# Time reversal invariance

## Time reversal invariance

A symmetry of the fundamental (microscopic) equations of motion of a system; if it holds, the time reversal of any motion of the system is also a motion of the system. With one exception (*K _{L}* meson decay), all observations are consistent with time reversal invariance (

*T*invariance).

Time reversal invariance is not evident from casual observation of everyday phenomena. If a movie is taken of a phenomenon, the corresponding time-reversed motion can be exhibited by running the movie backward. The result is usually strange. For instance, water in the ground is not ordinarily observed to collect itself into drops and shoot up into the air. However, if the system is sufficiently well observed, the direction of time is not obvious. For instance, a movie which showed the motion of the planets would look just as right run backward or forward. The apparent irreversibility of everyday phenomena results from the combination of imprecise observation and starting from an improbable situation (a state of low entropy, to use the terminology of statistical mechanics). *See* Entropy, Statistical mechanics, Time, arrow of

If time reversal invariance holds, no particle (a physical system with a definite mass and spin) can have an electric dipole moment. A polar body, for example, a water (H_{2}O) molecule, has an electric dipole moment, but its energy and spin eigenstates (which are particles) do not. No particle has been observed to have an electric dipole moment; for instance, the present experimental upper limit on the electric moment of the neutron is approximately 10^{-25} cm times *e*, where *e* is the charge of the proton. Even smaller upper limits have been reported for the electric moment of some nuclei. *See* Dipole moment, Neutron, Polar molecule, Spin (quantum mechanics)

Another test of time reversal invariance is to compare the cross sections for reactions which are inverse to one another. The present experimental upper limit on the relative size of the time reversal invariance-violating amplitude of such reactions is approximately 3 × 10^{-3}; unfortunately, this is far larger than any expected violation. *See* Nuclear reaction

If time reversibility holds, then by the *CPT* theorem *CP* invariance must hold, that is, invariance of the fundamental equations under the combined operations of charge conjugation *C* and space inversion *P*. Conversely, violation of *CP* invariance implies violation of *T* (time reversal invariance). In 1964, *CP* violation was observed in the decay of the long-lived neutral *K* meson, the *K _{L}*. For many years, no other evidence for

*T*or

*CP*violation was seen. From this it was deduced that the interactions which violate

*CP*are very weak and are evident in

*K*decay only because there are two neutral

_{L}*K*mesons that have practically the same mass and are therefore easily mixed.

*See*CPT theorem, Meson

Within the current understanding of particle physics, namely the so-called standard model, *CP* violation comes from the Kobayashi-Maskawa matrix of coefficients that relate the quark weak *i*-spin eigenstates with the quark mass eigenstates. It turns out that because the number of flavors is greater than four, the Kobayashi-Maskawa matrix can be nonreal, resulting in nonconservation of *CP* and *T*. *See* Electroweak interaction, Flavor, Quarks, Standard model, Weak nuclear interactions

It is also possible that *CP* violation comes from yet unknown interactions. More is being learned from observations since 2001 of *CP* violation in the decay of the neutral *B* mesons at the so-called *B* factories, particle accelerators built for the purpose of copiously producing *B* mesons. Initial results are consistent with the standard model. *See* Elementary particle, Particle accelerator, Symmetry laws (physics)