Charge, parity, and time reversal symmetry is a fundamental
symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
of
physical law
Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...
s under the simultaneous
transformation
Transformation may refer to:
Science and mathematics
In biology and medicine
* Metamorphosis, the biological process of changing physical form after birth or hatching
* Malignant transformation, the process of cells becoming cancerous
* Tran ...
s of
charge conjugation
In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-sy ...
(C),
parity transformation
In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point refle ...
(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.
[
] The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any
Lorentz invariant
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
local
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
with a
Hermitian {{Short description, none
Numerous things are named after the French mathematician Charles Hermite (1822–1901):
Hermite
* Cubic Hermite spline, a type of third-degree spline
* Gauss–Hermite quadrature, an extension of Gaussian quadrature m ...
Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonian ...
must have CPT symmetry.
History
The CPT theorem appeared for the first time, implicitly, in the work of
Julian Schwinger
Julian Seymour Schwinger (; February 12, 1918 – July 16, 1994) was a Nobel Prize winning American theoretical physicist. He is best known for his work on quantum electrodynamics (QED), in particular for developing a relativistically invariant ...
in 1951 to prove the
connection between spin and statistics. In 1954,
Gerhart Lüders and
Wolfgang Pauli
Wolfgang Ernst Pauli (; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics fo ...
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
John Stewart Bell
John Stewart Bell FRS (28 July 1928 – 1 October 1990) was a physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories.
In 2022, the Nobel Prize in Phy ...
. These proofs are based on the principle of
Lorentz invariance
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
and the
principle of locality
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of ins ...
in the interaction of quantum fields. Subsequently,
Res Jost
Res Jost (10 January 1918 – 3 October 1990) was a Swiss theoretical physicist, who worked mainly in constructive quantum field theory.
Biography
Res Jost was born on January 10, 1918, in Bern. He is the son of the physics teacher Wilhelm ...
gave a more general proof in 1958 using the framework of
axiomatic quantum field theory Axiomatic quantum field theory is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator algebras, but has also been studied in recent years ...
.
Efforts during the late 1950s revealed the violation of
P-symmetry
In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point refle ...
by phenomena that involve the
weak force
Weak may refer to:
Songs
* Weak (AJR song), "Weak" (AJR song), 2016
* Weak (Melanie C song), "Weak" (Melanie C song), 2011
* Weak (SWV song), "Weak" (SWV song), 1993
* Weak (Skunk Anansie song), "Weak" (Skunk Anansie song), 1995
* "Weak", a song ...
, and there were well-known violations of
C-symmetry
In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-sy ...
as well. For a short time, the
CP-symmetry
In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry ( parity symmetry). CP-symmetry states that the laws of physics should be th ...
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
T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal,
: T: t \mapsto -t.
Since the second law of thermodynamics states that entropy increases as time flows toward the futur ...
as well.
Derivation of the CPT theorem
Consider a
Lorentz boost
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...
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
Real may refer to:
Currencies
* Brazilian real (R$)
* Central American Republic real
* Mexican real
* Portuguese real
* Spanish real
* Spanish colonial real
Music Albums
* ''Real'' (L'Arc-en-Ciel album) (2000)
* ''Real'' (Bright album) (2010) ...
, 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
In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an anti ...
of antiparticles as the corresponding particles traveling backwards in time. This interpretation requires a slight
analytic continuation
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a n ...
, which is well-defined only under the following assumptions:
#The theory is
Lorentz invariant
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
;
#The vacuum is Lorentz invariant;
#The energy is bounded below.
When the above hold,
quantum theory
Quantum theory may refer to:
Science
*Quantum mechanics, a major field of physics
*Old quantum theory, predating modern quantum mechanics
* Quantum field theory, an area of quantum mechanics that includes:
** Quantum electrodynamics
** Quantum ...
can be extended to a Euclidean theory, defined by translating all the operators to imaginary time using the
Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonian ...
. The
commutation relation
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory.
Group theory
The commutator of two elements, ...
s of the Hamiltonian, and the
Lorentz generators, guarantee that
Lorentz invariance
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
implies
rotational invariance In mathematics, a function defined on an inner product space is said to have rotational invariance if its value does not change when arbitrary rotations are applied to its argument.
Mathematics
Functions
For example, the function
:f(x,y) = x ...
, so that any state can be rotated by 180 degrees.
Since a sequence of two CPT reflections is equivalent to a 360-degree rotation,
fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...
s change by a sign under two CPT reflections, while
boson
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
s 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
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic part ...
replaced by
antimatter
In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter. Antimatter occurs in natural processes like cosmic ray collisions and some types of radioac ...
(corresponding to a
charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* ''Charge!!'', an album by The Aqu ...
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.
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 violation
In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry ( parity symmetry). CP-symmetry states that the laws of physics should be th ...
s.
The CPT theorem can be generalized to take into account
pin group
The PIN Group was a German courier and postal services company. It belonged to PIN Group S.A., a Luxembourg-based corporate affiliation made up of several German postal companies.
History and shareholding
The PIN Group originally traded under ...
s.
In 2002
Oscar Greenberg
Oscar Wallace Greenberg (born February 18, 1932) is an American physicist and professor at University of Maryland College of Computer, Mathematical, and Natural Sciences. In 1964, he posited the existence of quarks that obeyed parastatistics as t ...
proved that, with reasonable assumptions, CPT violation implies the breaking of
Lorentz symmetry
In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same ...
.
[
]
CPT violations would be expected by some
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...
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
In theoretical physics, compactification means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with this dimension being infinite, one changes the theory so that this dimension has a finite length, a ...
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.
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.
[
]
See also
*
Poincaré symmetry and
Quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
*
Parity (physics),
Charge conjugation
In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-sy ...
and
T-symmetry
T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal,
: T: t \mapsto -t.
Since the second law of thermodynamics states that entropy increases as time flows toward the futur ...
*
CP violation
In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry ( parity symmetry). CP-symmetry states that the laws of physics should be th ...
and
kaon
KAON (Karlsruhe ontology) is an ontology infrastructure developed by the University of Karlsruhe and the Research Center for Information Technologies in Karlsruhe.
Its first incarnation was developed in 2002 and supported an enhanced version of ...
*
IKAROS scientific results
*
References
Sources
*
*
*
External links
Background information on Lorentz and CPT violationby
Alan Kostelecký
V. Alan Kostelecký is a theoretical physicist who is a distinguished professor of physics at Indiana University, Bloomington. He is noted for his work on Lorentz symmetry breaking in particle physics. He has been described as the world's leadin ...
at Theoretical Physics Indiana University
*
*
Charge, Parity, and Time Reversal (CPT) Symmetry at
LBLCPT Invariance Tests in Neutral Kaon Decayat
LBL
* – 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
YouTube is a global online video platform, online video sharing and social media, social media platform headquartered in San Bruno, California. It was launched on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim. It is owned by ...
video by
Veritasium
Derek Alexander Muller (born 9 November 1982) is an Australian-Canadian science communicator, filmmaker, and television personality, who is best known for his YouTube channel Veritasium. Muller has also appeared as a correspondent on the Net ...
* An elementary discussion of CPT violation is given in chapter 15 of this student level textboo
{{DEFAULTSORT:Cpt Symmetry
Quantum field theory
Symmetry
Theorems in quantum mechanics