|
|
Thread Tools | Display Modes |
#1
|
|||
|
|||
So, I was sat on the loo and thought...
one of those pointless hypothetical what-if questions...
So, assuming the rule of "you can't go faster than light" (E=MC2 and all that) what would happen if we could attach a really long rod to the earth? Presumably, if we made the rod long enough, the tip of it would be moving through its local space at the speed of light? I havent done the maths on it, but if you plug the speed of light into a calculation and throw in some trigonometry and the angular rotation speed of the earth, you can work out how long the rod would be. And what would happen if you made the rod even longer so it was going faster than light? I'll leave now... James |
#2
|
|||
|
|||
So, I was sat on the loo and thought...
On Mon, 27 Mar 2006 22:13:38 +0100, in uk.sci.astronomy , "JamesB"
james wrote: Presumably, if we made the rod long enough, the tip of it would be moving through its local space at the speed of light? Nope. I havent done the maths on it, but if you plug the speed of light into a calculation and throw in some trigonometry and the angular rotation speed of the earth, you can work out how long the rod would be. There's a flaw. The Newtonian 'laws of motion' we're using are only approximations. At small fractions of c, they're pretty accurate. At large fractions of c, they break down. And what would happen if you made the rod even longer so it was going faster than light? It can't - if you do the (relativistic) maths you;ll find out that it goes faster and faster, but never actually reaches c until it is infinitely long. I did this sort of sum all the time in my degree course. If two particles each travelling at c/2 are approaching head on, whats the velocity of one relative to the other? Answer: not c. Mark McIntyre -- |
#3
|
|||
|
|||
So, I was sat on the loo and thought...
"JamesB" james wrote in message ... one of those pointless hypothetical what-if questions... So, assuming the rule of "you can't go faster than light" (E=MC2 and all that) what would happen if we could attach a really long rod to the earth? Presumably, if we made the rod long enough, the tip of it would be moving through its local space at the speed of light? I havent done the maths on it, but if you plug the speed of light into a calculation and throw in some trigonometry and the angular rotation speed of the earth, you can work out how long the rod would be. And what would happen if you made the rod even longer so it was going faster than light? I'll leave now... James There was an article,"Relativity on a Turntable", on this in New Scientist about 30 years ago. In theory the relationship between radius and circumference becomes non-euclidian at high angular speed, which has the effect of shortening the path taken by the tip of the rod. There is an article that cites the NS article here http://freeweb.supereva.com/solciclos/gron_d.pdf I have half a suspicion that I have the original in the attic, does anyone want to go up and look for it? It'll be on the left; probably behind the tent. |
#4
|
|||
|
|||
So, I was sat on the loo and thought...
On Mon, 27 Mar 2006 22:43:46 +0100, in uk.sci.astronomy , "OG"
wrote: I have half a suspicion that I have the original in the attic, does anyone want to go up and look for it? It'll be on the left; probably behind the tent. Its not, the hippies borrowed the tent, remember? Mark McIntyre -- |
#5
|
|||
|
|||
So, I was sat on the loo and thought...
JamesB wrote:
one of those pointless hypothetical what-if questions... So, assuming the rule of "you can't go faster than light" (E=MC2 and all that) what would happen if we could attach a really long rod to the earth? Presumably, if we made the rod long enough, the tip of it would be moving through its local space at the speed of light? I havent done the maths on it, but if you plug the speed of light into a calculation and throw in some trigonometry and the angular rotation speed of the earth, you can work out how long the rod would be. And what would happen if you made the rod even longer so it was going faster than light? I'll leave now... James To move the point at lightspeed you would need al the energy (and then some)in the universe, and not even then can you force it to move at lightspeed. Any rod you can erect,will be pulled to pieces long before you are at lightspeed, and that before you would be able to get it upright(while putting it in place, you have to supply that infinite energy). |
#6
|
|||
|
|||
So, I was sat on the loo and thought...
In article , JamesB james wrote:
Presumably, if we made the rod long enough, the tip of it would be moving through its local space at the speed of light? If it could be done. And what would happen if you made the rod even longer so it was going faster than light? You can't, because raising the rod requires more and more energy as the tip gets faster, just as if you were accelerating it by pushing it. -- Richard |
#7
|
|||
|
|||
So, I was sat on the loo and thought...
You will not achieve your goal. If the rod is longer than 384,403km it will
hit the moon and break off rendering your experiment useless. ;?) Scott "JamesB" james wrote in message ... one of those pointless hypothetical what-if questions... So, assuming the rule of "you can't go faster than light" (E=MC2 and all that) what would happen if we could attach a really long rod to the earth? Presumably, if we made the rod long enough, the tip of it would be moving through its local space at the speed of light? I havent done the maths on it, but if you plug the speed of light into a calculation and throw in some trigonometry and the angular rotation speed of the earth, you can work out how long the rod would be. And what would happen if you made the rod even longer so it was going faster than light? I'll leave now... James |
#8
|
|||
|
|||
So, I was sat on the loo and thought...
"reconair" wrote in message ... You will not achieve your goal. If the rod is longer than 384,403km it will hit the moon and break off rendering your experiment useless. Bugger! Hey, some interesting answers there, I might have to do a bit more reading... I didn't realise that the laws all change a bit (or become unreliable) the closer to the speed of light you get... I did assume the whole thing would be impossible anyway (regardless of the fact you couldn't make anything that big in the first place!), just curious as to why! James |
#9
|
|||
|
|||
So, I was sat on the loo and thought...
So, assuming the rule of "you can't go faster than light" (E=MC2 and all
that) what would happen if we could attach a really long rod to the earth? Provided that you had a supply of long infinitely rigid light inextensible rods (of the sort beloved by A'level applied mathematics problems). If it were truly massless then you could get the end to move at the speed of light but no faster. Note that there would be horrific stresses from centrapetal forces needed to keep the thing from flying apart. Real materials would either be crushed under their own weight or torn apart by the stresses involved... You can make the end of a light beam sweep along a screen at any arbitrary speed though - but nothing physical is actually moving faster than the speed of light. Same with a very narrow angle pair of scissors the crossing point can be made to advance at c (at least in principle). Presumably, if we made the rod long enough, the tip of it would be moving through its local space at the speed of light? There is a real world situation where the problem of not being able to exceed light speed has interesting consequences (in classical physics magnetic field lines are close enough to your ideal rigid rods to be interesting). And sure enough in the magnetosphere of pulsars where strong gravity, fast spin and immense magnetic fields combine strange things happen at the light cylinder where the corotating frame would exceed c. See for example http://www.pparc.ac.uk/Nw/rel241.asp Regards, Martin Brown (posting via Google groups as my miserable ISP Wanadoo has discontinued Usenet) |
#10
|
|||
|
|||
So, I was sat on the loo and thought...
JamesB wrote: one of those pointless hypothetical what-if questions... So, assuming the rule of "you can't go faster than light" (E=MC2 and all that) what would happen if we could attach a really long rod to the earth? Presumably, if we made the rod long enough, the tip of it would be moving through its local space at the speed of light? I havent done the maths on it, but if you plug the speed of light into a calculation and throw in some trigonometry and the angular rotation speed of the earth, you can work out how long the rod would be. And what would happen if you made the rod even longer so it was going faster than light? I'll leave now... James Interesting that you have mentioned this as I have been grappling with a similar problem involving rotating frames. In essence: what is the velocity of a body relative to a frame rotating with the Earth? No rods or physical entities; just a rotating reference frame, and a slowly rotating one at that. In a simple, Newtonian way, one can calculate that the speed gained from frame rotation reaches light speed at ~27 AU. On this reckoning Neptune and Pluto are superluminal in a frame fixed to the Earth's surface. Obviously, some sort of relativistic approach is needed... Mark McIntyre wrote: And what would happen if you made the rod even longer so it was going faster than light? It can't - if you do the (relativistic) maths you;ll find out that it goes faster and faster, but never actually reaches c until it is infinitely long. I did this sort of sum all the time in my degree course. If two particles each travelling at c/2 are approaching head on, whats the velocity of one relative to the other? Answer: not c. ....I'm still looking for a solution; do you have one for rotating frames? One approach may be to use the relativistic velocity addition formula where one of the velocities is that of a local Lorentzian frame located at the body in question, moving with a velocity related to the rotation rate of the Earth frame. Problem is: what is the velocity of that Lorentzian frame? If you can help please let me know. John. |
Thread Tools | |
Display Modes | |
|
|