by Mokurai » Thu Jun 03, 2010 11:40 pm
Taking the question simply as it is, and ignoring how any of it would be possible, we have a pole rotating so that its outer end goes around a circle with a radius of one light-year in 10 seconds. It thus travels 2 pi light-years in 10 seconds, or about .628 ly/sec. This is obviously impossible. A year is about 365.25 days × 86400 sec/day, or 31.6 Msec. The end of the pole would have to move at 20 million c, which tells us just how impossible this scenario is. Even if we could make the pole of the still hypothetical tachyons, which would be able to travel at that speed, the pole would come apart even faster, since tachyons supposedly travel at greater than c relative to each other. So in fact none of the scene described happens. Well, we knew that anyway.
If it weren't for physics and law enforcement, I'd be unstoppable. But there it is.
Where does the question break down? First, the pole is supposed to be a light-year long, or about 6 trillion miles (10 quadrillion meters, 10 petameter, or 10 pm). Suppose we have a fantastically light and strong material with a mass of 1g/m but extreme rigidity. That gives us 10 pg total mass, on the order of a six-trillionth of the mass of the Earth, comparable to a modest-sized comet.
The centripetal force required for you to hold on to it is mass × acceleration as if all of the mass were concentrated a half light-year away at the pole's center of mass. The acceleration is v2/r. With the outer end moving at 1 km/sec, you would have to exert 10 Pg × 1 km2/sec2/10 Pm, or about 1,000 newton. A strong man can lift half a ton with his legs, exerting a force of 500 kg × 9.8 m/s, or nearly 5000 newton, so that isn't so bad. However, the force goes up as the square of the velocity. Incorrectly using this Newtonian formula in the super-hyper-megarelativistic range of ly/sec, many billion times faster, gives us a requirement for roughly a gazillion strong men just to hold on to the pole, and similarly for the tensile strength of the material. It exceeds even Larry Niven's scrith, as described in his Ringworld SF novels.
We could go on, and consider how much force is required to swing the pole (hint: even more), what its bending moment and required rigidity would be, the time required to get any effect from one end to the other, vibrations running along the length of the pole, the resulting hazards to interstellar navigation, etc. etc. Each of which gives the answer, No, No, ten to the umpteenth times No.
Now a beam of photons from a millisecond pulsar is another story. It isn't a straight-line beam, of course, but a spiral that wraps around a vast number of times between there and here, at intervals of a few hundred km.
Taking the question simply as it is, and ignoring how any of it would be possible, we have a pole rotating so that its outer end goes around a circle with a radius of one light-year in 10 seconds. It thus travels 2 pi light-years in 10 seconds, or about .628 ly/sec. This is obviously impossible. A year is about 365.25 days × 86400 sec/day, or 31.6 Msec. The end of the pole would have to move at 20 million c, which tells us just [b]how[/b] impossible this scenario is. Even if we could make the pole of the still hypothetical tachyons, which would be able to travel at that speed, the pole would come apart even faster, since tachyons supposedly travel at greater than c relative to [b]each other[/b]. So in fact none of the scene described happens. Well, we knew that anyway.
If it weren't for physics and law enforcement, I'd be unstoppable. But there it is.
Where does the question break down? First, the pole is supposed to be a light-year long, or about 6 trillion miles (10 quadrillion meters, 10 petameter, or 10 pm). Suppose we have a fantastically light and strong material with a mass of 1g/m but extreme rigidity. That gives us 10 pg total mass, on the order of a six-trillionth of the mass of the Earth, comparable to a modest-sized comet.
The centripetal force required for you to hold on to it is mass × acceleration as if all of the mass were concentrated a half light-year away at the pole's center of mass. The acceleration is v[sup]2[/sup]/r. With the outer end moving at 1 km/sec, you would have to exert 10 Pg × 1 km[sup]2[/sup]/sec[sup]2[/sup]/10 Pm, or about 1,000 newton. A strong man can lift half a ton with his legs, exerting a force of 500 kg × 9.8 m/s, or nearly 5000 newton, so that isn't so bad. However, the force goes up as the square of the velocity. Incorrectly using this Newtonian formula in the super-hyper-megarelativistic range of ly/sec, many billion times faster, gives us a requirement for roughly a gazillion strong men just to hold on to the pole, and similarly for the tensile strength of the material. It exceeds even Larry Niven's scrith, as described in his Ringworld SF novels.
We could go on, and consider how much force is required to swing the pole (hint: even more), what its bending moment and required rigidity would be, the time required to get any effect from one end to the other, vibrations running along the length of the pole, the resulting hazards to interstellar navigation, etc. etc. Each of which gives the answer, No, No, ten to the umpteenth times No.
Now a beam of photons from a millisecond pulsar is another story. It isn't a straight-line beam, of course, but a spiral that wraps around a vast number of times between there and here, at intervals of a few hundred km.