2}.

@ __Rydberg constant__: Zhao et al PRL(87) [most precise value].

@ __Combinations__: Sloggett et al PRL(86) [2*e*/*h* and *h*/*e*^{2}].

@ __Related topics__: Taylor et al 69 [and QED];
Hsu & Zee MPLA(05)ht/04
[*M*_{cc} ≈ (*M*_{P}
*M*_{U})^{1/2}];
Press AJP(80)aug [our size in terms of fundamental constants];
Crease pw(08)feb,
follow-up pw(08)dec [improving the definitions];
Page FP(09) [and size of animals];
Narimani et al ASS(12)-a1109 [cosmology in terms of dimensionless constants].

> __Particle properties__:
see charge; electron;
hadrons; neutrino;
neutron; particle
types; QCD phenomenology [quark masses].

> __Other constants__:
see Bohr Magneton; cosmological,
fine-structure and gravitational
constant; Coupling Constants;
Planck's Constant.

> __Related topics__: see
multiverse [cosmic natural selection];
units; variation of constants.

"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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