Translation (physics)

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In physics, translation is movement that changes the position of an object, as opposed to rotation.

A translation is the operation changing the positions of all objects according to the formula

$(x,y,z) \to (x+\Delta x,y+\Delta y, z+\Delta z)$

where $(Δ x,Δ y,Δ z)$ is a constant vector. Such an operation can be generalized to other coordinates, for example the time coordinate.

For an object without structure, just a subset of space, we can consider the range of the subset under the transformation. Alternatively, we can define a translation as an operation on objects, such that all properties such as color, composition, etc. correspond. The two should not be confused: a translation of space has no fixed points, the fixed points of translation in the other sense are the objects with the corresponding translational symmetry.

Because of Noether's theorem, the translational symmetry is equivalent to momentum conservation.