Tim Little wrote:
> On 2008-03-16, Ben Crowell <crowell07@[EMAIL PROTECTED]
>
wrote:
>> Mmm...I would consider diffraction to be a fundamental physical
>> limitation, not a minor engineering problem. If the laser is
>> at rest with respect to the galaxy, then it has to operate over
>> distances of light-years.
>
> You want to accelerate a 10^17 kg black hole at 100g over distances of
> at least a couple of light-years? Ouch. The project then needs at
> least 10^37 J of energy available.
Yeah, it's a crazy amount of energy. To get it up to a gamma of 10^4,
you need energy equivalent to 10^4 years worth of a sun's light
output. If you only want a gamma of 10, then it's only (!) 10 years :-)
But if you want to physically travel around a galactic civilization
within a human lifetime, you need a gamma of more like 10^4. This
is sort of a generic problem with any scheme for physical travel
around a galactic civilization.
>> In any case, there's another issue that seems more fundamental,
>> which is that 10^29 W converts via E=mc2 to 10^12 kg/s, which is
>> enough to double the mass of our black hole in hours.
>
> Oh, if you need more than that, then don't feed the beam into the
> hole: just let the hole's gravity bend it, say 150 degrees or so. As
> a bonus, you get nearly double the momentum transfer. Of course the
> red****ft will be a problem in any event since the gamma factor will go
> past 200.
The problem with that is that the beam is going to be spraying all over
the place, killing anybody in the vicinity. You don't get
large deflections like this unless the impact parameter of the beam
is comparable to the radius of the event horizon. The relative error in
the deflection angle is comparable to the error in the impact parameter
relative to the radius of the event horizon. So you still need a beam
collimated to 0.1 nm, or else you're basically spraying the scattered
beam in every direction uniformly, which means you've made a point
source of gamma rays with an intensity equal to hundreds of suns.
> On the plus side, the diffraction problem isn't as bad as you think:
> an on-site collimator can direct the laser to the correct location
> near the hole.
Three objections:
(1) Matter is essentially transparent to gammas of this energy, so a
collimator won't collimate.
(2) The small fraction of the beam that does interact with the
collimator will be plenty to destroy the collimator.
(3) I don't think you can make a collimator out of atoms that will
collimate to 0.1 nm.
>> Good point. Well, the exhaust velocity can be a small fraction of c
>> -- you want it to be a small fraction of c in order to get a decent
>> thrust-to-power ratio.
>
> Absolutely not: the mass/payload ratio is exponential in
> delta-V/exhaust and for 100g acceleration over 2 light years the
> delta-V is at least 6c. If converting mass directly into energy at
> arbitrary rates is a problem, then the whole project is doomed.
You're right. I hadn't figured that properly. Thanks!
I had beamed energy in mind, not an energy supply carried with the
****p (probably said that elsethread). (The thermodynamics of heat
engines make it impossible to built a relativistic drive that's
a heat engine, because it would burn itself up with its waste heat
-- unless someone can come up with some *really* creative way to
get rid of the heat.)
But anyway, as you point out, the sheer supply of reaction mass becomes
an insurmountable problem unless the gamma of the exhaust is comparable
to the gamma you're trying to achieve. So the exhaust is going to be
relativistic, but I don't think the hazard posed by the exhaust
to the crew module is the biggest obstacle.
I think so far the biggest issue is simply the absurd amounts of energy
required.
>> Maybe the magnet is on the end of a 10 km superconducting cable
>> trailing behind the thrust module.
>
> Heh, the cable is subjected to a tension of 10^20 N. I think ordinary
> matter is out of the question.
Mmm...interesting point. Let's say the cable has a tensile strength of
20 GPa (similar to the best known materials). Then the minimum diamater
for the cable is ~100 km, and if its mass is going to be less than the
mass of the black hole, then it's going to be limited to a length of
~10 km, i.e., it's more like a pancake than a cable. So yeah, it would
definitely be necessary to use magnetic forces or something to relieve
almost all the tension in the cable. In other words, the cable is really
just an energy-transmitting device, not a force-transmitting one.
The question is then whether it's possible, even in theory, to build
an electromagnetic system with these properties. The answer isn't
obvious to me. So maybe the tow-cable is a bad idea. The exhaust
beams coming out of the particle accelerators simply have to have
good enough collimation that the beam halo doesn't kill the passengers
at a distance of ~100 m.
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