I imagined this while watching Star Trek, and contemplating faster than light travel. Stay with me.

Say you have two steel rings connected to each other concentrically. The inner ring has a diameter of five centimeters, the outer ring, a diameter of ten centimeters.

Therefore, the inner circumference is 5π cm, and the outer circle's circumference is 10π cm.

Now, say there is a pin on each circle. The inner circle is accelerated so the pin moves at 5π cm/s, which means that the outer pin must be traveling at 10π cm/s.

Now let's scale this up a bit.

The fastest speed achieved by man is 10,400 km/h, or 2,888 m/s. If the inner circle was accelerated to this speed, objects on the outer circle would be revolving at 5,776 m/s. If the size of the inner circle was shrunk to a 1cm diameter, the outer circle's objects would revolve at 28,880 m/s. The outer circle would have to have a diameter 103 807 times the diameter of the inside ring for the outside ring's objects to be maintaining a velocity greater than C. A half centimeter inner ring would only need a 520 meter outer ring.

Would the forces involved in maintaining the structural integrity of the rings negate the ability of the inner ring to be accelerated to mach 8.5 with a finite amount of energy, or would it enable matter to be propelled faster than the speed of light at the outer edge of the structure?

I don't think there's enough energy around to spin something even that fast. First, you have to worry about the heat produced by friction, and second, the farther out from the center of the circle the outer ring becomes, the greater will be its moment of inertia, and the harder it will be to accelerate. I would have to go with the prediction that the forces involved would rip apart the apparatus before the speed could even come close.

Edit: For example, some of Stephen Hawking's work has shown that black holes lose some mass due to the speed of the particules at the edge of its gravitational field, which is immense. If a black hole can't even hold everything in, I doubt steel is going to stand up to those speeds.

Post has been edited 1 time(s), last time on May 27 2009, 3:08 am by Vrael.

Wikipedia:


"The equation shows that the energy of an object approaches infinity as the velocity v approaches the speed of light c, thus it is impossible to accelerate an object across this boundary."

You're not accelerating the edge of the disc though, you're accelerating the center, which is moving significantly less than c.

Yes well, you're accelerating the center of the disc, which is connected through inter-atomic forces to the outer edge of the disc, which is accelerated by those forces.

As great as Wikipedia is as a source, I never liked the idea of judging the bounds of the universe by a mathematical correlation discovered by a man. I suppose my beliefs in God negate my opinion, though.

If the bounds of the universe aren't discovered by man, who will they be discovered by? They aren't just going to fall into our laps from the sky.

I think that he was making the point that man (and his creations) are not infallible.

The rotation of the ring is already considered in the equation. The energy you're talking about is called rotational energy, but the equation I supplied from wikipedia uses total kenetic energy which includes rotational and linear energy.

And to accelerate the center, you need to apply force to the whole object.

Then you are referring to angular velocity/acceleration, which is completely different. Angular velocity is measured in degrees/radians over time not displacement over time.

Exactly, thanks for clarifying.

Say what you mean and mean what you say


Nevertheless, the particles at the edge of the disc still have a linear velocity which can be measured in displacement/time, and are experiencing a linear force in the direction of the centripedal acceleration (just the direction is constantly moving about the circle). It would be cool if some scientists did this up in space somewhere, strapped some rockets onto the bottom edge of a giant disc and fired them off so it would spin real fast. I doubt they'd be able to get the outer rim close to light speed, but I'm sure they could stick some instruments on the outer rim to make measurements or something useful like that.

Right, which then goes back to the original problem. Even if were referring to a point say 0.0000000001 nanometers or less from the center it would still mean the same thing. The stresses formed from the centripetal forces would far exceed the maximum tensile strength of just about any type of material known to man kind. Not to mention that achieving such tangential velocities with non-zero mass objects is already a problem to begin with.

I just watched Star Trek last night, most of the "physics" they spout out is pure nonesense, even one of the friends who I watched it with agreed as a physics major. Nevertheless it was a great movie (although i wish I knew a little more about its history)

Post has been edited 2 time(s), last time on May 28 2009, 2:09 pm by MillenniumArmy.

I hated how 1 drop of the red matter created the same effect as the who stockpile.

This. Once you start approaching light speed some of the object's energy starts to turn into mass and thus will naturally start slowing down.

Also yes the physics of it is pretty ridiculous. And somehow it's not a problem to put a giant blackhole within earth's solar system I guess.

What if we used a black hole as a sort of particle accelerator.

Say we have 1 atom flying around a black-hole near the speed of light, to where it is in orbit.

After this, we start adding more and more and more matter into the black hole to create a greater gravitational pull. As the gravity increases, the atom is pulled closer and orbits the black hole at an even faster pace than before, and maybe reaching the speed of light.

According to the equation:



You would need an infinite amount of energy to travel the speed of light, as dividing by zero results in zero once you reach the speed of light.

The atom would gain mass as it reaches near speed of light speeds, and then the atom would have a greater "pull" away from the black hole as it gains mass, maybe staying in its original orbit as we add more mass into the black hole, but what if we keep putting more mass into the black hole?

The critical point you missed about orbits, Cecil, is that the velocity and acceleration are perpendicular (for circular orbits). That is, the velocity is constant, and the acceleration is in the direction of the center of mass of the black hole, but does not affect the magnitude of the velocity, so it isn't going to accelerate that way, and if the acceleration due to gravity of the black hole increases and the atom is forced from its equilibrium orbit, the atom will accelerate towards the center of the black hole and not remain in orbit. Once the atom reaches the "light barrier" or whatever it's called (that spherical shell which acts as a barrier that light cannot escape because of the magnitude of the curvature due to the black hole), then we can't even tell what's happening anyway.

The "pull" would be greater in the direction of the black hole as the atom grows more massive, as we can see from the gravity equation
g = G*M1*M2/(d²)

where g is the acceleration due to gravity, M1 is the mass of the first object, M2 is the mass of the second, G is the gravitational constant, and d is the distance between their centers of mass.
Since M1 and M2 are directly related to g, any increase in either M1 or M2 (the black hole or the atom) will cause the force between them to grow, not diminish, and the atom will be sucked in even faster.

It doesn't matter what you're accelerating, nothing can go over C.

As it reaches C it's energy reaches infinity, meaning it basically explodes/burns up.