Rotating Disk Method to Attain Light Speed?

[aLeaf]

TL;DR

I thought of a disk rotating freely in space at 60 RPM, for example, as a way to move gross matter at and beyond the speed of light.
A point on the disk at a radius of 5/π meters would be moving at a speed of 10 m/sec, ∴ a point on the disk at a radius of (15x10⁷)/π meters should be moving at a speed of 3x10⁸ m/sec.

I thought of a disk rotating freely in space at 60 RPM, for example, as a way to move gross matter at and beyond the speed of light.

A point on the disk at a radius of 5/π meters would be moving at a speed of 10 m/sec, while a point on the disk at a radius of 50/π meters would be moving at a speed of 100 m/sec, right? So it would follow that a point on the disk at a radius of (15x10⁷)/π meters should be moving at a speed of 3x10⁸ m/sec.

I imagine that people who spend far more time cogitating on than I do would readily recognize where this construct fails. I look forward to reading your responses.

 

[Ibix]

The device distorts and disintegrates from internal stresses far before any part of it approaches lightspeed. If you posit arbitrarily strong materials you can get the rim arbitrarily close to lightspeed, but it will always disintegrate below lightspeed.

 

[aLeaf]

Disintegrate, as in atoms converting into photons? If so, then the disk itself would appear to us observing as a solid disk ringed by light...?

 

[Ibix]

Disintegrate, as in atoms converting into photons? If so, then the disk itself would appear to us observing as a solid disk ringed by light...?

No, just breaking apart, same as any other matter that you stress too much.

Make jelly and put it on a barstool. Spin the barstool and you'll get pelted with jelly fragments. Now replace the jelly with some other material. You have to spin the barstool faster the stronger the material is, but there is always a speed where the material will crack and fragments will fly off, and the speed of the rim at that point will always be below the speed of light.

 

[aLeaf]

Thank you for your replies.

 

[FactChecker]

The centrifugal force at the edge of the disk is proportional to the radius of the disk, which in this case is about 30,000 miles. Have you calculated that force? It might be very large. The disk would have to withstand that force.

 

[PeroK]

Thank you for your replies.

Why not simply accelerate a particle at constant acceleration until it surpasses $c$? That's what you are doing to a particle on the edge of your disk.

 

[SiennaTheGr8]

Here is a demonstration:

 

[PeroK]

No, just breaking apart, same as any other matter that you stress too much.

Make jelly and put it on a barstool. Spin the barstool and you'll get pelted with jelly fragments. Now replace the jelly with some other material. You have to spin the barstool faster the stronger the material is, but there is always a speed where the material will crack and fragments will fly off, and the speed of the rim at that point will always be below the speed of light.

That's a physical inevitability. Nevertheless, the kinetic energy of a spinning disk tends to infinity as the speed of rotation tends to some finite value - depending on the radius of the disk. It's not even theoretically possible to have part of the disk moving at $c$ from a calculation of the relativistic KE required.

 

[aLeaf]

The centrifugal force at the edge of the disk is proportional to the radius of the disk, which in this case is about 30,000 miles. Have you calculated that force? It might be very large. The disk would have to withstand that force.

Yes, nearly 48,000 Km. If the force at that radius was too great for the disk's material to hold together, then the material would fly off at a speed somewhere around c...

 

[PeterDonis]

If the force at that radius was too great for the disk's material to hold together,

Relativity says it must be. Relativity imposes a finite limit on the strength of materials, and that limit ensures that it is impossible to spin any material such that the speed of its rim would be $c$ or greater. The material must fail before that point is reached.

 

[aLeaf]

Why not simply accelerate a particle at constant acceleration until it surpasses $c$? That's what you are doing to a particle on the edge of your disk.

A rotating disk is an easier construct. Perhaps a method could be devised to engineer a disk of smaller size, commence spinning, and then gradually add more material at the periphery until the desired radius is reached...

 

[aLeaf]

Relativity says it must be. Relativity imposes a finite limit on the strength of materials, and that limit ensures that it is impossible to spin any material such that the speed of its rim would be $c$ or greater. The material must fail before that point is reached.

Perhaps.... but I am someone who does not accept theoretical impossible limits without testing them...

 

[PeterDonis]

I am someone who does not accept theoretical impossible limits without testing them...

Well, we don't have an actual test lab here, so all we can tell you is what the theory says.

 

[A.T.]

Relativity says it must be. Relativity imposes a finite limit on the strength of materials, and that limit ensures that it is impossible to spin any material such that the speed of its rim would be $c$ or greater. The material must fail before that point is reached.

The limits of the disc material strength could be overcome by applying the required centripetal forces externally. But even those centripetal forces tend to infinity, as the rim approaches a tangential speed of c.

A rotating disk is an easier construct. Perhaps a method could be devised to engineer a disk of smaller size, commence spinning, and then gradually add more material at the periphery until the desired radius is reached...

You could counter the above limit by making the radius tend to infinity, instead of increasing the angular velocity. But then you are effectively just moving in a straight line, which is simpler to analyse anyway.

 

[PeterDonis]

The limits of the disc material strength could be overcome by applying the required centripetal forces externally.

At that point the disc is not a single object, each piece of it to which an external force is applied is a separate, independent object. And then of course the very concept of "material strength" no longer applies. Effectively you've broken the disc already and now you're just up against relativistic kinematics, which, as you say, still stops you from accelerating anything to $c$.

 

[SiennaTheGr8]

Perhaps.... but I am someone who does not accept theoretical impossible limits without testing them...

Please report back with your test results!

 

[PeroK]

A rotating disk is an easier construct. Perhaps a method could be devised to engineer a disk of smaller size, commence spinning, and then gradually add more material at the periphery until the desired radius is reached...

The idea of a disk confuses the issue that within the disk you have particles being accelerated towards $c$. Each of those particles has kinetic energy tending to infinity. It doesn't matter how complex your overall structure is, a particle with mass cannot be accelerated to $c$.

Note that if you use Newtonian physics, then nothing stops you accelerating a particle beyond $c$. The question is, therefore, whether the Newtonian equation for kinetic energy is correct. Or, whether the relativistic kinetic energy is correct.

This has been tested many times. All of modern particle physics uses relativistic energy and momentum.

There is no longer any possibility that Newtonian physics is universally valid.

 

[PeroK]

Perhaps.... but I am someone who does not accept theoretical impossible limits without testing them...

Then you'll have to do a degree in experimental physics!

 

[PeroK]

You might like to read this:

https://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html

 

[aLeaf]

Well, we don't have an actual test lab here, so all we can tell you is what the theory says.

Maybe there is some old, abandoned lab space somewhere on the server where we could conduct thought experiments...?

 

[aLeaf]

Please report back with your test results!

This thread is my lab...

 

[aLeaf]

The idea of a disk confuses the issue that within the disk you have particles being accelerated towards $c$. Each of those particles has kinetic energy tending to infinity. It doesn't matter how complex your overall structure is, a particle with mass cannot be accelerated to $c$.

Note that if you use Newtonian physics, then nothing stops you accelerating a particle beyond $c$. The question is, therefore, whether the Newtonian equation for kinetic energy is correct. Or, whether the relativistic kinetic energy is correct.

This has been tested many times. All of modern particle physics uses relativistic energy and momentum.

There is no longer any possibility that Newtonian physics is universally valid.

That sounds very finalistic, relatively speaking

 

[aLeaf]

Then you'll have to do a degree in experimental physics!

Just as soon as I finish my post-doc in endocannabinoid pharmacodynamics.

 

[PeterDonis]

This thread is my lab...

We've already given you the results that this lab produces--they're the results that relativity predicts.

 

[Jaime Rudas]

I imagine that people who spend far more time cogitating on than I do would readily recognize where this construct fails.

Perhaps one of the first to analyze this situation was Paul Ehrenfest in his 1909 paper "Uniform rotation of rigid bodies and the theory of relativity" which is why it is now called the Ehrenfest paradox.

 

[Dale]

This thread is my lab...

Experimentally, rotating disks break apart when their tangential velocity is on the order of the speed of sound in the material. Even the speed of sound in diamond is not relativistic, let alone close to c.

 

[SiennaTheGr8]

I wonder... what's the speed of sound in unobtainium?

 

[Ibix]

This thread is my lab...

As Peter has pointed out, in this thread all you can do is apply the theory. You can call this "doing a thought experiment" if you like, but it's still just applying the theory. And the theoretical implications of relativity are clear - the kinetic energy of the disc depends on the linear speed of its parts and diverges as you approach $c$, as do the stresses on the disc. So it will disintegrate, and even if you just pretend it won't disintegrate it still can't reach $c$ because no amount of energy is sufficient.

You would need to do a real experiment and show that its results are inconsistent with relativistic predictions to challenge this.

 

[Ibix]

I wonder... what's the speed of sound in unobtainium?

The same as that of the sound of one hand clapping.