If I made a steel pole, 1m long, I could rotate it at 1 revolution a second pivoted about its centre lengthways, easily, right?
Assuming speed of light is 300,000M/sec
If I made a steel rod, in space, that was 300,000/PI metres in length, pivoted it about its centre, what would happen If I tried to rotate it at 1 revolution a second?
More importantly, If I were sitting on a stool mounted on the pivot so I was rotating along with the rod, what would I see as I looked down the length of the rod, from the centre of the described circle to the edge?
Also… I could halve my rate of rotation so long as I doubled the length of the Rod and get the same effect.
So, if I built a rod that was 460,800,000 metres long, in space, does it follow I could only rotate it at under 0.703125 degrees / sec?
What happens is that steel is an elastic substance, so you’ll just get torsion in the rod. At the distances you are talking, the rod will behave like a rubber band. The ends will start spinning long after the center, assuming the thing doesn’t just fall apart. Remember, if your steel rod is 1000’s of miles long, it will have considerable mass, so torqueing the middle would be like trying to torque a bolt that weighs several tons.
You can’t get around this by postulating a perfectly rigid substance, because all substances are held together by forces that are subject to speed-of-light restrictions.
But spinning one 1.17km long at 32,000 times a second is far fetched. The same problems arise. In order to get it to that speed, you have to torque it harder. A thin steel rod isn’t going to be very strong, a strong steel rod is going to be very big.
Instead, why don’t you just grab a neutron star that’s already spinning pretty fast, and tweak it?
The OP is basically a twist on the Superluminal Scissors thought experiment. For the sake of the OP and this thought experiment ignore how difficult it would be to spin the bar…it doesn’t matter.
Take some scissors that have blades 1 light year long with a handle (behind the pivot point) only a few feet long. If you snap the scissors closed (say in less than a second to bring the handles together) the point where the blades meet should travel down the length of the scissors at a speed much greater than the speed of light (and presumably the tips of the scissors would be moving faster than the speed of light).
The answer to this problem is that the scissors bend. You don’t need to consider what they are made of or how much energy you put into the system. They bend…period…and so does the bar mentioned in the OP. The material you make the bar or scissors out of doesn’t much matter because Special Relativity sets a theoretical upper limit to the rigidity of a material. So, the stiffest material you could ever create will still bend under the circumstances we are talking about here.
I disagree, slightly. The superluminal scissor thought experiment is mainly concerned with the idea that the place where the blades meet is changing faster than the speed of light. I don’t think you even need kilometer length scissors to set that up either–you just need blades that are hinged so that they are close to parallel when they are still open.
An important point is being missed: The faster the ends are going, the more energy it takes to move them faster. To get the ends moving a significant fraction of the speed of light would take so much energy [fill in suitable imagery of "a nearly unthinkable amount of energy]. To get the ends moving at the speed of light requires merely an infinite amount of energy.
Where you getting the energy from yellowalienbaby???
Also, as mentioned briefly before, it’ll fall apart due to the “centrifugal force” before you get any interesting speed. The bending by torsion of the bar is wholly insignificant when you accelerate it slowly. And I do mean slowly.
I have seen posts like this before here, and the thing I find astonishing is the notion that somehow circular motion is different.
Hey, yellowalienbaby, same question about the rod but moving in a straight line, no spinning. That way you can make it a mere millionth of a meter long. (Just the tip of the rod, see?) How do you get it moving to near the speed of light??? Why on earth is spinning discussed at all???
First, the speed of light is 300,000,000 m/s, not 300,000. I actually caught an error that got past RM Mentock!
I don’t think this is the same as the scissors thought experiment (oops - I see RM Mentock has now posted with that idea too).
But the answer that “the rod will bend” is not a satisfactory one. Let’s take a rod that’s 60,000 miles long, and very slowly accelerate it to the rate of one revolution per second. Maybe take ten years to build up to that speed. Or as slow as is required so that the bending is kept to a minimum. What would happen as you approach the rate of one revolution per second?
I think that the ends of the rod would have an increased mass, and would therefore be harder to accelerate, and the rod would bend more than it would at slower speeds for the same angular acceleration.
But what if I did this, and stopped at 90% of c? The ends of the rod would be travelling at 0.9 c, and in the steady-state the rod should again be straight. What would a person at the pivot point see as he looked down the rod?
Read the question a bit closer, FTG. He isn’t asking whether he can get the rod rotating at the speed of light. What the OP is asking is what happens at the end of a very long rod when you start rotating the center.
Here’s an analogous situation with the same flaw. Suppose I want to communicate to someone on Mars with no time lag. Why couldn’t I just get a really, really long string and communicate by jerking on the line (one for yes, two for no )? After all, no part of the line has to move more than a couple of inches. The problem is that the impulse has to propagate along the line, and it can only do that at speeds limited by the material properties of the substance.
That’s only part of it. IIRC the point where the scissor blades met could technically move faster than the speed of light since it doesn’t constitute information.
However, closing the blades does constitute information and it is information that cannot move faster than light. When I snap the handle shut I am sending a message to the tip of the blades to start moving. If we stick with my 1 light year long blade then it would take a year after closing the handle for the scissor tips to even start moving. If you picture that ‘wave’ moving along the blade you can see how they’d have to bend.
If you find it hard to swallow the idea of the blades closing as information then consider that you’ve just created a faster-than-light communication method. If I left the scissors half-open I could establish with you beforehand that if the tip goes up it equals a yes and down equals a no. You ask a question from the far end of the scissors (that takes a year te reach me) and I wiggle my handle one way or the other and you’ve just got your answer in a faster-than-light method. Needless to say (hopefully) that isn’t possible. The scissors bend instead.
Oops…forgot to mention how the rod is like the scissors.
By spinning the rod you are sending a signla to the end to move and change direction (afterall, the end of the rod ‘wants’ to move off in a straight line).
I don’t care how slowly you accelerate the rod. Even in the ‘steady-state’ mentiond by CurtC (i.e. stop accelerating the rod and just let it spin) the rod would stay seriously bent. Information is continuously propogating down the rod to the tip to tel it what speed to go and what direction to go in.
Your rod is bent.
Of course, as already mentioned, the tip of the rod would approach infinite mass as it got closer to light speed and would ultimately require an infinite amount of energy to get it there so this can’t happen anyway (and probably far before you got close the rod would tear itself apart).
To show how this is completely impractical, we’re talking about a 30,000 mile radius rod rotating at once per second. The thread about space elevators was discussing how a 20,000 mile cable couldn’t be made with enough tensile strength to support its own weight. With our spinning rod, the ends would require a centripetal force of 150 million g’s! This is a simple Newtonian calculation, and doesn’t take into account the increased mass due to relativistic effects.
But assuming we could make a rod that could withstand this, like out of Krell Metal*, why would it stay seriously bent after you stop accelerating it? I agree that it would appear to the observer in the center to be bent, because light from the tips would arrive later, after the closer-in parts had moved on.
Many things that aren’t really things can move faster than light. For instance the contact point of a water wave against a seawall, or the beam of a fast spinning searchlight against faraway clouds.
It’s not that it appears bent (although it might) it will be bent. If you don’t take my word for it the link Ring provided may be more believable.
Your spinning rod is like the scissors when you consider the tips of the two items. I’ve already discussed how the scissor tips won’t move for a year (assuming 1 light year long blades) after you close the handles.
In your spinning rod let’s also assume it is a 1 light year long rod (to highlight the point). If you speed up or slow down the rotation it will take 1 year for the tip to get the message.
Why doesn’t the rod straighten when going a constant speed? Because the rod’s tip is continuously being told by a signal sent from the center a year earlier what to do. The tip of the rod is continuously changing direction by spinning in a circle. Imagine if I let go of the rod I was spinning…it would take one year for the tip to get the message. Prior to that it would be moving based on what happened for the year prior to my letting go (spinning in a circle). After that the rod would fly off in a straight line and at that point it would be totally straight again (assumiong it somehow survived the insane warping effects it just underwent).
[sub]Actually, I’ve tried to picture in my head what shape our rod would take if it was a light year long with the tip spinning at .98c or better and I let go of it. It gave me a headache trying to visualize parts of it straightening out while other parts continued to move in a circle.[/sub]
As for Krell Metal (Forbidden Planet?) it doesn’t matter. As Ring’s link mentions Special Relativity puts an upper limit on the rigidity of any material. They say on the site that a SR-rigid-limit substance is FAR higher than any real substance.
Your rod would still bend even if it was Krell Metal or had a picture of Jolene Blaylock to stare at [sub]I just saw RMM’s post[/sub].
Actually, rotating something at 32,000 time a second is very hard to do. 32,000 rps = 1,920,000 rpm.
A rod 2" long (25 mm radius) spinning at 1.92 million rpm would experience a centrifugal stress of 103,034,880 gravities. The best ultracentrifuges made, titanium rotors and all, top out at 100,000 rpm and a million G’s or less. Here’s a G-force calculator for spinning objects.
