I need to mediate on this for a while: "Energy is conserved, but it is not invariant.".
Another example is momentum. Imagine any system where momentum is conserved. In the centre of momentum frame the total momentum is zero, by definition. But, in any other frame the total momentum will not be zero.
Thus momentum is conserved but not invariant. likewise energy.
Rest mass, for example, is not conserved, but it is invariant (the same in all frames).
Electric charge, for example, is both invariant and conserved.
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