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 (KL 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 (H2O) 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 KL. 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 KL decay only because there are two neutral 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)

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.
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Among the topics are the validity of random matrix theories for many-particle systems, the angular-momentum dependence of the density of states, group theory and the propagation of operator averages, electromagnetic sum rules by spectral distribution methods, compound-nuclear tests of time reversal invariance in the nucleon-nucleon interaction, strength functions and spreading widths of simple shell model configurations, and underlying symmetries of realistic interactions and the nuclear many-body problem.
Bodek, JU-Krakow, Poland 12:05-12:25 Two coils resonant Ramsey's method for the measurement of time reversal invariance violation in neutron transmission A.
This point is most apparent in the use of the crucial notion of Time Reversal Invariance (TRI).
Our dynamic collision model has a feature that makes it especially interesting in relation to time reversal invariance. To see this, observe first that, as a consequence of (2), if a unidimensional collision between point particles of the same mass is a dynamically possible process, its temporal reversal will also be one.
Herczeg, in Tests of Time Reversal Invariance in Neutron Physics, N.
This seems to be the concept of invariance embodied in the quote from Leggett above, and we can find this characterization of time reversal invariance explicitly in P.
Leggett and Davies would presumably agree that this example is 'encompassed' by CM, and this presumption comes in (small) part from the fact that the example is taken straight from Davies' own discussion of time reversal invariance.(7) According to Davies, moreover, solutions to (3) 'are clearly unphysical as they correspond to a body being spontaneously accelerated of the form an infinite velocity as a result of its contact with a viscous or frictional medium'.(8) I suspect that by 'unphysical' Davies means that instances of these solutions are 'never witnessed'.
Hence, the transmission processes, where the initial and final states of reaction coincide by definition, match very well the requirements of the time reversal invariance check-up.
Use of a tensor polarized deuteron target avoids the 1/A suppression, and a test using a few hundred MeV polarized proton beam is planned for the COoler SYnchrotron storage ring facility (COSY) at the Institut fur Kernphysik (IKP) Juelich, Germany by the Time Reversal Invariance Test at COSY collaboration (TRIC).
To be of interest as a test of P-odd time reversal invariance, data on displacements of zeros in (n, [gamma]) correlations should comprise measurements at several p-wave resonances within a given compound nucleus .
Why do some basic interactions violate time reversal invariance? Both of the above: How hot does the sun burn?

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