Time-reversal symmetry

Time-reversal symmetry is invariance of a physical law or process under reversal of the time coordinate, with time-odd quantities such as velocity and angular momentum reversed.

Time-reversal operator: An operator that implements time reversal on quantum states, typically as an antiunitary transformation. It expresses time reversal mathematically in quantum mechanics.
Time coordinate: A variable used to locate events along a temporal dimension. The symmetry transformation reverses this coordinate.
Time-reversal violation: A failure of physical laws or processes to remain invariant under time reversal. It is the direct opposite of the symmetry considered here.
Topological insulator: A material that insulates in its interior while supporting conducting states on its boundary, often protected by time-reversal symmetry. Its boundary states can persist because nonmagnetic perturbations preserve the symmetry.
Isaac Newton: An English mathematician and physicist who formulated the laws of motion and universal gravitation. Newtonian equations of motion are invariant under time reversal in their ideal conservative form.
Antiunitary operator: A norm-preserving operator that conjugates complex scalar coefficients while acting on quantum states. Quantum time reversal is antiunitary, rather than an ordinary unitary symmetry.
Parity (physics): A spatial reflection transformation that reverses the signs of spatial coordinates. Parity reverses space, whereas time reversal transforms temporal evolution.
CPT symmetry: The combined symmetry of charge conjugation, parity transformation, and time reversal in local relativistic quantum field theories. CPT can remain conserved even when time reversal alone is violated.
Quantum spin Hall effect: A two-dimensional topological phase with counterpropagating edge states carrying opposite spin orientations. Time-reversal symmetry protects its paired edge states against certain forms of scattering.
Ludwig Boltzmann: An Austrian physicist who developed statistical mechanics and a molecular account of thermodynamics. His work exposed the tension between reversible microscopic dynamics and irreversible thermodynamic behavior.

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