> The weird part is that one observer calculates the same value for any two objects.
That's not weird either, because the value being calculated has all object-specific information removed. See my response to andi999 downthread regarding rest mass.
That's the part that's "weird" in the sense of being very different from the similarly-named concept in classical mechanics of velocity vector magnitude.
But moreover, the rest mass isn't the issue here. Momentum in classical mechanics also takes mass into account but doesn't have the "weird" property that two objects of the same rest mass always have the same momentum magnitude.
That's not weird either, because the value being calculated has all object-specific information removed. See my response to andi999 downthread regarding rest mass.