Mass| 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 = 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];
Tsarouchas a1703 [from the distribution of matter in the Universe];
> 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];
Baskal et al a1911
[from Heisenberg's uncertainty relation];
Pérez & Ribisi a2101 [from Maxwell equations];
Coffey a2102 [ontology of mass and energy].
@ 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;
tachyons [imaginary mass].
* 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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