1236:
963:
561:
299:
1484:
1231:{\displaystyle {\frac {{\mathcal {D}}X}{ds}}={\frac {DX}{ds}}+\left(X,{\frac {DV}{ds}}\right){\frac {V}{(V,V)}}-{\frac {(X,V)}{(V,V)}}{\frac {DV}{ds}}-\left(V,{\frac {DV}{ds}}\right){\frac {(X,V)}{(V,V)^{2}}}V,}
1558:
714:
438:
1583:
1568:
49:
in the frame is due to the presence of mass/energy density and not due to arbitrary spin or rotation of the frame. It was discovered by Fermi in 1921 and rediscovered by Walker in 1932.
402:
73:
unit vector field in the frame field, are used to define non-inertial and non-rotating frames, by stipulating that the Fermi–Walker derivatives should vanish. In the special case of
757:
154:
787:
2196:
346:
902:
955:
146:
642:
591:
1374:
836:
113:
1330:
1298:
1271:
611:
2086:
1856:
926:
864:
1381:
2175:
838:
as defining an axis in the co-moving coordinate system, then any system transforming with proper time is said to be undergoing Fermi–Walker transport.
429:
806:
2054:
1489:
1849:
1807:
1781:
1749:
1699:; Michel, L.; Telegdi, V. L. (1959). "Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field".
647:
2002:
556:{\displaystyle {\frac {D_{F}a^{\tau }}{ds}}=2\mu (F^{\tau \lambda }-u^{\tau }u_{\sigma }F^{\sigma \lambda })a_{\lambda },}
1842:
2139:
1795:
1970:
1943:
1605:"Circular Holonomy, Clock Effects and Gravitoelectromagnetism: Still Going Around in Circles After All These Years"
1741:
62:
2076:
354:
294:{\displaystyle {\frac {D_{F}X}{ds}}={\frac {DX}{ds}}-\left(X,{\frac {DV}{ds}}\right)V+(X,V){\frac {DV}{ds}},}
2160:
2022:
1578:
790:
719:
1604:
2165:
2134:
1997:
1918:
762:
2124:
1948:
1908:
1708:
319:
2099:
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1953:
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1913:
1890:
1866:
418:
58:
2155:
2032:
2027:
1980:
1818:
1771:
1696:
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1616:
869:
42:
34:
931:
432:
for spin precession of electron in an external electromagnetic field can be written as follows:
122:
620:
569:
2170:
2119:
2064:
2044:
1930:
1803:
1777:
1759:
1745:
1338:
814:
794:
422:
38:
2109:
2049:
1975:
1716:
83:
66:
17:
1303:
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2129:
2039:
1985:
1885:
1791:
1767:
1733:
614:
596:
70:
811:
A coordinate system co-moving with a particle can be defined. If we take the unit vector
1712:
2059:
2014:
1992:
1880:
1479:{\displaystyle \left(V,{\frac {DV}{ds}}\right)={\frac {1}{2}}{\frac {d}{ds}}(V,V)=0\ ,}
911:
849:
74:
1273:
is not constant, it can be derived by taking the previous equation, and dividing each
2190:
1241:
Except for the last term, which is new, and basically caused by the possibility that
414:
2094:
1573:
413:
is Fermi–Walker transported along the curve. Vectors perpendicular to the space of
2114:
2104:
1763:
1729:
1720:
1965:
1834:
905:
46:
1823:
1677:
1621:
421:, e.g., polarization vectors, under Fermi–Walker transport experience
2069:
1553:{\displaystyle {\frac {{\mathcal {D}}X}{ds}}={\frac {D_{F}X}{ds}}.}
77:, the Fermi–Walker derivatives reduce to covariant derivatives.
1838:
807:
Proper reference frame (flat spacetime) § Comoving tetrads
1740:. Course of Theoretical Physics. Vol. 2 (4th ed.).
1498:
972:
1817:
Kocharyan, A. A. (2004). "Geometry of
Dynamical Systems".
1671:
Kocharyan, A. A. (2004). "Geometry of
Dynamical Systems".
69:
vector fields in a frame field, taken with respect to the
1584:
Transition from
Newtonian mechanics to general relativity
1569:
Basic introduction to the mathematics of curved spacetime
709:{\displaystyle a^{\tau }a_{\tau }=-u^{\tau }u_{\tau }=-1}
65:. In general relativity, Fermi–Walker derivatives of the
1376:, then we recover the Fermi–Walker differentiation:
61:, Fermi–Walker differentiation is a generalization of
1647:
1492:
1384:
1341:
1306:
1279:
1247:
966:
934:
914:
872:
852:
846:
Fermi–Walker differentiation can be extended for any
817:
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722:
650:
623:
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572:
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322:
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125:
86:
115:
sign convention, this is defined for a vector field
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908:vector). This is defined for a vector field
27:Mathematical technique in general relativity
2197:Mathematical methods in general relativity
1857:
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1620:
1603:Bini, Donato; Jantzen, Robert T. (2002).
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124:
85:
842:Generalised Fermi–Walker differentiation
1800:The Large Scale Structure of Space-time
1595:
397:{\displaystyle {\frac {D_{F}X}{ds}}=0,}
2055:Atomic, molecular, and optical physics
791:electromagnetic field strength tensor
7:
752:{\displaystyle u^{\tau }a_{\tau }=0}
1648:Bargmann, Michel & Telegdi 1959
25:
1659:Misner, Thorne & Wheeler 1973
613:are polarization four-vector and
316:is the covariant derivative, and
782:{\displaystyle F^{\tau \sigma }}
430:Bargmann–Michel–Telegdi equation
428:Using the Fermi derivative, the
2176:Timeline of physics discoveries
341:{\displaystyle (\cdot ,\cdot )}
1802:. Cambridge University Press.
1738:The Classical Theory of Fields
1461:
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1354:
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644:is four-velocity of electron,
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265:
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135:
129:
102:
87:
1:
801:Co-moving coordinate systems
53:Fermi–Walker differentiation
18:Fermi–Walker differentiation
2140:Quantum information science
1742:Butterworth–Heinemann
897:{\displaystyle (V,V)\neq 0}
793:. The right side describes
2213:
1971:Classical electromagnetism
950:{\displaystyle \gamma (s)}
804:
348:is the scalar product. If
141:{\displaystyle \gamma (s)}
1721:10.1103/PhysRevLett.2.435
637:{\displaystyle u^{\tau }}
586:{\displaystyle a^{\tau }}
63:covariant differentiation
2077:Condensed matter physics
1636:Hawking & Ellis 1973
1369:{\displaystyle (V,V)=-1}
831:{\displaystyle v^{\mu }}
1701:Physical Review Letters
2161:Nobel Prize in Physics
2023:Relativistic mechanics
1579:Arthur Geoffrey Walker
1554:
1480:
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638:
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587:
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407:then the vector field
398:
342:
295:
142:
109:
108:{\displaystyle (-+++)}
31:Fermi–Walker transport
2166:Philosophy of physics
1555:
1481:
1371:
1327:
1325:{\displaystyle (V,V)}
1295:
1293:{\displaystyle V^{2}}
1268:
1266:{\displaystyle (V,V)}
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2125:Mathematical physics
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606:{\displaystyle \mu }
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155:
123:
84:
59:Lorentzian manifolds
2100:Atmospheric physics
1939:Classical mechanics
1867:branches of physics
1792:Hawking, Stephen W.
1713:1959PhRvL...2..435B
419:Minkowski spacetime
2156:History of physics
1796:Ellis, George F.R.
1760:Misner, Charles W.
1615:(9–11): 983–1008.
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310:is four-velocity,
291:
138:
105:
35:general relativity
2184:
2183:
2171:Physics education
2120:Materials science
2087:Interdisciplinary
2045:Quantum mechanics
1776:. W. H. Freeman.
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1220:
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1136:
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989:
921:{\displaystyle X}
859:{\displaystyle V}
795:Larmor precession
474:
423:Thomas precession
383:
286:
240:
206:
183:
57:In the theory of
39:coordinate system
37:used to define a
16:(Redirected from
2204:
2110:Chemical physics
2050:Particle physics
1976:Classical optics
1859:
1852:
1845:
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1828:
1826:
1824:astro-ph/0411595
1813:
1787:
1768:Wheeler, John A.
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1678:astro-ph/0411595
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2130:Medical physics
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2040:Nuclear physics
2009:
2003:Non-equilibrium
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1609:Nuovo Cimento B
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615:magnetic moment
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415:four-velocities
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75:inertial frames
55:
43:reference frame
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1993:Thermodynamics
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1764:Thorne, Kip S.
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1734:Lifshitz, E.M.
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928:along a curve
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805:Main article:
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2135:Ocean physics
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2070:Modern optics
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2095:Astrophysics
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1730:Landau, L.D.
1704:
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1697:Bargmann, V.
1666:
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1914:Theoretical
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2105:Biophysics
1949:Analytical
1902:Approaches
1690:References
906:light-like
2065:Molecular
1966:Acoustics
1959:Continuum
1954:Celestial
1944:Newtonian
1931:Classical
1874:Divisions
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