I'll try to beat John to the punch here, though I'm sure he'll have his
own way of saying it.
|
| Yes, the behavior of quantities depends on our definitions!
| By our definition of 3 velocity, the above 3 velocity doesn't
| "APPEAR to another observer to asymptotically approach the
| speed of light" it is measured to do so, and DOES so. du/dt
| is a useful and easily measured quantity. Of what more use
| is du/dtau of Betelgeuse? What would improve if we ceased
| calling du/dt "velocity" and reserved that name for du/dtau?
|
The trajectory of the particles in the rings of Saturn don't "APPEAR" to
another observer, the guy making measurements off of the photographic
plate measures it to be an ellipse. After all you have to put the
measuring instrumenet to the photographic (digital image plate) plate to
make measurements of that trajectory and hence learn about orbits of
particles in Saturn's gravitational field.
Its no more abusive for one to use the word "appear" to describe the
elliptical shape of Saturn's rings then it is in the context of the
measured 3-velocity of an object by an observer.