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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
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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.
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186:. 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
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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.
266:
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
107:
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
422:
324:
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
487:
LĂĽders, G. (1954). "On the
Equivalence of Invariance under Time Reversal and under Particle-Antiparticle Conjugation for Relativistic Field Theories".
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was believed to be preserved by all physical phenomena, but in the 1960s that was later found to be false too, which implied, by
64:(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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have yielded negative results. A detailed tabulation of these results was given in 2011 by
Kostelecky and Russell.
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of antiparticles as the corresponding particles traveling backwards in time. This interpretation requires a slight
923:
Berg, Marcus; Dewitt-Morette, CĂ©cile; Gwo, Shangjr; Kramer, Eric (2001). "The Pin Groups in
Physics: C, P and T".
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can be extended to a
Euclidean theory, defined by translating all the operators to imaginary time using the
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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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182:, it would be possible for a 180° rotation to reverse the direction of time and of
45:
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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
30:"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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170:. This can be interpreted as a rotation of the time axis into the
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371:
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423:"This is the One Symmetry That the Universe Must Never Violate"
442:
Schwinger, Julian (1951). "The Theory of Quantized Fields I".
201:, which is well-defined only under the following assumptions:
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Bell, John Stewart (1955). "Time reversal in field theory".
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Gravitational interaction of antimatter § CPT theorem
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gave a more general proof in 1958 using the framework of
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The CPT theorem can be generalized to take into account
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Efforts during the late 1950s revealed the violation of
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Our universe may have a twin that runs backward in time
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Pauli, W.; Rosenfelf, L.; Weisskopf, V., eds. (1955).
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rotation parameter. If this rotation parameter were
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in the interaction of quantum fields. Subsequently,
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Background information on Lorentz and CPT violation
243:, so that any state can be rotated by 180 degrees.
250:change by a sign under two CPT reflections, while
193:This defines a CPT transformation if we adopt the
962:Charge, Parity, and Time Reversal (CPT) Symmetry
401:KosteleckĂ˝, V. A. (1998). "The Status of CPT".
538:John Stuart Bell and Twentieth-Century Physics
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111:. These proofs are based on the principle of
8:
999:– 8-component theory for fermions in which
611:Paul Sutter, Live Science. March 16th, 2022
334:experimental searches for Lorentz violation
254:do not. This fact can be used to prove the
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978:CPT Invariance Tests in Neutral Kaon Decay
138:, and there were well-known violations of
38:Charge, parity, and time reversal symmetry
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872:at Theoretical Physics Indiana University
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510:Niels Bohr and the Development of Physics
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320:CPT violations would be expected by some
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842:PCT, spin and statistics, and all that
97:connection between spin and statistics
7:
1007:property in these class of theories.
816:Introduction to Elementary Particles
797:Discrete symmetries and CP violation
195:Feynman–Stueckelberg interpretation
1011:This Particle Breaks Time Symmetry
25:
686:"CPT Symmetry and Its Violation"
212:The vacuum is Lorentz invariant;
925:Reviews in Mathematical Physics
818:. Wiley, John & Sons, Inc.
684:Lehnert, Ralf (November 2016).
142:as well. For a short time, the
134:by phenomena that involve the
125:axiomatic quantum field theory
1:
1156:Theorems in quantum mechanics
655:10.1103/PhysRevLett.89.231602
332:The overwhelming majority of
274:reversed (corresponding to a
262:Consequences and implications
158:Derivation of the CPT theorem
814:Griffiths, David J. (1987).
231:of the Hamiltonian, and the
215:The energy is bounded below.
799:. Oxford University Press.
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947:10.1142/S0129055X01000922
878:Reviews of Modern Physics
740:Reviews of Modern Physics
535:Whitaker, Andrew (2016).
190:plane could be included.
908:10.1103/RevModPhys.83.11
771:10.1103/RevModPhys.83.11
83:must have CPT symmetry.
624:Physical Review Letters
543:Oxford University Press
256:spin-statistics theorem
48:under the simultaneous
1059:C, P, and T symmetries
588:10.1098/rspa.1955.0189
466:10.1103/PhysRev.82.914
844:. Benjamin/Cummings.
568:Proc. R. Soc. Lond. A
241:rotational invariance
229:commutation relations
219:When the above hold,
199:analytic continuation
166:in a fixed direction
117:principle of locality
95:in 1951 to prove the
58:parity transformation
1146:Quantum field theory
795:Sozzi, M.S. (2008).
350:Quantum field theory
286:(corresponding to a
74:quantum field theory
900:2011RvMP...83...11K
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702:2016Symm....8..114L
647:2002PhRvL..89w1602G
580:1955RSPSA.231..479B
458:1951PhRv...82..914S
1125:Symmetry (physics)
967:2011-08-05 at the
711:10.3390/sym8110114
379:scientific results
359:Charge conjugation
237:Lorentz invariance
233:Lorentz generators
113:Lorentz invariance
54:charge conjugation
32:The C.P.T. Theorem
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851:978-0-691-07062-9
825:978-0-471-60386-3
806:978-0-19-929666-8
574:(1187): 479–495.
346:Poincaré symmetry
326:compact dimension
235:, guarantee that
207:Lorentz invariant
109:John Stewart Bell
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225:Hamiltonian
162:Consider a
144:CP-symmetry
99:. In 1954,
81:Hamiltonian
66:CPT theorem
18:PCT theorem
1140:Categories
1079:T-symmetry
1074:P-symmetry
1069:C-symmetry
1019:Veritasium
497:(5): 1–17.
389:References
363:T-symmetry
304:pin groups
284:antimatter
152:T-symmetry
140:C-symmetry
136:weak force
132:P-symmetry
1120:Pin group
1115:Chirality
1017:video by
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884:(1): 11.
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720:2073-8994
596:123577175
474:121971249
176:imaginary
154:as well.
78:Hermitian
60:(P), and
1151:Symmetry
1001:T-parity
965:Archived
840:(1964).
690:Symmetry
663:12484997
522:56040984
340:See also
309:In 2002
248:fermions
239:implies
121:Res Jost
115:and the
42:symmetry
1015:YouTube
916:3236027
896:Bibcode
789:Sources
779:3236027
759:Bibcode
698:Bibcode
671:9409237
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272:momenta
87:History
76:with a
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377:IKAROS
288:charge
280:matter
268:parity
252:bosons
227:. The
72:local
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951:S2CID
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912:S2CID
886:arXiv
775:S2CID
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403:arXiv
56:(C),
846:ISBN
836:and
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659:PMID
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518:LCCN
372:kaon
370:and
361:and
348:and
180:real
103:and
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868:by
767:doi
735:CPT
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651:doi
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188:x-y
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