In General > s.a. equivalence principle; newtonian gravity; physical theories.
* Idea: The concept of mass is related to two different physical phenomena, inertia and gravitation.
* Inertial mass: Defined by Newton's second law, F = mi a.
* Gravitational mass: The active and passive gravitational masses are defined by

Fgrav = mp g ,    g(x) = −G (ma / r2) (r/r)    (for each point source) .

* Relationships: In Newtonian mechanics, the two gravitational ones are proportional as a consequence of the third law, ma = mp = mg – an inequality would imply a violation of momentum conservation; The principle of equivalence states the proportionality of mi and mg (specifically, mp).
@ General references: Jammer 61; Pietschmann pr(86); Okun PT(89)jun; Jammer 00; Roche EJP(05); Okun 09; Re Fiorentin FP(09)-a1102.
@ Conceptual: Hubert a1512-proc [quantity of matter or dynamical property?].
@ Measurement: Poncharal et al Sci(99)mar + pn(00)mar [10−12 g, nanotubes]; Ilic et al JAP(04) + pw(04)feb + pn(04)feb [10−18 g, nanoelectromechanical device]; news pn(05)apr [zeptogram (10−21 g) sensitivity]; news pw(07)feb [nanocantilevers]; news ns(12)apr [yoctogram (10−24 g) sensitivity].

The Origin of Mass > s.a. hadrons [quarks]; higgs mechanism / boson; mach's principle; quantum particles; symmetry breaking.
* Effective mass: A quantity describing the response of a particle in a periodic potential, such as inside a continuous medium, to an applied force; It accounts for the detailed interaction between the particle and the surrounding potential.
* Electromagnetic mass: The quantity me = 4U/3c2 appearing in the Abraham-Lorentz equation (> see radiation); For an accelerated charged particle, the measured mass would be m = m0 + me; Note that, unless one uses a cutoff, for a point particle me = ∞, so one needs to renormalize it.
* Mass generation in quantum field theory: For gauge fields the known mechanisms are the Higgs mechanism and, in 3D, adding Proca/Pauli-Fierz or Chern-Simons terms.
@ General references: Nambu ThSc(92)may [symmetry breaking]; Wilczek CEJP(12)-a1206-talk [standard model].
@ Inertial origin: Haisch et al ThSc(94)nov; Rueda & Haisch FP(98)phy, PLA(98)phy; Haisch et al AdP(01)gq/00; Rueda & Haisch AdP(05)gq [passive mg]; Milgrom PRD(06)gq [in acoustic spacetime]; > s.a. inertia [fluctuations]; vacuum.
@ Effective mass: Chang et al PRL(14) + news phys(14)may [transition from bare mass to effective mass in a BEC, and time scales].
@ Gravitational origin: Novello a1003 [fermions, based on the Mach principle]; Novello CQG(11)-a1008; Novello & Bittencourt a1111; Szabados a1603, GRG(18)-a1802 [energy density of the the Einstein-Higgs-Maxwell system].
@ Mass generation in quantum field theory: Drechsler & Tann FP(99) [broken Weyl symmetry]; Deser & Tekin CQG(02)ht [in 2+1 dimensions]; Jaramillo & Aldaya MPLA(02)ht [diff-invariant theories]; Dvali et al PRL(06)ht/05 [topological, 4D]; Wilczek MPLA(06); Sevostyanov ht/06, IJMPA(08)ht/06 [gauge theory]; Nesbet a0711 [fermions, from self-interaction]; Sevostyanov IJMPA(08) [comparing mechanisms]; Marchuk NCB(11)-a1009 [for fermions]; Winterberg PS(12) [Planck-mass plasma]; Kronfeld a1209-in [and lattice gauge theory]; Novello & Bittencourt PRD(12)-a1209, Okun MPLA(12)-a1212 [origin of the mass of the Higgs boson]; Frezzotti & Rossi PRD(15)-a1402, a1811 [spontaneous chiral symmetry breaking]; Capitani et al a1901 [for fermions, lattice evidence].
@ Electromagnetic: in Rohrlich 65 [renormalization]; Haeffner phy/00 [??]; Ray Apeiron(07)phy/04 [Lorentz's conjecture]; Wanas IJGMP(07)gq; Bhadra PhD(07)-a0710 [overview]; > s.a. inertia.

In Special Relativity and Quantum Theory > s.a. special relativity / particles [unstable, mass uncertainty]; particle types; photon; renormalization.
* Predictions: Mass-energy equivalence, m = γm0, E = mc2; Examples of application are in particle decay or the Breit-Wheeler process.
* Remark: It is misleading to say that m converts to E (could I substitute "inertia" for "mass" here? mass is energy).
@ Mass and E = mc2: Poincaré AN(1900) [precursor]; Einstein AdP(05), BAMS(35), reprinted BAMS(00) [elementary]; Bainbridge PR(33) [verification]; Feigenbaum & Mermin AJP(88)jan; Okun PT(89)jun; Sandin AJP(91)nov; Kim qp/00-proc; Bodanis 00; Luetzelschwab AJP(03)sep [apparatus to measure]; Thomas EJP(05); Rainville et al Nat(05)dec + sr(05)dec + pn(06)jan [direct measurements]; Baierlein AJP(07)apr; Okun PU(08)-a0808, AJP(09)may; Okun a1010 [ammò]; Silagadze CJP(14)-a1103; Krause & Lee EJP-a1608 [implications for coupling of internal and center-of-mass dynamics]; Walstad a1711 [without special relativity]; Lebed IJMPD(19)-a1910-MGXV [breakdown from quantum effects].
@ History: Hecht AJP(09)sep, AJP(11)jun, TPT(12) [Einstein on mass and energy]; Pandya a0705; Boughn & Rothman a1108 + news pw(11)aug [Hasenohrl's 1904 calculation]; Weinstein a1204 [Poincaré and Einstein]; Weinstein a1205; Boughn EPJH(13)-a1303 [Fritz Hasenohrl]; Field EJP(14)-a1407 [Einstein and Planck in 1905-1906]; Klevgard a1412 [Einstein 1903-1925].
@ Derivations: Rohrlich AJP(90)apr [simple]; Gould ap/05/ApJ [without special relativity]; Ohanian SHPMP(09)-a0805, Mermin SHPMP(11), comment Ohanian SHPMP(12) [Einstein]; Ohanian AJP(12)dec [Felix Klein's proof].
@ In field theory: Faraoni & Cooperstock EJP(98)phy; Frasca a0807 [massive solutions of massless theories]; > s.a. yang-mills gauge theories.
@ In quantum mechanics: Jaekel & Reynaud EPL(97)qp/96 [as observable]; Bohm & Harshman NPB(00)hp [resonances, and Gamow vectors];
Greenberger a1011-conf [as observable, and time]; Holt a1406 [absolute mass is not observable, relational mass is].
@ Other topics: Horwitz & Belenkiy FP(02) [Schopenhauer & Hegel]; Cushman & van der Kallen DG&A(06)mp/05 [group theoretic interpretation]; Zenczykowski qp/05 [for quarks]; Benghi Pinto EJP(07) [bare vs effective mass]; Lebed JPCS(14)-a1404 [breakdown of the equivalence between gravitational mass and energy for a composite quantum body]; > s.a. superselection rules [mass superselection rule].

And Gravitation > s.a. bimetric theory; equivalence principle; gravitational energy; test-particle motion.
* Newtonian theory: The total (gravitational, active) mass inside a surface S can be defined, using the gravitational potential φ, by

M = S φ, j dS j .

* General relativity: Several definitions have been given, some of which are equivalent in general relativity but not in other theories.
* Kaluza-Klein: In the 4D reduction of the theory, the effective mass of a particle can vary along its worldline.
@ References: Rosen & Cooperstock CQG(92); Toussaint GRG(00)gq/99 [m as translation charge]; Petkov gq/01 [distance dependence of ma?]; Ehlers et al PRD(05) [and pressure]; Bel & Martin-Martin a0906 [proper mass]; > s.a. black holes; cosmological constant [minimum mass].
@ Inertial vs gravitational mass: Widom gq/06; Ohanian a1010 [in scalar-vector theories]; Zych et al PRD(19)-a1808 [for composite systems].

Related Topics > s.a. Center of Mass; schwarzschild spacetime; schwarzschild-de sitter spacetime; stars.
* Negative mass: While a positive gravitational mass attracts everything, a negative one repels everything; A positive and a negative mass will chase each other (conserving momentum); To avoid runaway motion, negative mass systems can not coexist with positive mass ones, and will have negative temperatures.
@ Negative mass: NS(90)mar17, 54-56; Price AJP(93)mar; Pollard & Dunning-Davies NCB(95); Cavalleri & Tonni NCB(97) [self-acceleration]; Manko SPMS-a1303 [exact solutions]; Hammond a1308 [physical consequences]; Madarász et al a1407 [existence of negative-mass particles implies the existence of tachyons]; Dias & Gonçalves AJP(14)oct [application to Helium-balloon-type dynamics]; Paranjape pt(17)may [and cosmology].
@ And geometry: Tolksdorf mp/02, mp/02 [mass as curvature].
@ Related topics: Donoghue & Holstein EJP(87) [T dependence?]; Mannheim GRG(93) [dynamical]; Wesson MPLA(04) [quantized?]; McCulloch JBIS-a0712 [cosmology and variations of inertial mass]; Coraddu & Mignemi EPL(10)-a0911 [in DSR]; Mashhoon & Wesson AdP(12)-a1106 [mass from extra dimension, and Mach's principle]; Kubiak v1301, AfrRP(14), v1403, v1404 [effective mass tensor in general relativity]; Lebed CEJP(13)-a1311 [inequivalence of the gravitational mass and energy of a quantum body]; McQueen Syn(15)-a1501 [additivity in Newtonian physics and special relativity]; > s.a. inertia.