Warning: mostly semantics & perhaps a bit of metaphysics
John D. clarified in part with:
| Rather than asking
| -- What is the X-component of Alice's velocity in Bob's frame?
| it would be conceptually preferable to ask
| -- What is V dot Xhat?
| where V is Alice's velocity and Xhat is a unit vector aligned
| with Bob's X-axis.
|
| The point is that V dot Xhat is manifestly invariant.
No argument that V dot Xhat is the invariant way to express the quantity
so that a person can calculate that quantity using any inertial frame to
perform the calculation; but I wonder if the quantity itself isn't a
frame-dependent quantity? Afterall, if I ask what is Alice's
x-component of velocity in Moe's frame I may get a different answer.
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