# Time Reversal

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## time reversal

[′tīm ri‚vər·səl]
(physics)
The replacement of the time coordinate t by its negative -t in the equations of motion of a dynamical system; the time reversal operator, a symmetry operator for a quantum-mechanical system, contains also the complex conjugation operator and a matrix operating on the spin coordinate.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Time Reversal

the mathematical operation of changing the sign of time in equations of motion that describe the development of a physical system in time. Such a change corresponds to a certain symmetry that exists in nature. Specifically, all fundamental interactions of elementary particles, with one exception (see below), have the property of T-invariance: time reversal, or the substitution t— t, does not change the form of the equations of motion. This means that for any possible motion of a system in nature there can occur time-reversed motion, wherein the system successively passes, in reverse order, through states symmetric to the states it traverses in “forward” motion. Such time-symmetric states have opposite directions for the velocities and projections of spins of all particles and the magnetic field. The consequences of T-invariance include certain relations between the probabilities of direct and inverse reactions, the prohibition of certain states of polarization of particles in reactions, and a zero electric dipole moment of elementary particles.

It follows from the general principles of modern quantum field theory that all processes in nature are symmetric with respect to the product of three operations: time reversal T, space inversion P, and charge conjugation C. The only experimentally observed processes in which violation of the combined inversion CP is observed are rare decays of the long-lived kL0-meson: the rare decay kL0 → 2 π and the lepton decays kL0 → π+ + e) + v̄e(v̄μ) and kL0 → π- + e++) + ve(vμ), in which weak (∼ 10-3) charge asymmetry has been detected. Theoretical analysis of experimental data on these decays leads to the conclusion that CPT-invariance is satisfied in the decays but T-invariance is violated. The nature of the forces that violate T-invariance has not been ascertained. These forces may be connected with the superweak interaction, which is a billion times weaker than the normal weak interaction.

Although elementary microprocesses, with the exception pointed out above, are reversible in time, the second law of thermodynamics dictates that macroscopic processes involving a very large number of particles proceed only in one direction— toward a state of thermodynamic equilibrium. Statistical physics explains this paradox by the set of microscopic states that corresponds to the state of macroscopic equilibrium being immeasurably greater than the set that corresponds to nonequilibrium states. Therefore, any disturbance, no matter how small, changes a system’s motion away from a state of equilibrium into motion toward equilibrium.

S. S. GERSHTEIN

References in periodicals archive ?
The paper is organized as follows: Section 2 explains how the time reversal is applied to the wire diagnosis.
Li, "Transmitting-mode time reversal imaging using MUSIC algorithm for surveillance in wireless sensor network," IEEE Trans.
Time reversal can aid engine makers by pinpointing flaws within the irregular microstructure of titanium that other scanning methods miss.
[1994b]: 'Is Classical Mechanics Time Reversal Invariant?', British Journal for the Philosophy of Science, 45, pp.
Liu, "Computational study of time reversal mirror technique for microwave-induced thermo-acoustic tomography," Journal of Electromagnetic Waves and Applications, Vol.
Ryzhik, "Time reversal and refocusing in random environment," SIAM Appl.
His exploration of time reversal appears in the Dec.
Savitt formulates his criterion by envisaging the dynamical evolution of a mechanical system from some state A to B; then asks (using the superscript R to indicate the time reversal of a state) if it is possible for the evolution from [B.sup.R] to [A.sup.R] to occur--possible in the sense of being allowed by the laws of classical mechanics.
With reference to small (in terms of wavelength) scatterers, we focus on Time Reversal MUSIC (TR-MUSIC) that has proved to be very effective in scatterer localization as it allows to obtain resolution which is finer than diffraction limits [14].
Using a technique called Time Reversal Acoustics (TRA), the scientists hope to produce an amplified beam of sound loud enough to overwhelm an intruder but focused enough to spare the surrounding wildlife.

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