Mass |

**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** = *m*_{i} **a**.

* __Gravitational mass__:
The active and passive gravitational masses are defined by

**F**_{grav} =
*m*_{p}** g** ,** g**(

* __Relationships__: In
Newtonian mechanics, the two gravitational ones are
proportional as a consequence of the third law, *m*_{a} = *m*_{p} =
*m*_{g} – an inequality would
imply a violation of momentum conservation; The
principle of equivalence states the proportionality of *m*_{i} and *m*_{g} (specifically, *m*_{p}).

@ __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.

* __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 *m*_{e} = 4*U*/3*c*^{2} appearing
in the Abraham-Lorentz equation (> see radiation); For
an accelerated charged particle,
the measured mass would be *m* = *m*_{0} + *m*_{e};
Note that, unless one uses
a cutoff, for a point particle *m*_{e} = ∞,
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 *m*_{g}];
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.

@ __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 [spontaneous chiral symmetry breaking].

@ __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* = *γm*_{0}, *E* = *mc*^{2}; 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 = mc__

@

@

@

@

@

**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} d*S*^{ 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 *m*_{a}?]; 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].

**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.

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