283:
In order to preserve this symmetry, every violation of the combined symmetry of two of its components (such as CP) must have a corresponding violation in the third component (such as T); in fact, mathematically, these are the same thing. Thus violations in T-symmetry are often referred to as
317:
of cosmological size, could also lead to CPT violation. Non-unitary theories, such as proposals where black holes violate unitarity, could also violate CPT. As a technical point, fields with infinite spin could violate CPT symmetry.
175:. Reversing the direction of one axis is a reflection of space in any number of dimensions. If space has 3 dimensions, it is equivalent to reflecting all the coordinates, because an additional rotation of 180° in the
279:
inversion) — would evolve under exactly our physical laws. The CPT transformation turns our universe into its "mirror image" and vice versa. CPT symmetry is recognized to be a fundamental property of physical laws.
478:
255:
The implication of CPT symmetry is that a "mirror-image" of our universe — with all objects having their positions reflected through an arbitrary point (corresponding to a
96:
derived more explicit proofs, so this theorem is sometimes known as the Lüders–Pauli theorem. At about the same time, and independently, this theorem was also proved by
411:
313:
models, as well as by some other models that lie outside point-particle quantum field theory. Some proposed violations of
Lorentz invariance, such as a
476:
LĂĽders, G. (1954). "On the
Equivalence of Invariance under Time Reversal and under Particle-Antiparticle Conjugation for Relativistic Field Theories".
371:
1013:
953:
135:
was believed to be preserved by all physical phenomena, but in the 1960s that was later found to be false too, which implied, by
53:(T). CPT is the only combination of C, P, and T that is observed to be an exact symmetry of nature at the fundamental level. The
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322:
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have yielded negative results. A detailed tabulation of these results was given in 2011 by
Kostelecky and Russell.
186:
of antiparticles as the corresponding particles traveling backwards in time. This interpretation requires a slight
912:
Berg, Marcus; Dewitt-Morette, CĂ©cile; Gwo, Shangjr; Kramer, Eric (2001). "The Pin Groups in
Physics: C, P and T".
213:
69:
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can be extended to a
Euclidean theory, defined by translating all the operators to imaginary time using the
38:
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An elementary discussion of CPT violation is given in chapter 15 of this student level textbook
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Invariance under simultaneous charge conjugation, parity transformation and time reversal
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KosteleckĂ˝, V. Alan; Russell, Neil (2011). "Data tables for
Lorentz and CPT violation".
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says that CPT symmetry holds for all physical phenomena, or more precisely, that any
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can be a complex number with unit radius. The CPT invariance is not a theorem but a
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171:, it would be possible for a 180° rotation to reverse the direction of time and of
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610:
Greenberg, O. W. (2002). "CPT Violation
Implies Violation of Lorentz Invariance".
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proved that, with reasonable assumptions, CPT violation implies the breaking of
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Since a sequence of two CPT reflections is equivalent to a 360-degree rotation,
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The CPT theorem appeared for the first time, implicitly, in the work of
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Kongelige Danske
Videnskabernes Selskab, Matematisk-Fysiske Meddelelser
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KosteleckĂ˝, V. A.; Russell, N. (2011). "Data tables for
Lorentz and
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109:
19:"CPT theorem" redirects here. For the album by Greydon Square, see
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Ying, S. (2000). "Space--Time
Symmetry, CPT and Mirror Fermions".
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159:. This can be interpreted as a rotation of the time axis into the
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821:
236:
510:
416:
412:"This is the One Symmetry That the Universe Must Never Violate"
365:
268:
431:
Schwinger, Julian (1951). "The Theory of Quantized Fields I".
190:, which is well-defined only under the following assumptions:
240:
555:
Bell, John Stewart (1955). "Time reversal in field theory".
911:
360:
372:
Gravitational interaction of antimatter § CPT theorem
112:
gave a more general proof in 1958 using the framework of
291:
The CPT theorem can be generalized to take into account
119:
Efforts during the late 1950s revealed the violation of
598:
Our universe may have a twin that runs backward in time
496:
497:
Pauli, W.; Rosenfelf, L.; Weisskopf, V., eds. (1955).
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rotation parameter. If this rotation parameter were
108:
in the interaction of quantum fields. Subsequently,
855:
Background information on Lorentz and CPT violation
802:
232:, so that any state can be rotated by 180 degrees.
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239:change by a sign under two CPT reflections, while
182:This defines a CPT transformation if we adopt the
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721:
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951:Charge, Parity, and Time Reversal (CPT) Symmetry
250:
146:
390:KosteleckĂ˝, V. A. (1998). "The Status of CPT".
527:John Stuart Bell and Twentieth-Century Physics
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100:. These proofs are based on the principle of
988:– 8-component theory for fermions in which
783:
600:Paul Sutter, Live Science. March 16th, 2022
323:experimental searches for Lorentz violation
243:do not. This fact can be used to prove the
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967:CPT Invariance Tests in Neutral Kaon Decay
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127:, and there were well-known violations of
27:Charge, parity, and time reversal symmetry
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861:at Theoretical Physics Indiana University
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499:Niels Bohr and the Development of Physics
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309:CPT violations would be expected by some
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831:PCT, spin and statistics, and all that
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86:connection between spin and statistics
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996:property in these class of theories.
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805:Introduction to Elementary Particles
786:Discrete symmetries and CP violation
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184:Feynman–Stueckelberg interpretation
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1000:This Particle Breaks Time Symmetry
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14:
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675:"CPT Symmetry and Its Violation"
201:The vacuum is Lorentz invariant;
914:Reviews in Mathematical Physics
807:. Wiley, John & Sons, Inc.
673:Lehnert, Ralf (November 2016).
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131:as well. For a short time, the
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123:by phenomena that involve the
114:axiomatic quantum field theory
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1145:Theorems in quantum mechanics
644:10.1103/PhysRevLett.89.231602
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321:The overwhelming majority of
263:reversed (corresponding to a
251:Consequences and implications
147:Derivation of the CPT theorem
803:Griffiths, David J. (1987).
220:of the Hamiltonian, and the
204:The energy is bounded below.
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788:. Oxford University Press.
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10:
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936:10.1142/S0129055X01000922
867:Reviews of Modern Physics
729:Reviews of Modern Physics
524:Whitaker, Andrew (2016).
179:plane could be included.
897:10.1103/RevModPhys.83.11
760:10.1103/RevModPhys.83.11
72:must have CPT symmetry.
613:Physical Review Letters
532:Oxford University Press
245:spin-statistics theorem
37:under the simultaneous
1048:C, P, and T symmetries
577:10.1098/rspa.1955.0189
455:10.1103/PhysRev.82.914
833:. Benjamin/Cummings.
557:Proc. R. Soc. Lond. A
230:rotational invariance
218:commutation relations
208:When the above hold,
188:analytic continuation
155:in a fixed direction
106:principle of locality
84:in 1951 to prove the
47:parity transformation
1135:Quantum field theory
784:Sozzi, M.S. (2008).
339:Quantum field theory
275:(corresponding to a
63:quantum field theory
889:2011RvMP...83...11K
752:2011RvMP...83...11K
691:2016Symm....8..114L
636:2002PhRvL..89w1602G
569:1955RSPSA.231..479B
447:1951PhRv...82..914S
1114:Symmetry (physics)
956:2011-08-05 at the
700:10.3390/sym8110114
368:scientific results
348:Charge conjugation
226:Lorentz invariance
222:Lorentz generators
102:Lorentz invariance
43:charge conjugation
21:The C.P.T. Theorem
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840:978-0-691-07062-9
814:978-0-471-60386-3
795:978-0-19-929666-8
563:(1187): 479–495.
335:Poincaré symmetry
315:compact dimension
224:, guarantee that
196:Lorentz invariant
98:John Stewart Bell
59:Lorentz invariant
29:is a fundamental
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1086:CP symmetry
685:(11): 114.
503:McGraw-Hill
214:Hamiltonian
151:Consider a
133:CP-symmetry
88:. In 1954,
70:Hamiltonian
55:CPT theorem
1129:Categories
1068:T-symmetry
1063:P-symmetry
1058:C-symmetry
1008:Veritasium
486:(5): 1–17.
378:References
352:T-symmetry
293:pin groups
273:antimatter
141:T-symmetry
129:C-symmetry
125:weak force
121:P-symmetry
1109:Pin group
1104:Chirality
1006:video by
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880:0801.0287
873:(1): 11.
743:0801.0287
709:2073-8994
585:123577175
463:121971249
165:imaginary
143:as well.
67:Hermitian
49:(P), and
1140:Symmetry
990:T-parity
954:Archived
829:(1964).
679:Symmetry
652:12484997
511:56040984
329:See also
298:In 2002
237:fermions
228:implies
110:Res Jost
104:and the
31:symmetry
1004:YouTube
905:3236027
885:Bibcode
778:Sources
768:3236027
748:Bibcode
687:Bibcode
660:9409237
632:Bibcode
565:Bibcode
443:Bibcode
261:momenta
76:History
65:with a
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366:IKAROS
277:charge
269:matter
257:parity
241:bosons
216:. The
61:local
978:arXiv
940:S2CID
922:arXiv
901:S2CID
875:arXiv
764:S2CID
738:arXiv
656:S2CID
622:arXiv
581:S2CID
459:S2CID
392:arXiv
45:(C),
835:ISBN
825:and
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648:PMID
536:ISBN
507:LCCN
361:kaon
359:and
350:and
337:and
169:real
92:and
971:LBL
969:at
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932:doi
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857:by
756:doi
724:CPT
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