Translational symmetry is a property of a system or object that remains unchanged when it is shifted or translated in space by a certain distance in a specific direction. In other words, if you can move the entire system a certain distance and it still looks the same, then it has translational symmetry. This concept is commonly observed in various fields such as physics, mathematics, and art.
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Invariance of an action, equation or configuration under a translation. For a continuous spatial translation symmetry, Noether's theorem supplies the conserved momentum; spacetime translation gives the canonical stress-energy tensor.