Mass  

In General > s.a. equivalence principle; newtonian gravity.
* 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).

The "Origin'' of Mass > s.a. Higgs Mechanism; mach's principle; quantum particles.
* 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.
@ 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.
@ 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, ht/06 [gauge theory]; Nesbet a0711 [fermions, from self-interaction]; Sevostyanov IJMPA(08) [comparing mechanisms].
@ Electromagnetic: in Rohrlich 65 [renormalization]; Haeffner phy/00 [??]; Ray Apeiron(07)phy/04 [Lorentz's conjecture]; Wanas IJGMP(07)gq; Bhadra a0710-PhD [overview]; > s.a. inertia.

In Special Relativity and Quantum Theory > s.a. [special relativity]; particles [unstable, mass uncertainty].
* Predictions: Mass-energy, m = m0, E = mc2.
* Remark: 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]; Feigenbaum & Mermin AJP(88)jan; Okun PT(89)jun; Sandin AJP(91)nov; Kim qp/00-in; 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; Pandya a0705 [history and response to criticism]; Okun PU(08)-a0808, AJP(09)may; Hecht AJP(09)sep [Einstein on mass and energy].
@ Derivations: Rohrlich AJP(90)apr [simple]; Gould ap/05/ApJ [without special relativity]; Ohanian SHPMP(09)-a0805 [Einstein's attempts].
@ 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].

And Gravitation > s.a. 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 , by

M = S , 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]; Widom gq/06 [inertial and gravitational]; Bel & Martin-Martin a0906 [proper mass]; > s.a. black holes; cosmological constant [minimum mass].

Negative mass > s.a. bimetric theory; schwarzschild spacetime.
* Properties: 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.
@ References: NS(90)mar17, p54-56; Price AJP(93)mar; Pollard & Dunning-Davies NCB(95); Cavalleri & Tonni NCB(97) [self-acceleration].

References > s.a. Center of Mass; particle types; photon; renormalization; stars.
@ I: Nambu ThSc(92)may [symmetry breaking].
@ General: Jammer 61; Pietschmann pr(86); Okun PT(89)jun; Jammer 00; Roche EJP(05); Okun 09; > s.a. physical theories.
@ 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].
@ 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].
@ 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 a0712 [cosmology and variations of inertial mass]; > s.a. inertia.

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