31:(plus or minus) for a set of quantities, in a case where the choice of sign is arbitrary. "Arbitrary" here means that the same physical system can be correctly described using different choices for the signs, as long as one set of definitions is used consistently. The choices made may differ between authors. Disagreement about sign conventions is a frequent source of confusion, frustration, misunderstandings, and even outright errors in scientific work. In general, a sign convention is a special case of a choice of
873:. The sign of the Ricci tensor does not change, because the two sign conventions concern the sign of the Riemann tensor. The second definition just compensates the sign, and it works together with the second definition of the Riemann tensor (see e.g. Barrett O'Neill's Semi-riemannian geometry).
286:
407:
81:. (Throughout this article, the signs of the eigenvalues of the metric are displayed in the order that presents the timelike component first, followed by the spacelike components). A similar convention is used in higher-dimensional relativistic theories; that is,
165:
292:
871:
805:
746:
521:
467:
1053:
1014:
1193:
960:
915:
1177:
1123:
It is often considered good form to state explicitly which sign convention is to be used at the beginning of each book or article.
281:{\textstyle {\begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}}}
564:
535:
402:{\textstyle {\begin{pmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}}
1210:
974:
591:
89:. A choice of signature is associated with a variety of names, physics discipline, and notable graduate-level textbooks:
1068:
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1132:
600:
661:
1093:
817:
751:
692:
1163:
1109:
967:
929:
473:
422:
1021:
982:
1187:
1168:
1137:
1119:
assigns a positive focal length to concave mirrors and a negative focal length to convex mirrors.
643:
150:
145:
120:
94:
66:
28:
1173:
934:
626:
32:
1097:
141:
70:
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654:
548:
1155:
1105:
1086:
918:
808:
686:
39:
1204:
1116:
883:
414:
158:
38:
Sometimes, the term "sign convention" is used more broadly to include factors of the
1159:
1142:
1061:
963:
682:
610:
665:(Wald) (Wald changes signature to the timelike convention for Chapter 13 only)
544:
131:
126:
1101:
1089:, such as the weight of the determinant of the covariant metric tensor.
20:
1072:
16:
Agreed-upon meaning of a physical quantity being positive or negative
1064:(in fact dictated by the choice of sign for time-dependence).
973:
Time dependence of a positive-frequency wave (see, e.g., the
651:
Spacetime and
Geometry: An Introduction to General Relativity
104:
814:
In fact, the second definition of the Ricci tensor is
476:
425:
301:
295:
174:
168:
111:
1024:
985:
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1047:
1008:
954:
909:
865:
799:
740:
515:
461:
401:
280:
811:, these two definitions differ by a minus sign.
607:Gravitation: an introduction to current research
1172:. San Francisco: W. H. Freeman. p. cover.
8:
1192:: CS1 maint: multiple names: authors list (
27:is a choice of the physical significance of
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296:
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169:
167:
886:in frames of reference and proper time:
138:Subject area primarily using convention
1185:
866:{\displaystyle R_{ab}\,={R_{acb}}^{c}}
800:{\displaystyle R_{ab}\,=R^{c}{}_{abc}}
741:{\displaystyle R_{ab}\,=R^{c}{}_{acb}}
597:The Mathematical Theory of Black Holes
748:, whereas others use the alternative
685:is defined as the contraction of the
7:
583:Graduate textbooks using convention
516:{\textstyle m^{2}=-p^{\mu }p_{\mu }}
52:, rather than just choices of sign.
1060:The sign for the imaginary part of
689:. Some authors use the contraction
462:{\textstyle m^{2}=p^{\mu }p_{\mu }}
93:Comparison of metric signatures in
14:
894:for past is universally accepted.
617:Introducing Einstein's relativity
1048:{\displaystyle \,e^{+j\omega t}}
1009:{\displaystyle \,e^{-i\omega t}}
809:symmetries of the Riemann tensor
35:for the case of one dimension.
1:
975:electromagnetic wave equation
1085:The sign of the weight of a
647:(Misner, Thorne, and Wheeler
1115:A sign convention used for
1080:first law of thermodynamics
1067:The signs of distances and
1016:(mainly used by physicists)
527:Common names of convention
1227:
1133:Orientation (vector space)
1055:(mainly used by engineers)
601:Subrahmanyan Chandrasekhar
968:classical electrodynamics
629:& Anthony N. Lasenby)
582:
526:
412:
156:
137:
119:
110:
103:
100:
1078:The sign of work in the
955:{\displaystyle \,F_{ab}}
1094:passive sign convention
1071:of optical surfaces in
1164:John Archibald Wheeler
1110:electrical engineering
1049:
1010:
956:
911:
877:Other sign conventions
867:
801:
742:
517:
463:
403:
282:
1050:
1011:
957:
930:field strength tensor
912:
868:
802:
743:
592:Landau & Lifshitz
518:
464:
404:
283:
1211:Mathematical physics
1022:
983:
935:
910:{\displaystyle \pm }
901:
882:The sign choice for
818:
752:
693:
625:(Michael P. Hobson,
474:
423:
293:
166:
97:
1138:Symmetry (physics)
1069:radii of curvature
1045:
1006:
952:
907:
863:
797:
738:
662:General Relativity
623:General relativity
513:
459:
399:
393:
278:
272:
121:Spacetime interval
95:general relativity
92:
674:
673:
627:George Efstathiou
101:Metric signature
33:coordinate system
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924:The sign of the
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573:Pauli convention
541:"Mostly minuses"
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142:Particle physics
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71:metric signature
61:Metric signature
51:
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44:
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1092:The active and
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926:electric charge
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890:for future and
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655:Sean M. Carroll
634:
619:(Ray D'Inverno)
578:
570:"Mostly pluses"
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551:sign convention
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25:sign convention
17:
12:
11:
5:
1224:
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1156:Charles Misner
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1117:curved mirrors
1113:
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1087:tensor density
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964:gauge theories
949:
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919:Dirac equation
906:
897:The choice of
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687:Riemann tensor
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157:Corresponding
154:
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139:
135:
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129:
124:
117:
116:
109:
102:
73:can be either
62:
59:
57:
54:
40:imaginary unit
15:
13:
10:
9:
6:
4:
3:
2:
1223:
1212:
1209:
1208:
1206:
1195:
1189:
1181:
1179:0-7167-0344-0
1175:
1171:
1170:
1165:
1161:
1157:
1153:
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1148:
1144:
1141:
1139:
1136:
1134:
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1126:
1124:
1118:
1114:
1111:
1107:
1103:
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1091:
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1084:
1081:
1077:
1074:
1070:
1066:
1063:
1059:
1040:
1037:
1034:
1031:
1027:
1018:
1001:
998:
995:
992:
988:
979:
978:
976:
972:
969:
965:
947:
944:
940:
931:
927:
923:
920:
904:
896:
893:
889:
885:
881:
880:
876:
874:
858:
851:
848:
845:
841:
835:
829:
826:
822:
812:
810:
807:. Due to the
792:
789:
786:
777:
773:
769:
763:
760:
756:
733:
730:
727:
718:
714:
710:
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697:
688:
684:
676:
664:
663:
659:
656:
652:
649:
646:
645:
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628:
624:
621:
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608:
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569:
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558:
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543:
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533:
532:
531:
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508:
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498:
494:
490:
487:
482:
478:
470:
454:
450:
444:
440:
436:
431:
427:
419:
417:relationship
416:
415:four momentum
411:
394:
388:
383:
378:
373:
366:
361:
356:
351:
344:
339:
334:
329:
322:
317:
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273:
267:
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234:
229:
224:
217:
212:
207:
204:
199:
192:
187:
182:
177:
171:
162:
160:
159:metric tensor
155:
152:
149:
147:
143:
140:
136:
133:
130:
128:
125:
122:
118:
99:
96:
90:
87:(−,+,+,+,...)
83:(+,−,−,−,...)
72:
68:
60:
55:
53:
41:
36:
34:
30:
26:
22:
1167:
1160:Kip S Thorne
1143:Gauge theory
1122:
1062:permittivity
891:
887:
813:
683:Ricci tensor
680:
660:
650:
642:
622:
616:
606:
596:
64:
37:
24:
18:
1169:Gravitation
644:Gravitation
123:convention
1149:References
567:convention
565:East coast
538:convention
536:West coast
151:Relativity
146:Relativity
67:relativity
56:Relativity
1188:cite book
1038:ω
999:ω
993:−
905:±
677:Curvature
611:L. Witten
509:μ
499:μ
491:−
455:μ
445:μ
305:−
265:−
235:−
205:−
132:spacelike
113:(−,+,+,+)
106:(+,−,−,−)
79:(−,+,+,+)
75:(+,−,−,−)
1205:Category
1166:(1973).
1127:See also
549:Lifshitz
127:timelike
1102:voltage
1098:current
917:in the
21:physics
1176:
1162:&
1073:optics
545:Landau
69:, the
1106:power
413:Mass–
29:signs
1194:link
1174:ISBN
1104:and
966:and
884:time
681:The
144:and
45:and
23:, a
1108:in
1096:of
977:):
962:in
85:or
77:or
65:In
19:In
1207::
1190:}}
1186:{{
1158:;
1100:,
928:,
1196:)
1182:.
1112:.
1082:.
1075:.
1041:t
1035:j
1032:+
1028:e
1002:t
996:i
989:e
970:.
948:b
945:a
941:F
921:.
892:−
888:+
859:c
852:b
849:c
846:a
842:R
836:=
830:b
827:a
823:R
793:c
790:b
787:a
778:c
774:R
770:=
764:b
761:a
757:R
734:b
731:c
728:a
719:c
715:R
711:=
705:b
702:a
698:R
657:)
653:(
613:)
609:(
603:)
599:(
547:–
505:p
495:p
488:=
483:2
479:m
451:p
441:p
437:=
432:2
428:m
395:)
389:1
384:0
379:0
374:0
367:0
362:1
357:0
352:0
345:0
340:0
335:1
330:0
323:0
318:0
313:0
308:1
299:(
274:)
268:1
260:0
255:0
250:0
243:0
238:1
230:0
225:0
218:0
213:0
208:1
200:0
193:0
188:0
183:0
178:1
172:(
49:π
47:2
43:i
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