GRED Answer: Twirling pole paradox

[RJN]

Guess the Result of the Experiment of the Day (GRED): The Twirling Pole Paradox

You hold a really long pole -- for example one light year long. You are out in space. You hold one end of this pole firmly to your stomach with the pole pointing out, and then you spin around in a circle. Therefore the free end of the pole makes a complete circle, with you at the center of the circle. Say it takes you 10 seconds to do this. Does the speed of the free end go faster than the speed of light?

What I believe to be the answer to this GRED is now posted below but accessible here: http://asterisk.apod.com/vie ... 43#p123533 . Answers and comments are still encouraged below.

The initial poll, where spoilers were not allowed, can be found here: http://asterisk.apod.com/vie ... 30&t=19641 . If you are new to this GRED and want to ponder this question without seeing spoilers, please go there now instead of scrolling down.

- RJN

[Chris Peterson]

At the least, this question exposes the risk of thought experiments. That's because in practice, the experiment is impossible. Accelerating an object with a rest mass greater than zero (e.g. your long stick) to the speed of light requires an infinite amount of energy. So while it is fair in a thought experiment like this to allow for a stick that is infinitely rigid and strong, there's no getting around the fundamental physical problem that there isn't enough energy in the Universe to actually move that stick fast enough to get the outer portion moving at c or faster.

[The Code]

Once again RJN, You have asked A question that grips my mind and gets me thinking. The End of your pole would reach 99.9999% the speed of light.

And this is what your question made me think: If it was possible. If I were able to have a Gravity Pole, Would my Gravity pole also keep me at a relative speed considering I had the same Mass as a black hole?

Thanks RJN

Mark

[Beta]

How about a slightly trickier version: imagine you are out in space with a spotlight, pointing it at a screen one light-year away. It makes a sharp spot of light on the screen. (It's a very good spotlight.) Now sweep the spotlight from side to side. Does the spot move faster than light?

Even trickier: how about a stadium wave?

[jman]

Say - can any of you guys calculate the centrifugal force on that pole? Or does it need a mass for that?

[Amir]

i think the other end of pole wouldn't reach c.

... Does the spot move faster than light?

i'd say yes it does. and i think it's not much related to this GRED, because that spot of light is not a "thing" & there is nothing preventing it from reaching to the speed of light. actually it's an image. it's like having a light-year-inch TV and watching something that is moving faster than light, in fact there is nothing moving. and in your experiment also nothing moves; there are just individual photons traveling normally and hitting the screen to form an Image.

[NoAstronomer]

Actually we don't need to *imagine* the spotlight experiment - the universe has thoughtfully provided us with natural spotlights that we can study. Of course the spotlight is a pulsar but the principle is the same.

Since I think we're (mostly) agreed that the end of pole would not reach the speed of light what would happen to it? Would it break or would it appear to deform?

[TomG]

The pole does not deform, time does.

[Wonder]

The pole would increasingly resist angular acceleration as any part of it approached the speed of light. It would appear to gain in moment of inertia. I think it would have to burst at some point, from the principle that stress itself has mass, which is why a black hole (atoms completely collapsing to singularity) has to happen at some mass no matter strong the atoms are. The increased mass inherent in the centripetal stress would add to centripetal forces, increasing the stress and mass and force.... waddaya think?

Some "things" can move faster than light. E.g., the phase fronts of GPS signals move slightly faster than light as they pass through the ionosphere, but the modulation on those waves moves slightly slower than c. So information can't move faster than light, and I'd like to say that matter and energy can't, but that kind of hangs on the definition of the "speed" of matter or energy, especially when dealing with continuous phenomena. Certainly particles cannot translate faster (I think of all particles as at least made up of discreet charges, which Maxwell's equations will then keep from going faster than light), but for instance, in one model of the proton (crackpot anti-quantum theory), the featureless charged surface of the spherical proton moves faster than c to produce the measured magnetic field from the measured charge and diameter, with no relativistic effects(!); but how do you define the "speed" of a featureless "thing" like that surface in rotation? It behaves more like an electric current than a moving object.

And then there is the matter of entanglement, where information does seem to move faster than light, but only for the use of the entangled particles, so guess what: we can't move information faster than c using it.

Thanks for the puzzler!

[Neil220155]

The speed of light is infinite, however it can only be measured to 186000mp sec, anything can travel "faster than light" including light.
But whatever speed you are travelling at, the greatest speed beyond your speed (frame of ref) is 186000mp sec.

[Chris Peterson]

The speed of light is infinite, however it can only be measured to 186000mp sec, anything can travel "faster than light" including light.
But whatever speed you are travelling at, the greatest speed beyond your speed (frame of ref) is 186000mp sec.

C is a (finite) constant, and is the same in every frame of reference. Light can travel slower than c (and usually does), but never faster.

[leider]

Since the pole is matter I am a bit reluctant to say it will exceed the speed of light. As for the spot light the answer is yes. Imagine a laser in a rotating barrel that sweeps a spot of laser light across the moon. If the laser barrel rotates at 1 radian / sec the laser spot moves across the moon at about 248000 miles / sec, much greater than C. The velocity of PROPAGATION of the light is still C. The spot is not propagating ACROSS the moon.
Best Wishes

Leider

[Kalen]

Since information travels at the speed of light, it would take a year before the end of the pole would know that it should start moving.

In the 10 seconds that it takes for one complete revolution, the end of the pole has not moved yet.

[DaveMorton]

If we're going to toss out Newton, why are we worried about Einstein? And while we're at it, if this is out in the middle of space, what are we using to gain traction to begin the spin in the first place?

Ok, that said, and my chuckling subsided, I would have to agree with an earlier poster that, all other things being equal, the tip of the pole would go no faster than 0.9999999...C
[snark]
and that's if you use a (somehow) uber-rigid hollow pole of metallic hydrogen only 3 molecules thick, and don't hit something with said pole (OWCH! Have you any clue what the odds are of executing a fill circle with a diameter of 2LY WITHOUT hitting something along the radius? the lotto is a better bet)
[/snark]

[edit]
Oh, and if said pole WERE able to be spun in a full circle in 10 seconds, the tip of the pole would end up traveling an average speed of 1,846,820,692,149.5727116059015616368 miles per SECOND, or roughly 9,900C, if my math is correct.
[/edit]

[John S]

Interesting thought experiment. First the answer is no, if the stick has anything greater than zero mass. Second, visually the the whole thing would look not too dissimilar to a super massive black hole with the end of the pole raping around it like the event horizon with the end only traveling near light speed. Or at least is what I see.


John Sanders
Norman OK
Just a Tech.

[hstarbuck]

[edit]
Oh, and if said pole WERE able to be spun in a full circle in 10 seconds, the tip of the pole would end up traveling an average speed of 1,846,820,692,149.5727116059015616368 miles per SECOND, or roughly 9,900C, if my math is correct.
[/edit]

With linear v = radius * angular v (in radians), and angular v = 2pi/T, I get that the tip of the pole would be traveling at around 20 million c. v = (c * 365*24*60*60* 2pi)/10 = c* 19.8*10⁶ m/s. I would say that it would be impossible for this to occur, so the conditions cannot be met. If we could accelerate a rocket ship for 10 years at 10 m/s² then it would just exceed the speed of light as well (3.1536*10⁸ m/s), but according to physics that I know, this is not possible. I do remember IPOD's or discussion on the Asterisk where it seems that light travels faster than c (could not find them), but this is apparent motion (I believe), not actual motion. Also, the redshift of the most distant objects gives for velocity relative to us greater than c, but this is do to the expansion of space. My current opinion: c is the speed limit of the universe--final.

[Duckingthequestion]

Since information travels at the speed of light, it would take a year before the end of the pole would know that it should start moving.

In the 10 seconds that it takes for one complete revolution, the end of the pole has not moved yet.

I agree, but what does the pole look like out to 10 light-seconds from your belly button? does it appear straight to you? What would the pole look like to someone hanging out 10 light-seconds from you?

[Mokurai]

Taking the question simply as it is, and ignoring how any of it would be possible, we have a pole rotating so that its outer end goes around a circle with a radius of one light-year in 10 seconds. It thus travels 2 pi light-years in 10 seconds, or about .628 ly/sec. This is obviously impossible. A year is about 365.25 days × 86400 sec/day, or 31.6 Msec. The end of the pole would have to move at 20 million c, which tells us just how impossible this scenario is. Even if we could make the pole of the still hypothetical tachyons, which would be able to travel at that speed, the pole would come apart even faster, since tachyons supposedly travel at greater than c relative to each other. So in fact none of the scene described happens. Well, we knew that anyway.

If it weren't for physics and law enforcement, I'd be unstoppable. But there it is.

Where does the question break down? First, the pole is supposed to be a light-year long, or about 6 trillion miles (10 quadrillion meters, 10 petameter, or 10 pm). Suppose we have a fantastically light and strong material with a mass of 1g/m but extreme rigidity. That gives us 10 pg total mass, on the order of a six-trillionth of the mass of the Earth, comparable to a modest-sized comet.

The centripetal force required for you to hold on to it is mass × acceleration as if all of the mass were concentrated a half light-year away at the pole's center of mass. The acceleration is v²/r. With the outer end moving at 1 km/sec, you would have to exert 10 Pg × 1 km²/sec²/10 Pm, or about 1,000 newton. A strong man can lift half a ton with his legs, exerting a force of 500 kg × 9.8 m/s, or nearly 5000 newton, so that isn't so bad. However, the force goes up as the square of the velocity. Incorrectly using this Newtonian formula in the super-hyper-megarelativistic range of ly/sec, many billion times faster, gives us a requirement for roughly a gazillion strong men just to hold on to the pole, and similarly for the tensile strength of the material. It exceeds even Larry Niven's scrith, as described in his Ringworld SF novels.

We could go on, and consider how much force is required to swing the pole (hint: even more), what its bending moment and required rigidity would be, the time required to get any effect from one end to the other, vibrations running along the length of the pole, the resulting hazards to interstellar navigation, etc. etc. Each of which gives the answer, No, No, ten to the umpteenth times No.

Now a beam of photons from a millisecond pulsar is another story. It isn't a straight-line beam, of course, but a spiral that wraps around a vast number of times between there and here, at intervals of a few hundred km.

[stevev]

There are a couple of simple things to consider about how the pole will behave:

At no time can any part of the pole move faster than (or even at) the speed of light.

No force can propagate along the pole faster than the speed of light, because the matter the pole is made of is held together by electromagnetic forces (you might hypothetically make a pole of neutronium or some other nuclear matter, which could be held together by the strong nuclear force instead, but even then that can't propagate faster than c).

So even if we somehow made this light-year-long pole, if you started to twist it at one end to try to spin it around in a circle, it will take at least a year for that push to reach the other end of the pole.

Because the far end of the pole can't go faster than the speed of light, and it's one light-year long, it cannot possibly make a complete rotation in any less time than about 6.283 (pi*2) years.

[Quizzer]

Let me try...

If the pole does not break, then it will stretch and seemingly be deformed into a spiral form.
The end will move at some finite speed < c, depending on the pole rigidity.
The momentum of turning the pole will move along the length of the pole with some finite speed < c (the speed of sound in the material probably? someone with material knowledge can answer this).
The spiral will become apparent by someone looking down on the pole from a few ly up (scale down to normal lengths with a rubber pole of a few meters to see the spiral)

The break or turn effect can be tested by taking a very long wood pole and trying to swing it around very fast.
There is a turn speed where the pole will break because of the forces dragging the end of the pole along (it will bend).
Scale this up to 1 ly and the answer stays the same, even for very rigid poles.

So, answer D) it will deform.

The force required to turn or break the pole is actually a nicer question to ask.
If someone on 0.5 LY cuts the pole in half, 5 months after you made the turn movement, what happens to the force you initially put into the turning movement?

[Phreethought]

Can someone elaborate on the stadium wave riddle? Thanks.

[bystander]

Can someone elaborate on the stadium wave riddle? Thanks.

Click to play embedded YouTube video.

[Beta]

Can someone elaborate on the stadium wave riddle? Thanks.

What I meant was to ask whether a stadium wave can travel faster than light.

The question is open-ended, and it's hard to elaborate without giving it away, but here are some things to think about. Let's define a true stadium wave as one in which people are going by what they see other people do. A cued wave involves another signal, like someone waving flags in the middle of the stadium. In a planned wave, people synchronize their watches beforehand and know when they're supposed to stand and sit. In a blind wave, people keep their eyes closed but hold hands with their neighbors. Also we might wonder whether the shape of the stadium matters, whether it's one long straight bank of seats or a big ring (hint, hint).

[RJN]

The answer is, I believe, "No, the pole end cannot exceed the speed of light." Since physical objects can carry information, and information cannot be used to communicate faster than the speed of light, then the free pole end has limited speed.

Most (80 percent at the time of this writing) of the voters in the initial poll got it right. Several of the people who answered below made good arguments. In particular the argument given by Kalen (here: http://asterisk.apod.com/vie ... 43#p123165) makes a key point. The fastest that information can travel ALONG the pole is c. Therefore, the free end of the pole will not even know that the person-held end has started moving for 10 years after its first motion, since the example pole is 10 light years long.

There is no such thing as an infinitely rigid and infinitely strong pole. Rigid poles must break. Elastic poles must not only bend but stretch. At no time will any part of any pole exceed c. At some time, given finite elasticity, even elastic poles will break.

Classical, intuitive, physical properties do not always work when taken to extremes. This is one example. We live in one strange universe!

- RJN

[hstarbuck]

The answer is, I believe, "No, the pole end cannot exceed the speed of light." Since physical objects can carry information, and information cannot be used to communicate faster than the speed of light, then the free pole end has limited speed.

Most (80 percent at the time of this writing) of the voters in the initial poll got it right. Several of the people who answered below made good arguments. In particular the argument given by Kalen (here: http://asterisk.apod.com/vie ... 43#p123165) makes a key point. The fastest that information can travel ALONG the pole is c. Therefore, the free end of the pole will not even know that the person-held end has started moving for 10 years after its first motion, since the example pole is 10 light years long.

There is no such thing as an infinitely rigid and infinitely strong pole. Rigid poles must break. Elastic poles must not only bend but stretch. At no time will any part of any pole exceed c. At some time, given finite elasticity, even elastic poles will break.

Classical, intuitive, physical properties do not always work when taken to extremes. This is one example. We live in one strange universe!

- RJN

Thank you RJN. However, I was looking for a different type of resolution. If the information takes years, that is ok because we have years. As long as the elastic pole does not break, then the outer regions will be following the inner and will be "catching up" as in a small scale version (depending on elasticity--analogous to spring constant k--I am inferring). This being a thought experiment all conditions can be met. So, what happens when the outer regions start catching up, and due to tangential velocity growing with radius, start approaching the speed of light. I think this simply puts the outer regions in the category of any massive object approaching c. Enter the realm of special relativity. From what I can gather from previous posts, my college physics curriculum, and a quick search of the net, infinite energy is needed to get a mass to reach c, and the mass would become infinite as well. Mass equals energy, right. Here is a link to a discussion I found on my brief search: http://www.phys.vt.edu/~jhs/faq/sr.html