CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously. This article or section does not cite its references or sources. ... A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ... In mathematics, a transformation in elementary terms is any of a variety of different operations from geometry, such as rotations, reflections and translations. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... In physics, a parity transformation (also called parity inversion) is the simultaneous flip in the sign of all spatial coordinates: A 3×3 matrix representation of P would have determinant equal to –1, and hence cannot reduce to a rotation. ... Two distinct views exist on the meaning of time. ...

History

Efforts in the late 1950s revealed the violation of P-symmetry by phenomena that involve the weak force, and there are well known violations of C-symmetry and T-symmetry as well. For a short time, the CP-symmetry was believed to be preserved by all physical phenomena, but that was later found to be false too. On the other hand, there is a theorem that derives the preservation of CPT symmetry for all of physical phenomena assuming the correctness of quantum laws and Lorentz invariance. Specifically, the CPT theorem states that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.
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. In 1954 Gerhard Lüders and Wolfgang Pauli derived more explicit proofs so that the theorem is sometimes known as the Lüders-Pauli theorem. At about the same time and independently the theorem was also proved by John Stewart Bell. These proofs are based on the validity of Lorentz invariance and the Principle of locality in the interaction of quantum fields. Subsequently Res Jost gave a more general proof in the framework of axiomatic quantum field theory. P-symmetry is simply the spatial symmetry exhibited during a reflection. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... C-symmetry means the symmetry of physical laws over a charge-inversion transformation. ... T-symmetry is the symmetry of physical laws under a time-reversal transformation— The universe is not symmetric under time reversal, although in restricted contexts one may find this symmetry. ... CP-symmetry is a symmetry obtained by a combination of the C-symmetry and the P-symmetry. ... In physics, a quantum refers to an indivisible, and perhaps, elementary entity. ... Lorentz covariance is a term in physics for the property of space time, that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. ... Lorentz covariance is a term in physics for the property of space time, that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... On a finite-dimensional inner product space, a self-adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose. ... The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space (or, in the case of ensembles, as a trace class operator with trace 1). ... Julian Seymour Schwinger (February 12, 1918 -- July 16, 1994) was an American theoretical physicist. ... The spin-statistics theorem in quantum mechanics relates the spin of a particle to the statistics obeyed by that particle. ... This article is about Austrian-Swiss physicist Wolfgang Pauli. ... John Bell (left) and Martinus Veltman (right) discussing Physics at CERN John S. Bell (June 28, 1928 – October 1, 1990) was a physicist who became well known as the originator of Bells Theorem, regarded by some in the quantum physics community as one of the most important theorems of... Lorentz covariance is a term in physics for the property of space time, that in two different frames of reference, located at the same event in spacetime but moving relative to each other, all non-gravitational laws must make the same predictions for identical experiments. ... In physics, the principle of locality is that distant objects cannot have direct influence on one another: an object is influenced directly only by its immediate surroundings. ...

Derivation

For a handwaving argument, take a Lorentz boost in a fixed direction, let's call it z. If we complexify the Lorentz group, an imaginary boost with a boost parameter of iπ will result in t going to -t and z going to -z. If we later perform an addition rotation by π in the xy-plane, we get a combination of P and CT. The combination CT appears here instead of T because we are dealing with a unitary transformation, not an antiunitary one. Assuming that the operation of taking a complex boost is valid as a symmetry, we still get a state which is described by the same laws. This gives us the CPT theorem. The term handwaving is used in mathematics and physics to describe arguments that are not mathematically rigorous. ... The Lorentz transformation (LT), named after its discoverer, the Dutch physicist and mathematician Hendrik Antoon Lorentz (1853-1928), forms the basis for the special theory of relativity, which has been introduced to remove contradictions between the theories of electromagnetism and classical mechanics. ... In mathematics, the complexification of a vector space V over the real number field is the corresponding vector space VC over the complex number field. ... The Lorentz group is the group of all Lorentz transformations of Minkowski spacetime. ... A unitary transformation is an isomorphism between two Hilbert spaces. ...

Consequences and Implications

A consequence of this derivation is that a violation of CPT automatically indicates a Lorentz violation. Lorentz violation refers to theories which are approximately relativistic when it comes to experiments that have actually been performed (and there are quite a number of such experimental tests) but yet contain tiny or hidden Lorentz violating corrections. ...

The implication of CPT symmetry is that a mirror-image of our universe — with all objects having momenta and positions reflected by an imaginary plane (corresponding to a parity inversion), with all matter replaced by antimatter (corresponding to a charge inversion), and reversed in time — would evolve exactly like our universe. At any moment of corresponding times, the two universes would be identical, and the CPT transformation would simply turn one into the other. CPT symmetry is recognized to be a fundamental property of physical laws. In classical mechanics, momentum (pl. ... In physics, a parity transformation (also called parity inversion) is the simultaneous flip in the sign of all spatial coordinates: A 3×3 matrix representation of P would have determinant equal to –1, and hence cannot reduce to a rotation. ... In physics, matter is commonly defined as the substance of which physical objects are composed, not counting the contribution of various energy or force-fields, which are not usually considered to be matter per se (though they may contribute to the mass of objects). ... In particle physics, antimatter extends the concept of the antiparticle to matter, wherein if a particle and its antiparticle come into contact with each other, the two annihilate —that is, they may both be converted into other particles with equal energy in accordance with Einsteins equation E = mc2. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ...

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. In physics, and specifically particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics. ...

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

C-symmetry means the symmetry of physical laws over a charge-inversion transformation. ... P-symmetry is simply the spatial symmetry exhibited during a reflection. ... T-symmetry is the symmetry of physical laws under a time-reversal transformation— The universe is not symmetric under time reversal, although in restricted contexts one may find this symmetry. ... CP-symmetry is a symmetry obtained by a combination of the C-symmetry and the P-symmetry. ... ...

See also

• Poincaré symmetry and Quantum field theory
• Parity (physics), Charge conjugation and Time reversal symmetry
• CP violation and Kaon

In physics and mathematics, the Poincaré group is the group of isometries of Minkowski spacetime. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... In physics, a parity transformation (also called parity inversion) is the simultaneous flip in the sign of all spatial coordinates: A 3×3 matrix representation of P would have determinant equal to –1, and hence cannot reduce to a rotation. ... C-symmetry means the symmetry of physical laws over a charge-inversion transformation. ... T-symmetry is the symmetry of physical laws under a time-reversal transformation. ... In physics, and specifically particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics. ... In particle physics, Kaons (also called K-mesons and denoted K) are a group of four mesons distinguished by the fact that they carry a quantum number called strangeness. ...

References

• Griffiths, David J. (1987). Introduction to Elementary Particles. Wiley, John & Sons, Inc. ISBN 0-471-60386-4.
• R. F. Streater and A. S. Wightman (1964). PCT, spin statistics and all that. Benjamin/Cummings. ISBN 0-691-07062-8.

Ray F. Streater is a physicist known for his contributions to axiomatic quantum field theory and his interest in this approach to quantum field theory. ... Arthur Strong Wightman is an American mathematical physicist. ...

External links

• http://www.arxiv.org/abs/math-ph/0012006
• http://www.lbl.gov/abc/wallchart/chapters/05/2.html
• Particle data group on CPT
• 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 propert in these class of theories.