I was thinking... What if I'd make a huge disc with a radius of R meters and start turning it in an angle speed (is that the word?) of w>300000000/R rad/sec. Then, every point on the edge of the disc (R meters from the center) will have a linear velocity of
V=w*R > 300000000 m/sec, faster than the speed of light...

According to the special theory of relativity, an object with mass cannot reach the speed of light and beyond, However, such a disc can be made theoretically and maybe even practically, but it's not supposed to work... I'm confused. Where am I wrong? :confused:

Well, first off, you have to assume that you can find a material strong enough to resist the forces involved.

Just for the sake of argument, let's assume you've found such a strong, perfectly rigid disk (Even though Relativity says that a perfectly rigid substance cannot exist,)

You start to turn it. the amount of force (torque) you will need to speed it up from rest depends on the moment of inertia of the disk. (Its mass and radius). As the disk Speed increases, Relativity says that the effective mass of the different partrs of the disk will increase, depending on their velocity.

Parts nearer the center will be moving more slowly than out at the rim. The effect will be to concentrate more mass towards the rim. This will increase the torque needed to increase the speed of the disk by increasing the moment of interia of the disk(from two effects, the increase of effective mass of the disk, and the increase in the effective arm of moment.)

As the rim approaches c, the mass at the rim approaches inifinty, as does the inertia of moment. Consequencely, the amount of torque needed to furhter speed up the disk, increases to inifinty.

You'll never be able to get the disk up to an rpm which would cause the rim speed to exceed c.

Right.
Also, if the turner has less mass than the disk, the turner turns faster than the disk.

Maybe if the disc has the size of several solar systems, the difference in torque between the center and the edge would be gradual to a point that you could use existing materials tensile strenght. Next problem would be how to accelerate such a huge mass...

"According to the special theory of relativity, an object with mass cannot reach the speed of light and beyond, However, such a disc can be made theoretically and maybe even practically, but it's not supposed to work... I'm confused. Where am I wrong?"

Special relativity does not say anything about rotating frames of reference, and hence the statement "mass cannot reach the speed of light" is invalid in this context.


Janus58,

There is no such thing as a perfectly rigid object, the disc will completely deform because the force you exert to rotate the disc will propagate at most at the speed of light. This will lead to enormous tearing forces at the edge, breaking up the disc. Your argument of "local mass increase" is not valid simply because special relativity does not apply; you don't know what will happen - you can only speculate on what will.

Bye!

Crisp

Originally posted by Crisp
[b][i]


Janus58,

There is no such thing as a perfectly rigid object,


You will note that I made that disclaimer in my post.

Hi Janus,

Indeed you did, but then you assumed that there is ;)

Bye!

Crisp

Originally posted by Crisp
Hi Janus,

Indeed you did, but then you assumed that there is ;)

Bye!

Crisp

Yes I did, "for the sake of argument".

Usually, when someone brings forth ideas like the "spinning disk", The first answer they get is that it is impossible due to structural reasons, Almost invariably, they reply with "But what if a strong enough material existed?"

Pointing out that Relativity forbids such an rigid object to exist almost never satisfies them.

I just decided to sidestep that whole issue.

Thanks everybody for the answers. It really helped. Overall I understood form your replies that the idea of the rigid disc is impossible and you give two reasons for it being impossible, that relativity doesn't allow the existance of a perfectly rigid object and that special relativity talks solely about linear movement. Did I get it right?

Originally posted by Crisp
Special relativity does not say anything about rotating frames of reference, and hence the statement "mass cannot reach the speed of light" is invalid in this context.


So, if I understand you right, the linear velocity of a massive rotating object can exceed the speed of light?

Thx again.

Every planatary system was once a massive rotating object of pretty good size. None of them rotate very fast. Maybe they can't. Look far enough out and it will seem that your line off sight will sweep at more than light speed, but no matter is moving. It is pure geometry.
Look off into the expanding universe and you reach a point that is moving faster than the speed of light and it becomes an event horizon.

Hi,

"So, if I understand you right, the linear velocity of a massive rotating object can exceed the speed of light?"

I didn't say that, I just said that SR alone won't do here... You would need to have a theory that is capable of handling rotating (non-inertial) frames of reference, and AFAIK that would lead you to General Relativity of which I know only very little. (I should note that I have heard of expansions of SR to non-inertial frames, but I never found any reliable text on it, perhaps lethe knows ?)

Bye!

Crisp

Originally posted by Crisp
I didn't say that, I just said that SR alone won't do here... You would need to have a theory that is capable of handling rotating (non-inertial) frames of reference, and AFAIK that would lead you to General Relativity of which I know only very little. (I should note that I have heard of expansions of SR to non-inertial frames, but I never found any reliable text on it, perhaps lethe knows ?)


Hmm... Interesting.. So I gather that the raw theory of relativity is pretty limited.
It supports only intertial frames of reference, frames of reference that have no Force affecting them, and thus it's not capable of handling accelerating frames of reference, am I right?

Originally posted by hlreed
Look far enough out and it will seem that your line off sight will sweep at more than light speed, but no matter is moving. It is pure geometry.
Look off into the expanding universe and you reach a point that is moving faster than the speed of light and it becomes an event horizon.

Yes, that is obvious, but I was talking about rotating objects that have mass.

Thanks.

theres an article in disvcovery about changing the speed of light to make faster then light speed travel possible (yea i know), but im out the door, so more when i get back

Originally posted by Crisp
(I should note that I have heard of expansions of SR to non-inertial frames, but I never found any reliable text on it, perhaps lethe knows ?)

My understand is that, since acceleration is a constant velocity at each moment, you can apply SR to non-inertial frames moment-by-moment, like the equations here do: The Relativistic Rocket (http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html).

Originally posted by hlreed
Look off into the expanding universe and you reach a point that is moving faster than the speed of light and it becomes an event horizon. So what if I rotate myself at one revolution per second. Any object roughly 50,000 kilometers from my axis of rotation will appear to be moving at c at any given instant. Is that correct?

My intuition says no. I seem to recall that with relativity, all bets were off if objects don't stay on a straight trajectory. Even traveling to Alpha Centauri at .9999c and using its gravity to make a quick u-turn and come right back was said to blow the relativistic effect. That was supposed to be why you can't really come back younger than the people who stayed on Earth.

So moving in a circle doesn't count.

Is any of this right?

If a particle covers a very small linear distance x in close to x/(3*10^8) sec. then it moves with the velocity close to that of light. if u take any point on the rim that moves 1 millimeter in a linear path at close to 1/(3*10^11) sec it seems to be moving in the speed of light(closely) if R is fairly large. Then SR effects over the short-distances affect the disk itself.

in other words, it comes down to applying force on a particle on the rim perpendicular to its linear path. it is simply not possible to move a particle, with mass, at the speed of light by applying force of any kind. besides over short-distances SR effects would spoil the concept of disk itself.

Fraggle Rocker:

<i>So what if I rotate myself at one revolution per second. Any object roughly 50,000 kilometers from my axis of rotation will appear to be moving at c at any given instant. Is that correct?</i>

Yes. But you are now observing the object from a rather special reference frame - one which is non-inertial.

I'll have to think about this one. However...

<i>Even traveling to Alpha Centauri at .9999c and using its gravity to make a quick u-turn and come right back was said to blow the relativistic effect. That was supposed to be why you can't really come back younger than the people who stayed on Earth.</i>

If you make a return trip to Alpha Centauri, you really will come back younger than your twin who stayed on Earth. I don't think you can avoid the relativistic effects, provided that you actually accelerate for part of the trip.

Use General Relativity for non-inertial frames of reference - basic tenant of it is that acceleration=gravity(locally). When your car goes around a curve, it feels like gravity is not straight down but diagonal - the vector combination of vertical gravity and horizontal acceleration.
Gen.Rel. also predicts age difference of alphacentauri trip, but only because of the acceleration used to get up to speed. If you could ignore the acceleration, watches would indeed stay synchronized - see thread on "twin paradox" which had alot of input on this subject - the best input was on the last 1 or 2 pages.
Aaron