Time-translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a common interval. Time-translation symmetry is the law  that the laws of physics are unchanged (i.e. invariant) under such a transformation. Time-translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time-translation symmetry is closely connected, via Noether's theorem, to conservation of energy. In mathematics, the set of all time translations on a given system form a Lie group.
There are many symmetries in nature besides time translation, such as spatial translation or rotational symmetries. These symmetries can be broken and explain diverse phenomena such as crystals, superconductivity, and the Higgs mechanism. However, it was thought until very recently that time-translation symmetry could not be broken. Time crystals, a state of matter first observed in 2017, break time-translation symmetry.