Noether proved that for every symmetry of the action there is a conserved quantity. The action is an expression (a function of the coordinates) from which the e

Noether proved that for every symmetry of the action there is a conserved quantity. The action is an expression (a function of the coordinates) from which the equations of motion can be derived. Examples of symmetries of the action are time reversal, spatial translation, spatial rotation, and complex phase rotation. The corresponding conserved quantities are energy, linear momentum, angular momentum, and charge. In general relativity, symmetries that exist in the action for a flat spacetime are violated in curved spacetime. So, in curved spacetime, the corresponding quantities are not conserved. One example is energy. The reason has to do with the fact that integrating a tensor along a closed loop in curved spacetime might yield a nonzero result due to the curvature itself, rather than due to the dynamics of what is being integrated. I don't think that the article goes into any of this. The introduction about general relativity did seem like a curve ball, even if it's historically accurate.