Timesymmetric

Timesymmetric, or time-symmetric, describes a property of a system in which the underlying dynamics are unchanged when the direction of time is reversed. In practice, this means that if a valid trajectory x(t) satisfies the governing equations, the time-reversed trajectory x(-t) (with appropriate reversal of momenta or velocities) also satisfies those equations.

In classical mechanics, many idealized systems are time-reversal invariant: for example, a frictionless harmonic oscillator or planets moving under conservative forces follow equations that do not prefer a forward or backward flow of time. In Hamiltonian form, time-reversal invariance typically requires that the equations of motion remain unchanged under t -> -t, with momentum variables mapped to their negatives. In quantum mechanics, time reversal is implemented by an antiunitary operator T; a system is time-reversal invariant if [H, T] = 0, with spinful particles requiring a spin transformation as part of T.

Real-world systems often break time symmetry through dissipation, driving, or coupling to an environment, leading to macroscopic irreversibility and the arrow of time. Nonetheless, the microscopic laws of classical mechanics and (non-dissipative) electromagnetism are time-reversal invariant, and time-symmetric concepts remain fundamental in formulating those theories.

Time-reversal symmetry has important implications in particle physics. The CPT theorem implies that violations of charge-parity (CP) symmetry entail time-reversal (T) violation. Experimental tests include observations of T-violating processes in meson systems, such as those reported by the BaBar collaboration, and searches for permanent electric dipole moments as probes of T violation.