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CPT symmetry

December 29, 2022

"CPT theorem" redirects here. For the album by Greydon Square, see The C.P.T. Theorem.

Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (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.[1][2] The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.

History

The CPT theorem appeared for the first time, implicitly, in the work of Julian Schwinger in 1951 to prove the connection between spin and statistics.[3] In 1954, Gerhart Lüders and Wolfgang Pauli derived more explicit proofs,[4][5] so this theorem is sometimes known as the Lüders–Pauli theorem. At about the same time, and independently, this theorem was also proved by John Stewart Bell.[6][7] These proofs are based on the principle of Lorentz invariance and the principle of locality in the interaction of quantum fields. Subsequently, Res Jost gave a more general proof in 1958 using the framework of axiomatic quantum field theory.

Efforts during the late 1950s revealed the violation of P-symmetry by phenomena that involve the weak force, and there were well-known violations of C-symmetry as well. For a short time, the CP-symmetry was believed to be preserved by all physical phenomena, but in the 1960s that was later found to be false too, which implied, by CPT invariance, violations of T-symmetry as well.

Derivation of the CPT theorem

Consider a Lorentz boost in a fixed direction z. This can be interpreted as a rotation of the time axis into the z axis, with an imaginary rotation parameter. If this rotation parameter were real, it would be possible for a 180° rotation to reverse the direction of time and of z. 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 x-y plane could be included.

This defines a CPT transformation if we adopt the Feynman–Stueckelberg interpretation of antiparticles as the corresponding particles traveling backwards in time. This interpretation requires a slight analytic continuation, which is well-defined only under the following assumptions:

  1. The theory is Lorentz invariant;
  2. The vacuum is Lorentz invariant;
  3. The energy is bounded below.

When the above hold, quantum theory can be extended to a Euclidean theory, defined by translating all the operators to imaginary time using the Hamiltonian. The commutation relations of the Hamiltonian, and the Lorentz generators, guarantee that Lorentz invariance implies rotational invariance, so that any state can be rotated by 180 degrees.

Since a sequence of two CPT reflections is equivalent to a 360-degree rotation, fermions change by a sign under two CPT reflections, while bosons do not. This fact can be used to prove the spin-statistics theorem.

Consequences and implications

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 parity inversion), all momenta reversed (corresponding to a time inversion) and with all matter replaced by antimatter (corresponding to a charge inversion) — would evolve under exactly our physical laws. The CPT transformation turns our universe into its "mirror image" and vice versa.[8] CPT symmetry is recognized to be a fundamental property of physical laws.

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 CP violations.

The CPT theorem can be generalized to take into account pin groups.

In 2002 Oscar Greenberg proved that, with reasonable assumptions, CPT violation implies the breaking of Lorentz symmetry.[9]

CPT violations would be expected by some string theory 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 compact dimension 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.[10]

The overwhelming majority of experimental searches for Lorentz violation have yielded negative results. A detailed tabulation of these results was given in 2011 by Kostelecky and Russell.[11]

See also

References

  1. ^ Kostelecký, V. A. (1998). "The Status of CPT". arXiv:hep-ph/9810365.
  2. ^ "This is the One Symmetry That the Universe Must Never Violate". Forbes.
  3. ^ Schwinger, Julian (1951). "The Theory of Quantized Fields I". Physical Review. 82 (6): 914–927. Bibcode:1951PhRv...82..914S. doi:10.1103/PhysRev.82.914. S2CID 121971249.
  4. ^ Lüders, G. (1954). "On the Equivalence of Invariance under Time Reversal and under Particle-Antiparticle Conjugation for Relativistic Field Theories". Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddelelser. 28 (5): 1–17.
  5. ^ Pauli, W.; Rosenfelf, L.; Weisskopf, V., eds. (1955). Niels Bohr and the Development of Physics. McGraw-Hill. LCCN 56040984.
  6. ^ Whitaker, Andrew (2016). John Stuart Bell and Twentieth-Century Physics. Oxford University Press. ISBN 978-0198742999.
  7. ^ Bell, John Stewart (1955). "Time reversal in field theory". Proc. R. Soc. Lond. A. 231: 479–495. doi:10.1098/rspa.1955.0189.
  8. ^ Our universe may have a twin that runs backward in time Paul Sutter, Live Science. March 16th, 2022
  9. ^ Greenberg, O. W. (2002). "CPT Violation Implies Violation of Lorentz Invariance". Physical Review Letters. 89 (23): 231602. arXiv:hep-ph/0201258. Bibcode:2002PhRvL..89w1602G. doi:10.1103/PhysRevLett.89.231602. PMID 12484997. S2CID 9409237.
  10. ^ Lehnert, Ralf (November 2016). "CPT Symmetry and Its Violation". Symmetry. 8 (11): 114. doi:10.3390/sym8110114. ISSN 2073-8994.
  11. ^ Kostelecký, V. A.; Russell, N. (2011). "Data tables for Lorentz and CPT violation". Reviews of Modern Physics. 83 (1): 11–31. arXiv:0801.0287. Bibcode:2011RvMP...83...11K. doi:10.1103/RevModPhys.83.11. S2CID 3236027.

Sources

External links

  • by Alan Kostelecký at Theoretical Physics Indiana University
  • Kostelecký, V. Alan; Russell, Neil (2011). "Data tables for Lorentz and CPT violation". Reviews of Modern Physics. 83 (1): 11. arXiv:0801.0287. Bibcode:2011RvMP...83...11K. doi:10.1103/RevModPhys.83.11. S2CID 3236027.
  • Berg, Marcus; Dewitt-Morette, Cécile; Gwo, Shangjr; Kramer, Eric (2001). "The Pin Groups in Physics: C, P and T". Reviews in Mathematical Physics. 13 (8): 953–1034. arXiv:math-ph/0012006. doi:10.1142/S0129055X01000922. S2CID 119560073.
  • Charge, Parity, and Time Reversal (CPT) Symmetry 2011-08-05 at the Wayback Machine at LBL
  • CPT Invariance Tests in Neutral Kaon Decay at LBL
  • Ying, S. (2000). "Space--Time Symmetry, CPT and Mirror Fermions". arXiv:hep-th/0010074. – 8-component theory for fermions in which T-parity can be a complex number with unit radius. The CPT invariance is not a theorem but a better to have property in these class of theories.
  • This Particle Breaks Time Symmetry – YouTube video by Veritasium
  • An elementary discussion of CPT violation is given in chapter 15 of this student level textbook [1]

December 29, 2022
symmetry, theorem, redirects, here, album, greydon, square, theorem, charge, parity, time, reversal, symmetry, fundamental, symmetry, physical, laws, under, simultaneous, transformations, charge, conjugation, parity, transformation, time, reversal, only, combi. CPT theorem redirects here For the album by Greydon Square see The C P T Theorem Charge parity and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation C parity transformation P and time reversal 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 1 2 The CPT theorem says that CPT symmetry holds for all physical phenomena or more precisely that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry Contents 1 History 2 Derivation of the CPT theorem 3 Consequences and implications 4 See also 5 References 6 Sources 7 External linksHistory EditThe CPT theorem appeared for the first time implicitly in the work of Julian Schwinger in 1951 to prove the connection between spin and statistics 3 In 1954 Gerhart Luders and Wolfgang Pauli derived more explicit proofs 4 5 so this theorem is sometimes known as the Luders Pauli theorem At about the same time and independently this theorem was also proved by John Stewart Bell 6 7 These proofs are based on the principle of Lorentz invariance and the principle of locality in the interaction of quantum fields Subsequently Res Jost gave a more general proof in 1958 using the framework of axiomatic quantum field theory Efforts during the late 1950s revealed the violation of P symmetry by phenomena that involve the weak force and there were well known violations of C symmetry as well For a short time the CP symmetry was believed to be preserved by all physical phenomena but in the 1960s that was later found to be false too which implied by CPT invariance violations of T symmetry as well Derivation of the CPT theorem EditConsider a Lorentz boost in a fixed direction z This can be interpreted as a rotation of the time axis into the z axis with an imaginary rotation parameter If this rotation parameter were real it would be possible for a 180 rotation to reverse the direction of time and of z 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 x y plane could be included This defines a CPT transformation if we adopt the Feynman Stueckelberg interpretation of antiparticles as the corresponding particles traveling backwards in time This interpretation requires a slight analytic continuation which is well defined only under the following assumptions The theory is Lorentz invariant The vacuum is Lorentz invariant The energy is bounded below When the above hold quantum theory can be extended to a Euclidean theory defined by translating all the operators to imaginary time using the Hamiltonian The commutation relations of the Hamiltonian and the Lorentz generators guarantee that Lorentz invariance implies rotational invariance so that any state can be rotated by 180 degrees Since a sequence of two CPT reflections is equivalent to a 360 degree rotation fermions change by a sign under two CPT reflections while bosons do not This fact can be used to prove the spin statistics theorem Consequences and implications EditThe 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 parity inversion all momenta reversed corresponding to a time inversion and with all matter replaced by antimatter corresponding to a charge inversion would evolve under exactly our physical laws The CPT transformation turns our universe into its mirror image and vice versa 8 CPT symmetry is recognized to be a fundamental property of physical laws 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 CP violations The CPT theorem can be generalized to take into account pin groups In 2002 Oscar Greenberg proved that with reasonable assumptions CPT violation implies the breaking of Lorentz symmetry 9 CPT violations would be expected by some string theory 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 compact dimension 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 10 The overwhelming majority of experimental searches for Lorentz violation have yielded negative results A detailed tabulation of these results was given in 2011 by Kostelecky and Russell 11 See also EditPoincare symmetry and Quantum field theory Parity physics Charge conjugation and T symmetry CP violation and kaon IKAROS scientific results Gravitational interaction of antimatter CPT theoremReferences Edit Kostelecky V A 1998 The Status of CPT arXiv hep ph 9810365 This is the One Symmetry That the Universe Must Never Violate Forbes Schwinger Julian 1951 The Theory of Quantized Fields I Physical Review 82 6 914 927 Bibcode 1951PhRv 82 914S doi 10 1103 PhysRev 82 914 S2CID 121971249 Luders G 1954 On the Equivalence of Invariance under Time Reversal and under Particle Antiparticle Conjugation for Relativistic Field Theories Kongelige Danske Videnskabernes Selskab Matematisk Fysiske Meddelelser 28 5 1 17 Pauli W Rosenfelf L Weisskopf V eds 1955 Niels Bohr and the Development of Physics McGraw Hill LCCN 56040984 Whitaker Andrew 2016 John Stuart Bell and Twentieth Century Physics Oxford University Press ISBN 978 0198742999 Bell John Stewart 1955 Time reversal in field theory Proc R Soc Lond A 231 479 495 doi 10 1098 rspa 1955 0189 Our universe may have a twin that runs backward in time Paul Sutter Live Science March 16th 2022 Greenberg O W 2002 CPT Violation Implies Violation of Lorentz Invariance Physical Review Letters 89 23 231602 arXiv hep ph 0201258 Bibcode 2002PhRvL 89w1602G doi 10 1103 PhysRevLett 89 231602 PMID 12484997 S2CID 9409237 Lehnert Ralf November 2016 CPT Symmetry and Its Violation Symmetry 8 11 114 doi 10 3390 sym8110114 ISSN 2073 8994 Kostelecky V A Russell N 2011 Data tables for Lorentz and CPT violation Reviews of Modern Physics 83 1 11 31 arXiv 0801 0287 Bibcode 2011RvMP 83 11K doi 10 1103 RevModPhys 83 11 S2CID 3236027 Sources EditSozzi M S 2008 Discrete symmetries and CP violation Oxford University Press ISBN 978 0 19 929666 8 Griffiths David J 1987 Introduction to Elementary Particles Wiley John amp Sons Inc ISBN 978 0 471 60386 3 R F Streater and A S Wightman 1964 PCT spin and statistics and all that Benjamin Cummings ISBN 978 0 691 07062 9 External links EditBackground information on Lorentz and CPT violation by Alan Kostelecky at Theoretical Physics Indiana University Kostelecky V Alan Russell Neil 2011 Data tables for Lorentz and CPT violation Reviews of Modern Physics 83 1 11 arXiv 0801 0287 Bibcode 2011RvMP 83 11K doi 10 1103 RevModPhys 83 11 S2CID 3236027 Berg Marcus Dewitt Morette Cecile Gwo Shangjr Kramer Eric 2001 The Pin Groups in Physics C P and T Reviews in Mathematical Physics 13 8 953 1034 arXiv math ph 0012006 doi 10 1142 S0129055X01000922 S2CID 119560073 Charge Parity and Time Reversal CPT Symmetry Archived 2011 08 05 at the Wayback Machine at LBL CPT Invariance Tests in Neutral Kaon Decay at LBL Ying S 2000 Space Time Symmetry CPT and Mirror Fermions arXiv hep th 0010074 8 component theory for fermions in which T parity can be a complex number with unit radius The CPT invariance is not a theorem but a better to have property in these class of theories This Particle Breaks Time Symmetry YouTube video by Veritasium An elementary discussion of CPT violation is given in chapter 15 of this student level textbook 1 Retrieved from https en wikipedia org w index php title CPT symmetry amp oldid 1118955794, wikipedia, wiki, book, books, library,

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