timesymmetry

Timesymmetry, or time-reversal symmetry, is the invariance of physical laws under reversing the time coordinate t to -t. If a process described by a set of equations evolves as x(t), the time-reversed trajectory x(-t) should also satisfy the same laws. This concept appears in classical mechanics, quantum mechanics, and statistical physics, though its presence and meaning can vary by context.

In classical mechanics, Newtonian dynamics with conservative forces is time-reversal invariant: a trajectory that is allowed forward in time remains valid when time is reversed and momenta are flipped. This reflects the idea that microscopic equations of motion do not, by themselves, prefer a direction of time.

In quantum mechanics, time reversal is represented by an antiunitary operator T. A Hamiltonian H is time-reversal invariant if [H, T] = 0. Many interactions, such as electromagnetic and strong interactions, respect time reversal, while certain weak-interaction processes exhibit T violation. Due to the CPT theorem, violations of CP symmetry imply corresponding T violations in a relativistic quantum framework.

In statistical mechanics, microscopic dynamics are typically time-reversal symmetric, but macroscopic irreversibility arises from entropy and initial conditions. Equilibrium states often preserve a form of time-reversal symmetry at the microscopic level, whereas dissipative or driven systems show an emergent arrow of time.

Timesymmetry remains a foundational idea for formulating physical laws and interpreting experiments. Its study helps distinguish fundamental reversibility from the apparent irreversibility observed in everyday phenomena.