No, what I meant was that when we switch to measuring the bead's travel in the blade-comoving frame, we need to take time dilation into account. An observer fixed to the blade will say that more time has passed while the bead moves from one end of the baseline to the other. Not very much more at ordinary speeds, but "exactly the same time" is a very exacting claim to make.Chris Peterson wrote:Yes, obviously this "vertex" is a physical object and cannot exceed c.Henning Makholm wrote:Ignoring any relativistic effects, of course. :–)Chris Peterson wrote:Make your blade edge and baseline out of stiff wires, and put a bead at their intersection. If you now move the blade edge down, the bead moves horizontally along the baseline wire, marking the intersection of the two. It will travel different distances on each wire, in exactly the same time.
(We could imagine that the bead keep bouncing back and forth along the baseline and just coincidentally followed the vertex. An observer on the blade will see the "bead clock" ticking slower. (At first sight this argument would seem to be ruined by symmetry, but it is really not symmetric: the two observers agree that the baseline runs at right angles to their mutual velocity whereas the blade edge doesn't, and that makes a difference)).