 Time translation symmetry

Invariance under a shift of the time coordinate, with other required background structures held fixed. A continuous time-translation symmetry gives an energy conservation law through Noether theorem. A generic expanding cosmological background is not stationary and need not supply a corresponding globally conserved total energy.

Time translation symmetry is a concept in physics, particularly in the context of classical mechanics and field theory, that indicates that the laws of physics do not change over time. This means that the physical laws that govern a system remain invariant regardless of when the system is observed.