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 mp, 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 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: 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, NA = 6.02214078(18) × 1023 (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/(cm2 · 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 = π2/15\(\hbar\)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.
> Corrections, quantum effects: see modified QED; variation of constants.

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, KJ = 2e/h; von Klitzing constant, RK = h/e2.
@ Rydberg constant: Zhao et al PRL(87) [most precise value].
@ Combinations: Sloggett et al PRL(86) [2e/h and h/e2].
@ Related topics: Taylor et al 69 [and QED]; Hsu & Zee MPLA(05)ht/04 [Mcc ≈ (MP MU)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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