There's possibly another, more subtle, interpretation. It may be that the structure of spacetime does not necessarily exhibit this conservation. However, all s

There's possibly another, more subtle, interpretation. It may be that the structure of spacetime does not necessarily exhibit this conservation. However, all scientifically observable phenomenon must, by definition, exhibit space, time and rotational invariants. Otherwise they can't be scientifically observable i.e. by repeatable experiments. From Noether's theorem, this means that the scientifically observable phenomena must exhibit at least energy, momentum and angular momentum conservation. Either in the laws that govern the phenomena or the consequences of a, potentially violating, law that do conserve. It's an interesting take on the duality, at least it is to me.