3 ms·
> This isn't weird. The magnitude of any four-vector is frame invariant in relativity. Lorentz transformations in relativity are the analogue of rotations in or
by tgb 6y ago
> This isn't weird. The magnitude of any four-vector is frame invariant in relativity. Lorentz transformations in relativity are the analogue of rotations in ordinary Euclidean space, and have the same property of preserving the magnitudes of vectors.
The weird part isn't that two observers agree on the vector magnitude. The weird part is that one observer calculates the same value for any two objects. Frame-invariance isn't the relevant property.
- pdonis 6y ago> 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.
- tgb 6y agoThat'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.