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Start with a really long rope. This could be something with a high strength-to-weight ratio like carbon nanotubes, but doesn't have to be.
Get yourself a rocket ship and a black hole. Attach said rope to your rocket ship, and send the free end of rope toward the black hole. Your ship should start
out far away from the black hole, and when the rope reaches the black hole it should form a straight line between your ship and the black hole.
Now the fun part. As the end of your rope enters the black hole, it will pull on your ship at the maximum strength of the rope without breaking. This is because near the black hole your rope is going through gravitational stretching, which is caused by differences in the gravitational force near a black hole. This gravitational stretching will be constantly breaking your rope near the black hole end, resulting in a constant pull on the rope at the maximum strength of the rope.
We now have a constant strong force on your ship. It will accelerate towards the black hole at a constant rate. Eventually, if your rope is long enough, you and your ship will be traveling near the speed of light.
Of course, you will now be traveling near the speed of light towards a black hole (that's bad, right?). Don't worry; just turn on your side thrusters enough so that you miss the black hole. Let go of the rope just as you pass the black hole, and you'll be blackholeapulted off on your merry way toward whatever interstellar destination you choose.
Short comment on waugs' rigid rod theory
http://web.archive....tel/rass/rigid.html
[Worldgineer, Oct 05 2004, last modified Feb 14 2005]
superluminal scissors
http://math.ucr.edu...ty/SR/scissors.html
[Worldgineer, Oct 05 2004, last modified Oct 17 2004]
FTL FAQ
http://www.phys.nck...eedOfLight/FTL.html
See section 4 [waugsqueke, Oct 05 2004, last modified Oct 17 2004]
About meters and light-speed
http://math.ucr.edu...speed_of_light.html
The length of the meter is Officially defined in terms of the speed of light. [Vernon, Jan 03 2005]
(?) Tidal Force formula (or most of it)
http://www.daviddar...a/T/tidalforce.html
[Worldgineer, Jan 03 2005]
Elephants on a rope
Elephants-on-a-rope
If carbon nanotubes can't do the job, the elephants are ready. [robinism, Jan 08 2005]
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Annotation:
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Danger on a galactic scale ... |
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We already use the planets as gravitational slingshots, and there's no reason to suppose the same couldn't be done with black holes, with or without rope. |
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But I would like to see some calculations, not just a vague "you will now be traveling near the speed of light" and a magic rope strong enough to tow you to such speeds. |
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[Dr.C] No magic rope necessary. Let's use 30 lb. fishing line and a 10 ton ship. Force=mass*acceleration, so a = F/m = 30lbf/20000lbm = 133(kg*m/s^2)/9072kg = 0.0147 m/s^2 |
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This means every second you'll be going 0.0147 meters per second faster. After one minute you'll be going 0.88 m/s, one hour: 52 m/s, one day: 1267 m/s, one year: 462,000 m/s. So, using fishing line it'll take you 495 years to approach the speed of light. However, if you use something 500x stronger (steel cable should work, or 500 strands of fishing line) you'll be there in under a year. |
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//it will pull on your ship // I doubt it somehow. |
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What do you think would happen? |
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the damned rope would break <g> |
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if black holes are so big and clever, why don't they suck the entire universe into them? or perhaps we have just been spewed out the other side. |
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For the same reason we don't all fall into the sun. (sorry if I gave you something else to worry about) |
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4 year-old, having read Worldgineer's comments: "Daddy, why *don't* we fall into the sun? |
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Daddy: "Now that you ask... I confess I don't kn...aaaauugh! <falls into sun> |
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no worries, world. I am more concerned with things down here. |
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Worldgineer: now let's see some calculations of how near the rope has to be to the black hole to get a 15,000-lb tug, and how far the spaceship has to be to be able to accelerate for a year and still be a safe distance from the black hole. And that at least will give us the length of this rope. |
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(I think we're back to the same objections we had to nuclearfarts' daft idea.) |
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//how near the rope has to be to the black hole// Somewhat close to the event horizon. I could do the calc's, but what does it matter? |
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//how far the spaceship has to be to be// I was afraid you would ask that. Damn calculus. Although the velocity-time graph will be a nice straight line between 0 and the speed of light, the distance-time curve will look a bit like a graph of e^x. I'm sure I can do the calculus, but instead let's just take 2/3 of the final velocity as an approximation for our average velocity. 2/3 speed of light x one year = 447,076,800 (miles/hr) / 8760 hours = 51 thousand miles of 500 strand fishing line. I said it was a long rope, didn't I? |
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Oh, and I take offense to you lumping this in with the planetary grapple. |
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Why? You're doing the same thing, substituting a black hole for a planet and avoiding the monofilament cable bullshit. And you divided instead of multiplying there. |
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dammit the fuse has blown in my side thrusters
>>>>>>>>>>>>>>>>>>>>>>>>O |
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(_!_) Aren't there time-compression effects to take into account? That is, sure the rope falls into the black hole, but it takes forever to do so, no? |
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[DC] My understanding of the grapple idea is that a base station reels in a ship when it's ready to come back home. It's poorly thought out, based on bad science and physics, and has at least a dozen reasons why it can't be done. Hence, offense taken. |
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Crap - you're right. It's 447,076,800 (miles/hr) * 8760 hours = 3.9 trillion miles of rope. Ouch. |
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So, in the end, just as dopey, right? |
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BUT, you can still use the gravitation well of the black hole to slingshot the spaceship, just as current space shots use the gravitational wells of the planets. No idea if that will get you up to relativistic speeds, tho. |
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You really stretched things out there, [worldgineer] but that's okay it all snapped back. <g> |
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Can I give you a Schrödinger croissant for the stretching principle? Wait, I should give it to [phoenix] for the time factoring. Maybe? Well, maybe not... |
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This sounds like a variation on the rigid rod theory, which I might link to (or you could just look up yourself, World). egnor brought it to my attention here. |
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Won't work because you're going to need an exceedingly long rope and the molecular structure and mass of an exceedingly long rope such as this will not 'transmit' the movement that fast. |
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[DC]No, still offended. In the end, 3.8 trillion miles of rope isn't so much. To put it into perspective, at about 1000 pounds per mile you're still only talking about 1/9,000,000th the mass of the moon. Compare that to the mass of fuel required to approach the speed of light in conventional designs, and it's tiny. |
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[waugs] I can't find anything on rigid rod theory, but are you saying it will act like a giant rubber band? I can imagine, but don't see how this would change anything. The tension will eventually transmit to the ship. |
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world, I may have missed it but how are you sending the end of the rope into the black hole from the rocket? |
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You don't miss anything, po. I had left it out for simplicity. I figure you just tie a little rocket on the end and aim it at the black hole. |
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[worldgineer], others' ingenuity is far shorter than your own 3.8 trillion miles of same. |
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So, how do you propose fabricating moon rock into a giant ball of nanotubing? <g> |
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// The tension will eventually transmit to the ship.// |
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No it won't. It'll reach a maximum transmission rate and never exceed that... significantly below the speed of light. |
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It's the same issue as the rigid rod theory exactly.. the only difference is you have a black hole pulling on one end of the rod. |
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The theory goes like this: you're in capsule A, I'm in capsule B and we are some ridiculously huge distance apart, say 9 million light-years or whatever, doesn't matter. Extending between us is a 9 million light-year long thin metal rod, one end of which protrudes into your capsule and the other end of which protrudes into my capsule. |
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(A)------------[9 million light years]------------(B) |
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If you push outward on your end of the rod, toward me, how long will it take for the corresponding end of the rod inside my capsule to move inward? |
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It seems like it should be an instantaneous reaction... allowing the person in capsule A to transmit information ("I pushed the rod.") to capsule B instantly across a 9 million light-year distance, far exceeding the speed of light. However it is not so... the actual rate of transmission is limited by the mass and molecular structure of the rod and is not even close to light speed. |
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There are whole websites devoted to just this topic, I'm sure you can find one without much difficulty. (If you can't find that, look for the superluminal scissors theory... same basic concept.) |
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Well, [waugsqueke], show us the math. <edit/ comment was made before several edits by [waugsqueke] to his/her previous annotation as originally posted, however, still waiting for the math> |
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Btw, what's that theory called having to do with instantaneous particle transmission... |
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//You don't miss anything, po. I had left it out for simplicity// hey man - you are hilarious. you think that minor detail would escape this lot <g> |
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[waugs] Ok, now I see what you're talking about. But that concept only applies to the speed of compression/tension waves in a stationary object. Shirley you're not saying that if you slowly accelerate a rigid rod the maximum speed it can ever go is the speed of sound of the material it's made out of? |
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[Tig] I'm not sure how to make carbon nanotubes in the first place. I was just trying to woo back people who were afraid of the //trillion miles of rope// and hope they realize that it's not as long as it sounds. |
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No, that's not what I'm saying... speed of sound is not involved here at all. |
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Look up the web sites. All answers will be found there. I'm too lazy and I don't feel like spending the entire day in one idea, explaining concepts that are already documented on other web sites. |
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see link. If that's not what you're talking about, please tell me what you mean. I'm not trying to speed anything up faster than the speed of light here, and that seems to be the only limitation in any of the links I've found about the rigid rod example you have given. |
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and so waugs is too tired to elaborate on his rigid rod. hhhmmmm. |
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I'm not afraid, [worldgineer]. This idea has me calf-roped. One hard-matter croissant. |
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re link: that is what I'm talking about, though that's just about the shittiest web site I've ever seen on the topic. There are much better than that out there. You're probably better off to search on superluminal scissors. |
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I know you're not trying to achieve light speed, but you're trying to get close to it, and you won't get close. That's what I'm trying to point out. |
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Tiger Lilly: You asked "Btw, what's that theory called having to do with instantaneous particle transmission" |
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I believe you are talking about "estranged pairs". This is a quantum theory principle that roughly suggests that you can fool an elementary particle into being into places at once. This offers advantages as a means of communication over conventional methods. |
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[waugs] I just chose that link because it was the shortest one I could find that would get my point across. I've now linked to superluminal scissors for you, but still don't get your point. If I can't get close to light speed with this method, how fast can I go? Why can I only go that fast - what physical property of a solid has a speed limit? |
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I have an estranged pear. |
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// If I can't get close to light speed with this method, how fast can I go? // |
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I don't know the answer, which is why I directed you to other sites that might be able to tell you. |
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Well I'm tired of asking questions of you that I already know the answer to (and yes, I read many websites of the type to which you are referring). The answer is that there is no absolute limit on speed below the speed of light. Yes, the rope will end up going quite fast. However, relative to itself, it's nearly stationary. I don't see your point and I'm afraid it's because you don't have one. |
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This is not exactly the same as the superluminal scissors, but I do see what you're getting at (finally). Tugging on one end of a trillion mile rope ain't gonna have much effect on the other end for a very long time. The question then becomes whether the tug on the rope can be propagated along its length fast enough that it won't ever exceed the strength of the rope. Given that we're dealing with a black hole here, probably not. |
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I'm still not gong to bother with the math myself, but if you have the technology to build a rope 4 trillion miles long, I rather imagine you would have alternative, and much more reliable, means of generating a 15,000-lb force. |
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Of course it has to do with the superluminal scissors, and the rigid rod theory. It's the same thought experiment. And the idea clearly states that eventually the person would be traveling "near the speed of light". I would not consider that a 'fraction' of it, though 'fraction' is sufficiently vague as to cover it I suppose. 60 mph is a fraction of the speed of light, if you want to be that vague. |
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World, it seems almost like you are deliberately misunderstanding me. I'm at a bit of a loss to explain why you are not seeing this is essentially the same issue. It's clear as day to me. You seem almost offended that I discovered a problem with your idea. |
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Let me draw your attention to this one line on the superluminal scissors link. I can't make it any clearer than this: |
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"As a practical matter, this theoretical upper limit to the rigidity of the metal in the scissors is far higher than the rigidity of any real material, so it would, in practice, take much much longer to close a real pair of metal scissors with blades as long as these." |
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Substitute rope for metal and this is exactly the same thought problem. Compression wave force works the same whether you push or pull, or squeeze like a lever. |
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If you still say that it is not the same problem, then we have some sort of fundamental misunderstanding that I don't know how to solve. Perhaps egnor will be along sometime soon, maybe he can explain it better than I can. |
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I promise I'm trying my hardest to understand your point. No, you don't have to consider the rope to be a rigid body for this to work. No, I'm not saying that the rocket will move instantaneously with the other end of the rope. I just don't see how your cases apply to mine. |
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//World, it seems almost like you are deliberately misunderstanding me// waugs. this guy is genuine. well worth the trouble - believe me! |
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Obviously, Worldgineer is drunk, and Boondoggle Industries has terminated him – several times now, actually. But even if physics were to behave as bizarrely as this, there is still one tiny flaw to his plan…wait, I just thought of another one…and two more. No point in writing them down even, because it suddenly occurs to me that World' has been reading the help page, and that this idea falls into the “impossible in interesting ways” looney bin. |
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See the link to FTL FAQ I just added. (One of the best I've seen on the topic - I very much recommend browsing around it. I particularly like "The moon revolves round my head faster than light!" paradox.) |
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But specifically I want to draw your attention to section 4, where you will find this quote: |
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"...hold a long string or rod vertically in a gravitational field and let go of the top end. The point at which you let go will start to move immediately, but the lower end cannot move until the effect has propagated down the length at the speed of sound in the material." |
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String/rope... gravitational field/black hole... let go of the top/pull on the bottom. Now can we be settled on the fact that we are talking about the same thought experiment? |
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//Substitute rope for metal and this is exactly the same thought problem.// |
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[waugsqueke], have you ever tried cutting anything with a rope, ever? |
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[po] Hah! I'm glad that you clarified that -- I was wondering if you were referring to waugs. |
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[waugs] Yes, I get the same thing you keep repeating. New thought experiment for you. Say the speed of sound in that string is 50mph. Now take that string and the mass who's gravity is pulling it and move them both 100mph in the direction of the massive body. Drop the string. Does it still move towards the massive body? My point is that the rope may be traveling really fast compared to the black hole, but the rope itself doesn't know this and will keep propagating it's tensile force at the speed of sound relative to the rope and the rope alone. |
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[plut] Impossible? I'm hurt. Interesting, flattered. Net balance. |
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Crap. This is way more time and effort I really feel like putting into one idea. |
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// the rope may be traveling really fast compared to the black hole // |
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What's making the rope move? I thought it was just the pull of the black hole. If you have some external force making the rope move towards the black hole, then that will obviously affect the speed of the thing tied to the end of it. My annotations were based on the presumption that the black hole is supplying the force here. |
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No, just the gravitational force of the black hole. |
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Okay. So we're talking about the force of the gravitation of the black hole acting on the rope then, and this would happen according to the examples I outlined above. Same thing. |
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Waugs is now at the end of the rope, world’ dangles him there a minute -- whoops, there go his feet… |
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Just remember, "A fool can ask questions that a wise man cannot answer." Whatever your opinion of waugsqueke, you don't necessarily want to be that fool. |
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[waugs] New thought experiment. Say you have a material with a very low sound propagation speed. In fact, let's call it real slow - 1 mph. You have a rope made out of this material. In our lab, we replace the gravity of a black hole with a couple of pullies and a crank arm. Now, you start turning the crank arm such that the rope is moving at 1 mph. You then speed up a bit and start cranking at 1.1 mph. What happens to the rope? |
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Plutes is right... end of my rope. My point has been made ten times now. You're not seeing it and nothing I say from here on will make you see it. |
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You've got all the brain time I'm prepared to give to this idea, sorry. |
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If you couldn't pull a rope faster than the speed of sound, you couldn't crack a whip. What ON EARTH does the speed of sound have to do with anything? |
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I believe waugs was saying that the maximum speed force can be transmitted through a rope is at the speed of sound in that material. This means that if the rope is traveling toward the black hole at the speed of sound relative to the black hole, the rope can't transmit any force. I don't buy it, hence my most recent thought experiment. |
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//"A fool can ask questions that a wise man cannot answer." // |
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Yes. And a wise man can question a fool but the fool will never learn why. |
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For the record, World... your last paragraph is totally incorrect. That is not what I am saying at all, which clarifies to me that you have not understood anything I've said in this whole idea. |
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I was trying to read between the lines because you have effectively said nothing. The last material anno you posted was about the speed of sound, and I've been trying to figure out your point since then. |
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Thankfully, there has been no mention of a Polepantergeist. |
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*After skipping past the second half of the anno's* |
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You people are too clever by half. First half of annos's = clever. Second half (assuming they are comparable in cleverness= too clever by half. Or would that be first 2/3, final 1/3? Too drunk to care. Have pizza in oven. Bye. |
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Dang. waugs, tell me what happens in this scenario. It sounds like it'd work, but if you've found a problem, I don't understand it either, and would like clarification. Just be a text-based simulator for me and World, okay? Right up to and through the point it fails, according to your perspective. Also explain what made it fail. |
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Man, how many times do you want me to go over the same crap (only then to be told I've effectively said nothing)? Not again, sorry. |
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Everything you need to know to understand why this won't work is included in the link I added. |
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[thumbwax], there is always the Apraphulin Multiplexer. |
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Okay. Good info. But--as it seems to me--just because the *effect* doesn't move at relativistic speeds doesn't mean that the *material* won't. If it does mean that, please explain how. Even if Wg won't, I'll listen. |
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<pedantic>You misspelled your closing markup tag.</pedantic> |
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<obvious>And UnaBubba.</obvious> |
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[UB]: good job explicating [waug]'s objection. However, assuming those problems could be overcome (work with me here) there is still the problem that as the ship approaches the speed of light, it will greatly increase in mass. The side thrusters would have to provide an impossibly large amount of thrust in order alter the vector of the craft. Essentially you end up having to solve the rocket-propelled light-speed travel problem as well (i.e. huge amounts of fuel on board). |
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World, how would the black-hole's gravity affect the entire length of rope? I think it would only affect the portion in the shpere of influence, creating much movement but little acceleration. |
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Damn it [dijontoothpaste], I almost posted your annotation exactly. Had you said that way up the top of the page, I wouldn't have bothered reading the rest! |
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I *don't* want to know about Rigid Rod's Tiger Theory. |
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Are you referring to [Rods Tiger]'s string theory? If not, what do tigers have to do with rigid rods? Also, why the two strings? |
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This must be that string theory thingamajiggie I never could quite grasp the meaning of... |
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There's a problem with the rope, and you can use fishing as an example. Say the fishing rod is the “black hole”, the line is your “rope”, and the hook is your spacecraft. Snag on something, and pull the line tight (the “constant force”). Then it gives way -- "the rope pulling your ship". The hook flies toward the pole. But the line bunches up -- it gets into a huge tangle. That’s what will happen to your rope. You’ll have a trillion miles of macramé. If the rope broke at that point, you and your knots are flying in some weird trajectory. You’re blackholeapulted, but not in a direction you chose. The “constant force” was instead a brief violent toss. And it may recur if the black hole catches the rope again. It's the same as if you used a Slinky or a rubber band. Just tie a rope to the Earth, a few hundred thousand miles out to see the effect -- you get yanked once and the rope goes slack.
As thoroughly discussed already, the rope is the weak link in this idea. Lose the rope. Instead, bring your ship near the black hole, using whatever power you were gonna use for the rope. Now let gravity sling you around. |
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I once caught a singularity t h i s b i g. |
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//I once caught a singularity t h i s b i g.// |
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Is a singularity not of infinitessimally small size by definition? |
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A couple of problems for the idea: |
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(1) Physics makes the slingshot idea impossible - ship would only reach c at the event horizon and that's exactly the point at which escape becomes theoretically impossible for a ship at the speed of light |
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(2) Gravity field gradient makes the idea impractical. Even if you elected to go _through_ the black hole, you'd likely pop out the other side as a high energy beam (X-rays perhaps?) rather than a fully operational starship. |
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OTOH, if the idea was to fly in the general vicinity of a black hole and slingshot around nearly parallel lines of the gravity field gradient, then yes(~ish)! The problem is then that the range at which that is practical and safe is so large that you'd have to be going at extraordinary velocities to make it worthwhile. |
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This idea derivation makes more sense with planetary bodies, moons maybe stars, and maybe, just maybe neutron stars (but someone'd have to do the math on the last one to be sure). |
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Let me know if someone has already mentioned this (i tried to read all the annos, but may have missed a couple), but i see as a glaring problem that it would take a little while to make 4 trillion miles of rope, then a wee bit longer to fire it into a black hole 9 million light years away. |
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If we start now, we may magage it in about 50 billion years (give or take...) |
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It wouldn't take *that* long. We have a nice black hole in our own back yard. It's just over 30 light years away in the center of our Milky Way. Now, I'm thinking if could get Nolan Ryan in on this... |
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Yeah, but one of the earlier annos said we'd need to use a black hole 4 trillion miles away to give time to accelerate before getting sucked into it... |
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My physics is crap, so i am taking everyones word for this... |
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And I disagree with Wags. I don't think the case is the same. |
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Basically the idea relies on the force on the string increasing as we get closer to the black hole.
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Ignoring all the difficulties of manufacturing rope etc |
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We can accept that at some point close to the black hole the force will break the string.
But the point above it would feel a force close to the maximum the string could bear. |
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This force would propagate the entire length of the string. Not at light speed. Just at the standard physical rate for such string.
Thus it would apply a force to your spaceship at the other end of the string. This would accelerate at whatever rate..
The force would be constant (provided the string can break cleanly and not whip back and 'yank' and break it higher up - a problem someone else suggested.) |
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As the ship accelerates the string does too. Hurrah! |
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For what it is worth - I think I have the solution to avoiding the black hole. What you need are two black holes, right, and two pieces of very long, strong sacrificial string... |
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Eh. I give up on this one. It might work, but man, the rope. 4,000,000,000,000 miles of it! |
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[Curry] You have to look at where the string would break - always near the black hole, and you'll realize that although the lag will certainly be long, the rope won't break (except near the bh) and won't exert a huge force on the ship (because the rope only has so much strength). |
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[Loris] Nice idea if you want safety. I'm going to trust our engineers to get us out of the way of the bh in time. |
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[galu] Now you're scared about the string length too? Sure it's a long string, but I'm not convinced it's past our capability. Do you know how many miles worth of french fries America consumes each year if laid end to end? Certainly we can apply our mastery of potato technology to string production. |
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Uhh... Just a quick sidebar here: How many semesters of science did you take? |
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I think it would take more than just side thrusters to avert certain doom (of course the rope idea is totally feasible). |
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But you get a + vote for sheer courage :) |
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You wouldn't want to have just one rope attached to the front of the ship - it would take a long time to get the end of the rope all the way to the black hole. No, this would be like a rope tow skilift, with one end being paid into the black hole and the other end being spun out of some planetary body. Ships would grab onto the rope, ride up to speed, then let go. |
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Maybe a junior sized version of this could be done between the moon and Jupiter to get ships out of the solar system. |
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[Tiger Lily] - // We have a nice black hole in our own back yard. It's just over 30 light years away in the center of our Milky Way. // - I'm pretty sure now that we're not from the same planet. |
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Just as I suspected. I thought you might be an alien. |
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[Lurch], is a well-rounded 30,000 light years better? No biggie. Often, I find that zeroes add nil. |
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I was really wondering about the lack of time lag. |
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You da' alien! <long pause> No, *You* da alien! <long pause> etc... |
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So... you're a symbiant? ;-) |
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One problem, (providing that it will work 447,076,800 : 1) this black-hole-apult has only one shot, this is the hugest waste of 60 billion pounds of carbon that could have been used to make duplicate paper. |
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The benefits(going really fast) will not outweigh the time and resources spent. |
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[Trod] That's a cost-benefit analysis that I'm not willing to define. The cost seems to be far lower than existing technologies, so cost is relative. On what basis do you say it's not worth it? It all depends on how much exploration knowlege is worth. Was the trip to the moon worth it? |
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[everyone with the side thruster issue] I'm not convinced the energy required to move the ship sideways is an issue. We're talking about a 4 trillion mile trip here, a small push sideways near the beginning should do it. |
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[everyone with the no nearby black hole issue] Well, this is a big one. I'm going to call this idea a partial idea. Just as the zipper is useless without clothes, I'll be happy with this idea sitting on a shelf until either: 1) We find a way to create a black hole somewhat near us; 2) We make contact with another society far away with access to a black hole, but don't have a way to use it; or 3) We find out what all of the dark matter is - there may be closer black holes than we know. |
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wow. if the idea doesn't deserve a croissant, then this multipage discussion of it does. thanks to all of you enlightening ones!!! |
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I love the category. Considering the time it would take to reach the fraction of light speed, the cost of creating the rope and the chance of crashing into a black hole, I'd say this is an even less useful form of public transportation than British Rail. |
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Thanks UB. I thought "whats the worst possible time to go back to halfbaking" and the answer was clear - right in the midle of my A level exams. No-one ever accused me of being sane though. |
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Hang on - I understand why a solar sail could accelerate a ship to near light speed, as the photons pushing it are traveling at light speed. This rope would not be moving at light speed: the rope would be moving at the maximum speed it could pull its long-assed self along without breaking. This is not going be anywhere near light speed. Say it is 1000 mph (strong rope). A rope pulling at 1000 mph is not going to be able to accelerate a ship faster than 1000 mph. It would be like a waterskiier zooming ahead of the boat towing her. The maximum speed of the ship is the speed of the rope. |
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Bung, I have some rope in my garage going 67,000 mph (revolving around the sun). Why can yours only go 1,000? Speed has to be relative to something else. There is no maximum speed lower than the speed of light for an object with constant unbalanced forces. The reason a waterskiier seems to have a maximum speed is that you have opposing forces (drag from water and air) acting on the boat and the skiier. |
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The original spec used 30-lb-strength fishing line and a 10 ton ship. Since it turns out that the line has to be 4 trillion miles long and weighs about 2 trillion tons, the mass of ship + line is about 2 trillion tons. 30-lb-strength line will accelerate that combined mass very, very slowly. So the line will have to be about a trillion times longer. Of course the longer line will weigh even more... |
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<homer simpson>Doh!</hs> Cyber's right. I guess we'll have to use carbon nanotube rope after all. |
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my favorite scientific phrase.. the "spagetification effect" as you get closer to a black hole the end closest to it has more gravity pulling it.. this tears it apart first at the molecular level then at the atomic level.. so it wouldnt matter how strong the rope is.. but then again, the same thing begins to happen to your ship as you pass the black hole.. first the ship splits in half.. then again and again in a long spagetti string of particles right into the black hole.. sorry, i've never liked the idea of using black holes for anything.. but im not saying its a bad idea |
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Well I never told you to get _that_ close. |
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Wow, kudos to everyone involved, especially [Worldgineer] and [Waugsqeke], for producing this epic. For what it's worth here are my own thoughts:
1) This idea really has nothing to do with the speed of light. Its just a way to accelerate a spaceship using gravity. It also doesn't really have anything to do with black holes. If it works, it would work with any gravity well.
2) It also has nothing to do with the sort of gravitational sling-shotting used by NASA. That uses the velocity of an orbiting planet to increase the velocity of a space-ship with_respect_to_the_sun - NOT with respect to the planet.
3) The breaking of the string complicates matters. Here is a simpler version of the same basic idea. You are a million miles above a moon. The force of the moon's gravity accelerates you towards the moon. When you pass by the moon (you don't hit it because you had a little tangential velocity to start with) you are going very fast, but as you go up the other side of the gravity well, the force on you is exactly the same as when you came down, so by the time you are a million miles from the moon on the other side, you stop, and fall back.
How can you escape the gravity well (or at least climb higher up it?) You need the force on the way down to be greater than the force on the way up. So... you ask for a volunteer. You suspend said volunteer on a string half a million miles long. The acceleration due to the moon's gravity is four times greater on your suspended chum than on you (because of the inverse square law). Because you should be accelerating at different rates, but you are linked together by the string, you both accelerate at a rate which is halfway between his and yours. When he passes the moon, you let go of the rope, and you are no longer linked. He is going slower than he would have been without the rope, and so climbs to less than his original height in the gravity well. You are going faster than you would have been, and so climb higher than your origninal height. Possibly you escape the gravity well altogether and shoot off to explore the endless wastes of deep space.
What does this have to do with [World]'s idea? Well if you extend my one-chum model to a model of many smaller chums, then you have [World]'s string theory.
Wow this anno was even longer than a blackholeapault carbon nano-filament. |
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That's some chum you've got there, moggy! //He is going slower than he would have been without the rope, and so climbs to less than his original height in the gravity well. // Really, an interesting alternative to the sentence "he falls to an extremely messy death". After that, he really will be chum! |
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Any idea which generates this much comment and debate deserves a pastry for that alone! |
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Seriously though, spacemoggy's analogy raises an interesting question: |
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If the best way to accomplish this slingshot effect is to let go of your sacrificial mass all at once, at perigee, how effective will this idea really be if you are losing small bits of rope the whole time? |
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[moggy]'s idea would be quite effective if you don't have a black hole but do have a spare friend. However, with the blackholeapult method you are having the maximum pull on your rope continuosly. The more granular (less chums) that [moggy]'s method is, the more this force will fluctuate. |
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<Hopes to never be moggy's 'spare friend'> |
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[Worldgineer] I thought I mostly understood what waugsqueke was talking about, except that the relevant speed *is* the speed of sound. In your example of the mass and rope moving at 100mph where the rope has a speed of sound of 50mph, after 1 hour, 50 miles of rope is feeling the pull from the rope right next to the mass. The rope has travelled 100 miles. If the mass hadn't been moving, the rope would have fallen onto it half an hour ago. |
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If the remaining rope wasn't under much tension to start, it's not at the end of an hour. On the other hand, maybe the tension can be transmitted while the rope's still moving slowly. |
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I must finish the post now, my brain's starting to hurt. |
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Could you just use a planet instead of a black hole? |
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Has no one yet considered this (yet another) difficult factor? If the rops is , say 4 trillion miles long, how long will it take to get the end of the rope to the black hole from where you are? |
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Anyway, the "snapping" factor of the limited tension-response of a rope is slightly diminished by the fact that the gravity of the black hole acts on the entire length of the rope simultaeneously (and on the ship too!), albeit to a lesser and lesser degree the farther away you get. How much effect this will have remains to be seen--inverse square law and all that, we'd have to know the mass of the black hole to figure out the actual force being exerted on any point of the rope. |
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I see two problems with this idea. First has to do with initially deploying the rope toward the black hole. You are carrying it HOW along with your spaceship? If fully deployed, what about some piece of space debris colliding with it and snipping it? So, NOT fully deployed. Which means you have to "stand back" from the black hole and throw the rope toward it. You can't just "drop" it because the spaceship will be dropping toward the hole, too! How long is this rope going to take to arrive? --oh, I see [5th Earth] already asked that. Well, I second the question! |
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Second, please recall the Larry Niven short story "Neutron Star", in which a spaceship passing close to a strong gravity source gets its passenger ripped apart by tidal forces. I'm quite sure this idea suffers from that problem, too. |
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[casp] I disagree with your arguement, or perhaps I just don't understand it. The string doesn't know or care how fast it's moving. |
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[5th] & [V]'s first issue was addressed: //world, I may have missed it but how are you sending the end of the rope into the black hole from the rocket?[po]//
//You don't miss anything, po. I had left it out for simplicity. I figure you just tie a little rocket on the end and aim it at the black hole.[World]// |
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[V]'s 2nd issue is a valid one, but only if you have to come fairly close to the event horizon. I don't think that's a requirement for this idea. |
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[Worldgineer], You might be surprised just how much tidal force you are going to have to deal with in this idea, mostly because of the SPEED involved. That is, suppose you whip around the black hole at, say, 10% of the speed of light (I know you want more but this should still reveal the scope of the problem), exactly 29,979,245.800 meters per second (per definition of length of meter; see link). You want the hole's gravity to do the curving of your path at that speed, to avoid the centrifugal effect. So, only the tidal effect must be considered. To simplify things I'll assume a straight/hemicircular/straight (and not hyperbolic) path as your ship approaches and goes around and leaves the hole. If the radius of the hemicircle is exactly 1000 km (remember that a stellar-mass black hole may be less than 10km wide), and we assume the hole has enough gravity to force this curve to happen at that distance and speed, THEN the following numbers apply (15 significant figures): |
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(A) The length of the hemicircle is about 3,141,592.6535898 meters (there ARE times when all those digits of pi come in handy!)
(B) The amount of Force we compute comes from the formula F=(m)(v)(v)/r
(C) We FIRST set m=1 kg (part of your body), v=29,979,245.800 mps, and r=1,000,000m (radius in meters)
(D) Thus F=898,755,178.736818 Newtons (balanced by gravity, so no effect on body)
(E) We now do the same for another 1kg part of your body which is 1/2 meter farther (radius) from the hole
(F) It will traverse a larger hemicircle, about 3,141,594.22439 meters long
(G) At 1/10 light-speed, it traverses that distance in the same time as before, 0.10479225109759 second
(H) The velocity of that second part of your body is thus about 29,979,260.7897 mps
(I) The formula then yields 898,755,628.116512 Newtons of force
(J) The DIFFERENCE between the two results, 449.379695 Newtons, is what the hole's gravity does NOT balance
(K) Now, the gravity at the Earth's surface is about 9.8 Newtons/kg
(L) Thus the tidal effect of the blackholapult is more than 45 Gs across that 1/2 meter distance between your body parts, in the case just described.
(M) Experiencing that many Gs for only a tenth of a second is survivable (though not comfortable! --probably even injurous). But remember, you want your blackholapult to accelerate you to nearly light-speed, 10 times faster than I've computed here, and thus associated with 100 times as many Gs. |
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Thanks, [Vernon], I always appreciate good math (and at least 7 of those sig figs did end up to be useful). But then I don't think we'll even need to get near 1,000 km from the black hole for this to work well. |
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Something else is bothering me about your scenario. From my link, //Tidal forces are proportional to d/R³, where d is the density of the gravitating mass and R is the distance from it.// This is much different than your equation, which seems to be describing centrifugal force around a circle. This wouldn't be the case, as any path my ship takes would be along a straight line - it only appears curved because space is curved locally. |
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[Worldgineer], that proportionality d/R³ is at least a description of how the tidal effect changes under different situations. Double the radius of the curve (from 1000km to 2000km, and the EFFECT (across that 1/2meter difference AT the 2000km mark) lessens by a factor of 8 (only a little more than 5 million Gs!). OK? |
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Next, while I don't have all the data handy, I wouldn't be surprised if that formula gave similar results to the one I used, which was indeed for the centrifugal effect. (Note the description at the link DOES mention centrifugal forces and differences.) For their example of astronaut-ripping, they want 6 times the mass of the Sun inside a radius of 5300km. Remember the normal radius of all the mass of our single Sun is about 700,000km, so squeezing it down and sextupling it means ENORMOUS density. |
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Also remember that I assumed you could whip around the hole at 10% of lightspeed. (Note it is also the speed that is the real problem, since it is SQUARED in the centrifugal force equation.) I arbitrarily specified that the hole have whatever mass necessary to allow it. From the preceding, it is easy to conclude that at the safe distance from a 6-sun hole, your velocity is going to be lots less than 10% of c -- which sort-of puts a hole in the middle of this whole Idea, as a way to go fast. :) |
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Finally, reference frames aside, any slinging around a large mass is going to include at least SOME arc. The radius used in the equations is independent of how much arc is traversed! That's why I could make the simplifications I did, and still get pretty good (I think) answers. |
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I buy your arguement for equivalent equations, but don't see why you have to fly that close. Let's see how close we can fly safely:
at 10% c, 20 N/kg max: ~4,740,000,000m
at ~100% c, 20 N/kg max: ~47,400,000,000m, or about 30,000,000 miles
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Although this sounds like a huge number, we're working with 4 trillion miles of rope here - about 130,000 times this length. |
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[Worldgineer], Now we are back to the question of how long it takes the rope to arrive at the hole, before it can do its job. A 4-trillion-mile length is about 2/3 of a light-year. It takes LIGHT 2/3 of a year to reach the hole, and you KNOW the rope is going to be rocketed there lots slower than that (otherwise you'd use that method to directly accelerate the spaceship!), so how long is the spaceship willing to wait in place, before any rope-caused acceleration begins? |
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Next, there is the speed-of-sound-in-rope thing (a reasonable estimate is 1760 yards or 1 mile per second, and 4 trillion seconds is well over 100 years), as previously discussed at length, for maximal acceleration to reach the spaceship. |
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Next, there is the rope-breaks thing, which was mentioned previously, but without so much focus as the other. Note that you are expecting the rope to accelerate the spaceship at the end of the rope. HAVE you also noted that obviously the ROPE is getting accelerated, too? Thus the MASS of the rope, all 4 trillion miles of it, as well as the mass of the spaceship, is "dangling" from the end of the rope, relative to the pull caused by the black hole. I think no rope-material known or hypothesized can support/accelerate that much mass without breaking. Sorry. |
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Nevertheless, if you can solve that, I do see that this Idea MIGHT get your ship close to light-speed reasonably well before it reaches the black hole. Then it becomes a matter of ensuring you can give your spaceship enough sideways vector to miss the hole, before you get within the tidal rip-apart distance.
Good luck! |
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The speed of sound in diamond is 12,000 m/s, so it may take on the order of 10 years to reach the ship assuming we use another closely-packed array of carbon molecules like carbon nanotubes (actually, carbon nanotubes have stronger bonds than diamond, which may play in our favor). |
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As for the time to rocket the rope over, yes it will take a while. But then manufacturing the thing will take a while as well. I think it's worth the wait for interstellar travel. |
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[edit: Numerical correction deleted]
[World] Okay, I'm not sure its a problem for the idea even if I'm right. |
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[caspian], THANK YOU. It seems I typoed a comma instead of a period, and didn't really think about it.... The prior text has been edited appropriately. Thanks again! |
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[Worldgineer], there is another problem with the rope, that I've added to my prior annotation.... |
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[Vern], assuming you've only edited your last comment, I believe the only part I haven't addressed is the paragraph that ends in: //I think no rope-material known or hypothesized can support/accelerate that much mass without breaking.// |
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But that's the beauty of this! It does break, but at the black hole end. I've discussed this earlier, but the maximum force is at the black hole with it's high tidal forces. Therefore the rope will be transmitting it's maximum tensile strength continuously. |
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Though you've focused on the rope breaking, the real issue of the extra mass is slower acceleration. This was a huge problem with fishing line, and will still likely be an issue with carbon nanofiber, but unless you know the mass per trillion miles of carbon nanofiber I don't know how large a problem this will be. Actually, it's more complicated than that - you can only calculate it's mass as a function of fiber thickness, and to find fiber thickness you need to know the maximum tensile strength you need, and to find the maximum tensile strength you need to know the amount of mass you need to accelerate at a few g's. Therefore it's solvable but iterative and involves some optimization. |
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Perhapsif we use custard, syringes and a blimp, it will work somehow |
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[Worldgineer], OK, but you sort-of have an upside-down situation that you may not have properly considered. First, let's consider an ordinary situation like using a rope to lift a piano to the 100th floor of a skyscraper (all right, maybe not so ordinary, heh). Now let's pretend we're doing this on an asteroid like Vesta, where gravity is small, yet also dimishishes significantly with distance The biggest mass being moved here is the piano, and it is closest to the source of gravity. At any point of the rope along the wall of the skyscraper, the rope has to carry the load of the pulled piano and the load of the rope below it. But that load is not equal everywhere, because of the diminishing of gravity with distance. In this particular case the rope probably won't break. |
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Now, in your blackholapult, the spaceship, the main load, is at the LOWEST point of the system, while only rope is at the highest-gravity region. This may sound nice, but we know the rope is going to break. WHERE? It is going to break at a place rather far from the black hole, where the weight of the rope below is greater than its strength. ONCE THAT HAPPENS, the force that pulls the rope (and faraway spaceship) is going to be as SMALL as the force on the rope above the place where it broke. I submit that this force is going to be a LOT less than 1G!!! |
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For evidence, consider the Sun. If you stood on its visible surface (420,000 miles from center) and didn't vaporize, you'd experience about 27Gs. If you built a shell around the sun having radius 6 million miles or so, and stood on that, you'd experience 1G. If you had a rope that held out for 100 million miles before it broke, well, perhaps you can see that the gravity at that point is going to be LOTS smaller, on the remaining rope, than you want! |
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I do admit that I was thinking of the rope-gravity problem wrong, but I think you're considering this a static system, which it isn't. Sure, in a static case you'll have maximum force at the end of the rope near the space ship - being pulled by the little bit of gravity between the point below it plus all of the bits of gravity acting on all other points. But don't forget that tidal forces are proportional to d/R³, which will provide quite a rapid increase of force on the black hole end. |
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[Worldgineer], you seem to be confusing the constant acceleration you want (which IS due to a "static" (simple straight fall) location in a gravity well) with tidal forces (which ONLY appear when object at least partially orbits the central mass. From 4 trillion miles away, I can assure you that the system as you describe it contains no significant tidal force. I only brought them up because when the spaceship finally reaches the vicinity of the hole, it has to slingshot part-way around it, and THEN it could see significant tidal forces (which have NOTHING to do with accelerating it as a whole!). |
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Another aspect of the rope-breakage problem occurs to me. Let's pretend you have a stationary winch located some billions of miles from the hole (let's not worry HOW it's become stationary). You unwinch the rope, and of course it starts to fall toward the hole under its own weight. At this distance, of course, the rope weighs very little, but the more you unwinch, the more total weight is being supported AT the place where the rope becomes part of the reel. How much can you unwinch before it breaks? Why do you think it will break closer to the hole than farther away? I suspect THIS is the fundamental flaw in this Idea. |
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I think we have a difference in vocabulary. I think "tidal force" is a gradient in gravitational force that is noticable near massive objects. Half of a 1lbm object further from the the black hole weighing .5 lb with the closer half weighing .6 lb (sorry about any lb, lbm confusion - damn IP units). |
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It appears you are going back to a static model with your winch example, unless you plan on letting it out quickly. Sorry for introducing a new model, but I don't think I've made myself clear. Picture a tug of war contest, with a team of pullers on one side, and a brick wall on the other. The team has 10,000 people equally spaced 10 feet apart. People at the end of the rope are the strongest (representing close to the black hole), and people near the wall are the weakest. |
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After a while of pulling, we are representing the static case. The most force is exerted on the rope between the person closest to the wall and the wall. If everyone slowly increases in strength, the rope will break near the wall. However, if the strongest person suddenly gets a burst of strength stronger than the tensile strength of the rope (as would happen with a fast moving rope into a d/R³ relationship gravitational field), the rope will snap at the end puller - the momentum of the rope in front of this person will keep the force from travelling all the way to the wall. |
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The vocabulary difference is that your definition of "tidal force" is mistaken, because REAL tidal force is not applicable to this Idea, except as the spaceship gets near the black hole. |
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Consider yourself in a spacesuit in orbit. Suppose you decide to use attitude thrusters to keep your feet pointed at the world you are orbiting, and your head at the stars. Your center of mass is approximately at your abdomen, and your orbit is computed using the LOCATION of your abdomen. However, your feet are in a smaller orbit, and your head is in a larger orbit. Both are being forced (by being parts of your body) to orbit the world at the same speed, even though their natural tendencies is to orbit the world at different speeds. Those tendencies ARE tidal-force effects, and they ONLY happen when the path of a moving body follows an orbit-type curve around some large gravitating body. THAT's when different orbital radii are relevant! |
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Tidal effects do NOT happen to rope falling straight toward a black hole. |
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Regarding your tug-of-war description, you are forgetting the ADDITIVE nature of all those tugs. At ANY point along the rope, the total tug (strain) is equal to the the sum exerted by all the tuggers from there to the end. This sum only increases as the rope gets longer and more tuggers are added. And so it eventually breaks FARTHER from the end of the rope, before it breaks nearer. Which leaves only feeble tuggers after the break, until the whole rope and spaceship moves closer to the hole. |
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HOWEVER. If the rope breaks after only 10 miles of strong tuggers, there is no reason to think it can't ALSO break after 1000 or 10000 miles of feebler tuggers. Because the total tug is ADDITIVE. Yes, I'm sure you're thinking about diminishing series such as 1+0.1+0.01+0.001... which conveniently add up to some maximum fixed value that might be less than your rope can handle. You even have the inverse-square-law to help you here -- but have you done the math (calculus) that proves it works like that in this case? |
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Because the main thing against it is the sheer extent of a black hole's gravity well. We currently envision using carbon nanotubes in the Earth's gravity well for a mere 23,000-mile Space Elevator, from 1G to some small fraction of that -- but relative to the Sun's gravity well (to say nothing of a probably-six-times-as-massive black hole), the diminishing from the 1G mark to the equivalent fraction takes a VASTLY greater distance! So I can easily envision the intial end of your rope approaching the black hole and reaching the billion-mile mark from it, when the accumulated tug on the NEXT billion miles causes the rope to break at the two-billion-mile mark! This is NOT the way to get the large acceleration you want! |
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I believe that you're right - I was thinking of r³, not r². It looks like we're at the point that we'll need to use some math. |
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Tensile strength of carbon microfiber, psi: 7,300,000
Density of carbon microfiber, lbm/ft³: 141.5
Desired acceleration, ft/s²: 20
Assumed mass of rope+ship (likely far off without more calculation): 20 tons
Gravitational constant: 3.322e-11 lbf*ft²/lbm²
Mass of sun: 4.4E30 lbm |
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Force required: 40,000 x 20 lbm*ft/s² = 24,865 lb
Thickness required: 24,865 / 7,300,000 = 0.0034 in²
Mass per mile: (0.0034 in²) / (144 in²/ft²) * (5,280 ft) * (141.5 lbm/ft³) = 17.64 lbm |
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Let's start at, say, 1,000 miles from the center of a 6-solar mass black hole. The force exerted on a mile of rope is:
F = G * m1 * m2 / r²
F = 3.322e-11 * 4.4E30 * 6 * 17.64 / (1000 * 5280)²
F = 554,925,000 lbf, so it will easily snap here. |
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Let's try 10,000 miles out:
F = 5,549,250 lbf, nope, still snapping. |
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100,000 miles out:
F = 55,492 lbf, still snapping. |
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Looks like it's around 150,000 miles out that a 1-mile length of rope would break. That's much further than I'd imagined, and your prediction is likely close to true. I guess we could make the rope such that it's diameter is reduced at the black hole end, so that it always breaks there. |
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To Wordgineer and all the annotaters on this idea: This is a briliant idea! And so are all your annotations. Here are my thoughts: The speed of sound is not a constant, it depends on the medium it travels through. So if the ROD is RIGID I see no reason why the speed of sound may not appraoch the speed of light, or beat it. And yes the scissors are important, it is the same basic idea. However, getting the rope to the black hole takes much longer than the actual trip the ship wants to make. So once the rope is in position it can be forever elongated by just adding more rope and passing ships can just tag along on a rope that is allways falling. If this rope is then not falling to the center of the black hole but just passing through on the perimeter it could be extended to the next black hole and back again to the first. Just so long as it does not get pulled in to the center this provides a sort of intergalactic skilift or a black hole merrygoround. So according to stringtheory and the overall octavionality of reality this should produce a whole new style of music if we tap the vibrations in the rope. Eat your heart out Hotblack Desiato! |
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Oh, and a plus for the name of this idea! |
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If only there was some way to combine this idea with the "Elephants on a rope." (see link) |
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Phew! Just read all that. Interesting if a little exhausting. [zeno] To make music with this, how about six ropes of varying diameters launched into the same black hole at different times. A giant plectrum spaceship and some sort of pick up... |
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Setting aside if it is possible to reach light speed, if the rope could be made strong enough, etc etc. As I read it, the rope is being pulled into the hole, then at this end you'll have to continously manufacture a rope with whatever specs you desire, (right?).
Me thinks that is the first problem that should be solved. Otherwise you'll be putting a lot of effort for a few trips (which will have to be fast, since the rope is going to be falling with near lightspeed) |
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The way I've planned it, you manufacture the rope first, then send an end in to the black hole. |
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How can you manufacture infinite rope in advance?? |
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Not infinite, just 4 trillion miles of it. It's a one-time shot. Dangle the end in the black hole, and hold on tight. |
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Ok, got confused by Zeno there. |
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Well, I thought about it some more, I keep getting back to this idea. I do believe black holes spin very fast, so if we find some way to transfer this spinning-energy to the rope it might not be necessary to let the rope vanish in the black hole. And also speed could be highly increased if the black hole is swirling us around at the end of the very long rope. And which would be worse: hanging on until we reach the center or letting go just in time? |
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Can you interact with the spin of a black hole? They do emit energy and mass, so I guess that may be possible. Though I don't know how you'd make that work. |
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Just a few more annos and this idea will officially become the HBlackhole. |
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Let's break through the anno-event-horizon. |
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zeno, sorry, the transmission of any energy wave or information through any medium whatsoever cannot approach the speed of light. See Worldgineer's rigid rod link. (or not, apparently the link is broken). |
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(link fixed - thanks [ray] and (waybackmachine)) |
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Thanks, Steel and World. I don't really get it.
the link clearly says that Information or compression waves can at most travel through any medium with the speed of sound in that medium, so I wonder what is the speed of sound compared to the speed of light in a diamond or any substance even harder. ` |
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I think the speed of sound in any medium is determined by the rigidity of that medium. The electro magnetic forces holding the atoms in place ensure sound can not travel faster than light. But since sound has no mass and is only the movement/vibration of particles , it is in effect only information and can therefore approach the speed of light. |
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I clearly see now why it can not go faster than light but other than that it seems to me the only limitation to the speed of sound in a rigid rod would be how rigid the rod is. In other words: if the rod is perfectly rigid then speed of sound will approach speed of light. I do not believe this is negated in the aforementioned link. By approaching the speed of light I mean getting close to it. do you think this way of thinking is wrong? If so can you explain why? |
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Speed of sound in diamond: about 12,000 m/s
Speed of light: 299,792,458 m/s |
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Unless you can think of a material that's close to 25,000 times as rigid as diamond, it's not really approaching the speed of light. |
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That's beautifull World, just beautifull. And it rather proves what I said. In the rigid rod experiment the rod is not made of any material known to man. It is hypothetical, the rod is really rigid in our thoughts. The speed of sound moves faster than light inside the perfectly rigid rod. |
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The real rod is held together by electromagnetic forces so really it can not be rigid because nothing can travel through the rod faster than these electromagnetic forces. The rod is therefor not rigid at all but only as rigid as the electromagnetic forces allow. Sound will not approach the speed of light. |
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A perfectly rigid rod will never be reality a rod can not be made so rigid. But just as a thought this links the speed of light barrier to the strength of electromagnetic forces. Not their speed but their strength. I've lost were I want to go with this thought, sorry, maybe you can finish. I'm off to the grocerystore. And the fishbowl moves! |
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