Can a String Travel Faster than the Speed of Light?

[mausten]

Fast than speed of light...

Hi guys & girls,

I have a question regarding traveling faster than the speed of light, a small theory, which I am hoping someone can explain to me why this wouldn't work. Note: I'm a total amateur science enthusiast, so please forgive me if this sounds really dumb.

Here's the scenario:

A stone on the end of string 1m in length that takes 1s to travel the circumference is traveling approximately 22mph. If a marker was placed 50cm along the string, it would take the marker 1s to complete a full circle, traveling at 11mph. Correct?

If the string was 7,000 miles long (11,480km) and it took 1s for the end of the string to travel the circumference, by my calculations (probably somewhat wrong), this would enable to end of the string to travel faster than the speed of light.

Hypothetically, if this huge structure was created in Space and a speed of 22mph (1 revolution per second) was achieved 1 meter, why would the end of the string not be traveling at the speed of light?

If you can let me know why I am wrong, that would be extremely helpful! :)

Thanks,

Mark

 

[Drakkith]

You could never accelerate the structure up to full speed because the end of the string would require more and more energy to accelerate as the speed increased.

 

[mfb]

If a marker was placed 50cm along the string, it would take the marker 1s to complete a full circle, traveling at 11mph. Correct?

Correct.

If the string was 7,000 miles long (11,480km) and it took 1s for the end of the string to travel the circumference

You cannot let the string rotate once per second if it has this length.

 

[CompuChip]

The first part of your reasoning is correct, except for the numbers. The relevant equation here is $v = \omega r$. If you get the angular velocity to $2 \pi$ rad/s, then for r = 1 you get a linear velocity of $v_0 = 2 \pi$ m/s which is approximately 22 km/h or 14 mph (miles per hour). Let's assume that you meant the former, then at r = 1/2 from the point of rotation you will find $v = \pi = \tfrac12 v_0$.

The error in your calculations is probably that you are (implicitly or explicitly) using the same relation in the relativistic case. I'm not sure what the correct formula is (you can derive it using the correct velocity addition formulas and expressions for the acceleration parallel and perpendicular to the direction of motion) but my educated guess is that you would get something like
$v = \tanh(\omega r)$ instead (noting that $\tanh(x) \approx x$ if $|x| \ll 1$).

[EDIT]What mfb says: you cannot let the end rotate with linear velocity greater than c and all points closer will have lower velocity anyway[/EDIT]

 

[Dale]

As Drakkith mentioned, it would take an infinite amount of energy. Additionally, it would require a string with an infinite tensile strength.

 

[mausten]

Thank you for the very quick replies CompuChip, mfb & Drakkith, much appreciated. And also, I apologise for the double posting of this topic.

I understand that theoretically, the end of the string cannot travel faster than the speed of light; E=MC2. But why not? If for example the 'string' was made from a nano tube that was 7,000miles long; hypothetical speaking, what force would be needed?

Also, let's imagine you take a bendy rod and twist it into a circle. Let go of one side and it springs back to its original state (sorry for the ultra layman's terminology!), there is enough kinetic energy/tension (?) in the rod for it to spring back. My head tell me, that the bigger the rode, the higher the energy build up until its release and return to original state. So, IF, the rod was big enough and twisted enough times - the whole 7,000 miles of tube, would there not be enough 'stored'/kinetic/tenstion energy to reach the required velocity to travel faster than the speed of light - much like the 'crack' at the end of a whip?

For this to work the rod would have to be much thinner at the 'cracking' end, than at the start, as to allow the energy to efficiently transfer and travel to the end.

I'm a total novice who likes to day dream.

 

[DeIdeal]

What you don't seem to understand or know is that it simply isn't possible for anything with non-zero mass to travel at FTL speeds – carbon nanotubes or not, it would still imply that an infinite amount of energy would be required to accelerate the mass. It doesn't matter how thick it is or how strong it is, it would still break at some point of the acceleration process.

E=mc² has little to do with it, try $E=mc^2/\sqrt{1-v^2/c^2}$. What happens if v=c?

 

[Dale]

If for example the 'string' was made from a nano tube that was 7,000miles long; hypothetical speaking, what force would be needed?

Infinite, as already stated repeatedly.

 

[mausten]

Hmmm... dammit. What if the 'string' was placed into a negative kelvin state - thus meaning that more 'natural' (?) energy would be needed to return to normal state, thus increasing velocity faster than normal...

Believing in God is easier than believing you can't accelerate faster than the speed of light.

Thank you for your clarification dudes & dudettes.

I'll go back to my hole and leave you to answer some proper questions now...

 

[CompuChip]

Believing in God is easier than believing you can't accelerate faster than the speed of light.

Except you can prove the latter from a few simple hypothesis and a sufficient dose of math :-)

(You can try that with the former too, if your name is Isaac Newton, but I would not recommend it).

 

[ghwellsjr]

I understand that theoretically, the end of the string cannot travel faster than the speed of light; E=MC2. But why not? If for example the 'string' was made from a nano tube that was 7,000miles long; hypothetical speaking, what force would be needed?

Also, let's imagine you take a bendy rod and twist it into a circle. Let go of one side and it springs back to its original state (sorry for the ultra layman's terminology!), there is enough kinetic energy/tension (?) in the rod for it to spring back. My head tell me, that the bigger the rode, the higher the energy build up until its release and return to original state. So, IF, the rod was big enough and twisted enough times - the whole 7,000 miles of tube, would there not be enough 'stored'/kinetic/tenstion energy to reach the required velocity to travel faster than the speed of light - much like the 'crack' at the end of a whip?

For this to work the rod would have to be much thinner at the 'cracking' end, than at the start, as to allow the energy to efficiently transfer and travel to the end.

I'm a total novice who likes to day dream.

The trouble with your day dreams is that they are still dreams.

You are thinking that it is possible to have a rod/tube/string that is 7000 miles long. Such structures do not exist in our universe. That is almost the diameter of earth. All such structures collapse under their own gravitational mass into spheres. So you can't even start your scenario. You are imagining that their exists a material that is strong enough and light enough to take on the shape of your attached drawing but there isn't and there can't be.

 

[mfb]

The trouble with your day dreams is that they are still dreams.

You are thinking that it is possible to have a rod/tube/string that is 7000 miles long. Such structures do not exist in our universe. That is almost the diameter of earth. All such structures collapse under their own gravitational mass into spheres. So you can't even start your scenario. You are imagining that their exists a material that is strong enough and light enough to take on the shape of your attached drawing but there isn't and there can't be.

Sorry, but I think that explanation is misleading. It looks like it would be just an engineering issue. It is not (and a 7000-miles rod in space can be built).
The speed of light is a very fundamental physical limit. Even if you have a perfect material with infinite tensile strength and whatever, even if you have an arbitrary amount of energy available and put it all into the rod, the resulting speed will be below the speed of light.

Hmmm... dammit. What if the 'string' was placed into a negative kelvin state - thus meaning that more 'natural' (?) energy would be needed to return to normal state, thus increasing velocity faster than normal...

That does not make sense.

 

[mausten]

Quote by mausten
Hmmm... dammit. What if the 'string' was placed into a negative kelvin state - thus meaning that more 'natural' (?) energy would be needed to return to normal state, thus increasing velocity faster than normal...
That does not make sense.No, you're right, that doesn't make sense. I read somewhere last week (sorry have forgotten the source - maybe this is simular, they used the same example about making cobustion engines over 100% efficient http://www.chemistry2011.org/news/P...luteTemperatureAreTheHottestSystemsInTheWorld) about atoms being cooled to below absolute zero. The article went on to explain that if atoms are cooled below absolute zero they release more energy in returning to their 'normal state'.

I was thinking that if this FTLD (Faster Than Light Device - Mark2013TM :-) ) was super duper cooled to -x kelvin, that it might just work. Imagine a little transported pod on the end of the whip/rod, that accelerated you to 'X' x faster than the speed of light and let released you onto your desired trajectory.

 

[mfb]

Negative temperatures (on the Kelvin scale) are not cold. They are hotter than anything with positive temperature, and you have to put thermal energy into a system to reach a negative temperature.
This has nothing to do with the motion of a rod.