# Time Reversal

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## time reversal

[′tīm ri‚vər·səl]*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.

## 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 *k*_{L}^{0}-meson: the rare decay *k*_{L}^{0} → 2 π and the lepton decays *k*_{L}^{0} → π^{+} + e^{–} (μ^{–}) + *v*̄_{e}(*v*̄^{μ}) and *k*_{L}^{0} → π^{-} + e^{+} (μ^{+}) + *v*_{e}(*v*^{μ}), 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