I wanted to open a topic illustrating some concepts in the treatment of rigid objects since there seems to have been much confusion lately in this area. I created exercises labeled P,Q,R below. By rigid object, I mean that the object cannot change proper distance with any of its immediate material. This is somewhat more loose than Born rigidity. For a 3D object, the only difference is that I allow the object no not have a rest frame. An accelerating Born-rigid object is already necessarily moving at different speeds at different positions, but I think it is presumed to be simultaneously stationary everywhere in it's (momentary) rest frame. As for non-3D object, one cannot stretch the object, similar to above, but one can bend it. So it's ok to send a 1D rigid wire through a pulley for instance. One can fold a 2D sheet, but cannot tear it or stretch it. Second note: The only way to apply changes to motion of a rigid object is to apply appropriate force everywhere at once. There is no 'engine in the back' so to speak, since any force applied by the engine at the rear of say a rocket is incapable of affecting the front sooner than a light signal could get to it. Hence a rocket must shorten when the engines fire, which violates rigidity. So no rocket technology. More like rail-gun and such. Third note: Kind of keeping things to about 3 digits of precision. Light speed is presumed to be 300,000 m/sec. We have no limits to acceleration rates or speeds (up to c of course). P) Finite movement of a 3D object This is a 3D object, basically a subway train that is all one piece. It is a light-year long, and stationary relative to the straight track it's on. We want to move it 1.08 e-12 meters (a light hour). The doors are that proper separation apart, and we want to bring the next door to a halt at the stations which are also a light hour apart in the track frame. How long does it take? I get just over 5½ days to do it. I'll be discussing some interesting tricks to attempt to improve on that, but it seems that it cannot be done faster. This is the only one for which I have an easy answer. Q) Rotating a 2D disk Imagine a flat disk, negligible thickness so we can treat it as 2D if it helps. It has an arrow printed on it pointing 'up' to 12 O Clock (up the y axis). We want to rotate the disk a quarter turn to 3 O Clock (to the +x axis direction). It is a light-hour in radius, and has a hole in it ½ light-hour in radius, so it's kind of a donut disk, like a 45 record. The most 'legal' way to accomplish things is to rotate the object about the x axis until the arrow points in the z direction, then rotate along the z axis to bring what was at the 3 O Clock position down to the 6 O Clock place. Finally we rotate about the y axis bringing the arrow down to 3 O Clock. 3 rotations, moving the outermost points π/2 light hours each time, so it takes 3/2 π hours to do it, or about 283 minutes. Seems like too much work. Method B: We can fold a 2D object, no? So crumple the whole thing up into a small wad, rotate the wad, and un-crumple it. That takes an hour each way to move all the stuff at the edge to the middle and back, with negligible time to rotate the wad. We've reduced the time to 120 minutes. Can we do better? I think we can. R) Rotating a 2D toilet paper roll This time we have a tube, a rolled paper in a cylinder, a light-hour in radius again. We want to rotate that a quarter turn jut like above, but this time the Ehrenfest paradox is far less in our way. We still cannot rotate the roll as it is because it will contract, so the idea is to accelerate all the parts inward, and increase the rotation to always match the contracted length of the circumference. We rotate half-way to our destination and then do the same dance in reverse, slowing the rotation to a stop. Shouldn't be hard, but I need to write a program to do the integration. The neat thing is that every particle of the object can move at c at all times. It just can't ever move at that speed in a direction tangential to the surface of the material, which would contract it infinitely. Comments? Can anybody propose any actual numbers for the above problems? Does anybody deny what I've written above? I've presented not too many numbers (none at all for the 3rd problem so far).