Virtually indestructible materials, say adamantium.

[jay_598]

virtually indestructible materials, say "adamantium."

I want to know if this would be possible. Imagine a bicycle wheel, with the spokes and all, in your mind. Now, visualize the center of the wheel, where all the spokes more or less meet. Rotate it in your mind say at the center about 5 centimeters per second. At the center of the wheel it is moving relativley slow. But, at thhe edge of the wheel, maybe 12 inches or more from the center, the edge seems to move much more quickly. It really isn't moving faster than the center because the center and the edge are connected. Rather , the edge is covering more distance.
Oaky here is where it gets interesting.
Let's say it is the year 2500 ad and the United galactic Federation of Planets decides to build a huge wheel in space far away from any planets or stars gravitational fields. This wheel will be 1,000,000 miles in diameter and made from virtually indestructible materials, say "adamantium." Okay, they completed construction and this wheel has the ability to rotate at the center extremely fast. Is it possible to accelerate the wheel to the point where the edge exceeds the speed of light? Thing about the bike wheel. Can we implement the same reasoning with a million mile wide wheel in space?

 

[dx]

It really isn't moving faster than the center because the center and the edge are connected. Rather , the edge is covering more distance.

The edge is covering more distance. This means its going faster by definition. If a point near the center covers x meters in one second and a point near the edge covers 5x meters in one second, it means that the edge is going 5 times faster. Being connected doesn't mean they have to move at the same speed. The edge is connected to the center. The center is not moving at all. Does that mean the edge is not moving?

 

[f-h]

Voila, you have just proven that in special relativity there is no such thing as a perfectly rigid body.

 

[HallsofIvy]

Let me also point out that, since the spokes (radii) are moving, at each instant, perpendicular to their length, the spokes do not contract. The circumference of the wheel, however, is moving in the (instantaneous) direction of its length and so is subject to contraction: the circumference is NOT 2 pi times the radius and so the geometry of relativity cannot be Euclidean.

 

[Severian596]

Thing about the bike wheel. Can we implement the same reasoning with a million mile wide wheel in space?

Hi Jay_598. I think it's safe to say that we've all asked the same question. In my opinion you've constructed a scenario based on your real life experience that you can accelerate a wheel's edge to a velocity that's much higher than its center simply by applying some rotational force. The velocity of the edge is much greater than its center. But really this is just a simple machine...in the end you're applying a force (the torque) to a mass (the edge of the wheel). Eventually you'd have to apply enough force to accelerate the mass beyond c, and we can't generate forces that large.

 

[JesseM]

Let me also point out that, since the spokes (radii) are moving, at each instant, perpendicular to their length, the spokes do not contract. The circumference of the wheel, however, is moving in the (instantaneous) direction of its length and so is subject to contraction: the circumference is NOT 2 pi times the radius and so the geometry of relativity cannot be Euclidean.

You could treat a rotating wheel from the point of view of an inertial frame in special relativity, assuming its mass and energy were not enough to significantly distort spacetime; in such a frame, the circumference would still be 2 pi times the radius. It's true that the wheel would "want" to contract while the spokes would not, but neither is perfectly rigid--the spokes might be physically compressed by the wheel as it tried to shrink, or the material of the wheel might be physically stretched out so that its circumference would not shrink by the full Lorentz-contraction factor that you'd predict if it were rigid. On this thread I suggested an analogy:

Suppose you had a rubber band that was stretched larger than its natural size, but pushed into a circular shape by a bunch of springs arranged like spokes on a wheel, with the rubber band as the tire. Since the rubber band wants to shrink, won't it push down on the springs and thus shrink both the circumference and the radius of the circle until there's an equilibrium in the forces?

I imagine it'd be some combination of the spokes being compressed in the radial direction and the wheel's material being stretched in the circumferential direction, but either way, the radius of the rotating wheel would still be 2 pi times the radius.