Scientific question (super long pole)

[numerosdecimus]

The situation I'm describing goes again some laws concerning the relationship between density/resistence of the substance/compound, but I have to ignore them for the effects of this situation to be determined.

The other day I discussed with a friend what would happen if I tried to spin a enormously long pole which was direct to space in which the pole's lenth would be the total radius of the orbit.

Imagine this pole is hyper light weighted, a pole with a lengh of 1000 million kilometers (thus the radius of the orbit would 1000 million kilometers) and it would only weight 1Kg and the pole would be resistant enough to maintain it's structural integrity.

We know that it's impossible for an seaction of the pole to reach the speed of 3*10^5, it doesn't matter if it only weights 1KG. However, what would the phenomenons be, is where me and my friend completely disagree.

He says the pole would start to "bend" when we start approaching the radius aproximate to 3*10^5 kilometers.

I say I wouldn't be able to move the pole in the first place, no matter how light it would be and no matter how much strength I apply because of the direct proportionality between distance, speed (v=w*r) and mass.

Just a curiosity, I was wondering if your guys here at Athenaeum could give an answer of what could happen.

[ajm317]

Well, any real pole would certainly bend, and then break.

If we're talking about a pole made out of a magical material that doesn't bend or break though, you would be able to move it some, but getting the pole to move faster and faster would require progressively more and more energy on your part. You would have to provide an infinite amount of energy to get the end of the pole up to c.

[Medicus]

Diamond, maybe?

[numerosdecimus]

Lets say for instance I try to spin the pole 1 degree right. Due to how long the pole is even if I try for instance to move the pole 1cm there already is a certain section of it (it only needs to be long enough) that would supposedly equal c and others that would surpass c. For instance I try to move the pole 1cm, but a certain section of the pole which is 1*10^7 Km away from me would already supposedly surpass the speed of light.

When my friend say "bend", he means both the pole and space around it would start to bend as we approach the sections of the pole that are very close to c. However, what happens to those sections that would reach greater than c speed is a mystery.


That's why my opinion would be that it would be impossible to move the pole in the first place. Assuming I try to move the pole 1dm, by trying to do that the pole's mass would increase further and further according to how the sections of the pole are from me. If I move the pole, a certain section of it which would reach the speed of 2.87*10^5 m/s and it's mass would increase, but if I would approach a section of it which supposedly would reach the speed of 3*10^5 m/s, then it would have infinite mass.


About the properties of the material/substance giving it's mass, I would ignore it, if possible, I just need the pole to be light enough(despite it's length) but still strong enough not to bend physically, so yes, you could say it's a magical material of sorts.

[Juvenal]

If the pole is 1000 million kilometres long, then that is approx 55.5 light minutes.

There is no such thing as instant action-at-a-distance in physics except for quantum-entanglement.

Therefore if you start turning the pole from the centre, then no matter how light or rigid it is, the other end won't start moving for at least 55.5 minutes - therefore the rod would bend - so your friend is right.

[numerosdecimus]

If the pole is 1000 million kilometres long, then that is approx 55.5 light minutes.

There is no such thing as instant action-at-a-distance in physics except for quantum-entanglement.

Therefore if you start turning the pole from the centre, then no matter how light or rigid it is, the other end won't start moving for at least 55.5 minutes - therefore the rod would bend - so your friend is right.

I forgot about that.

However, don't forget that v=w*r, so if I spin the pole 1 degree, although the section of the pole close to me will spin at a certain speed and without mass changes, if I look at another section of the pole 250000 Km away that section will have a speed close to C and it's mass would have increased significantly.

What if I go for a compromise? (I can't lose this because I made a bet with him )

Ok, so the staff is 3*10^5 Km long. So, it would take about a second for the other end of the pole to move, however, due to the direct proportionality between the mass of the section of the pole and that section's distance from me, then I would be able to move the pole for less than a second.

He didn't mention the increase of mass in his argument.

[chris_uk_83]

This is a brilliant question, and if I could I'd give you a merit sticker for it! (I'm training to be a physics teacher!). Just let me check I understand exactly what you're asking.

You rotate a long pole about one of its end points and you're looking at the difference in speed between the pivot end and the other, clearly faster moving end. You keep rotating it faster and faster, until the middle is moving close to the speed of light. Since the far end is clearly moving faster than the middle, it must be travelling faster than the speed of light. But nothing can travel faster than the speed of light.....huh? Paradox?

I'm off to research this one. I'll get back to you.

[numerosdecimus]

This is a brilliant question, and if I could I'd give you a merit sticker for it! (I'm training to be a physics teacher!). Just let me check I understand exactly what you're asking.

You rotate a long pole about one of its end points and you're looking at the difference in speed between the pivot end and the other, clearly faster moving end. You keep rotating it faster and faster, until the middle is moving close to the speed of light. Since the far end is clearly moving faster than the middle, it must be travelling faster than the speed of light. But nothing can travel faster than the speed of light.....huh? Paradox?

I'm off to research this one. I'll get back to you.

Yes, that's more or less my question.

I also tried to make every factor as apparently "possible" as it could be by saying the pole is super light (however still super resistant) all to give the impression that it would be possible for the person to actually spin the pole, but he would find out that it's not possible.

[chris_uk_83]

http://www.physicsforums.com/archive.../t-108038.html This link ought to be of some help.

They reckon that it's impossible to accelerate the far end of the pole up to the speed of light, no matter how much torque you apply, all you do is increase the energy of the pole. Which can be interpreted as increasing its mass. As previously stated, yes, the pole would have to bend in order for the torque to be transmitted along it; no movement can ever be instantaneous.

[David Deas]

So whats next? What happens when you walk forward 2 MPH on a ship traveling 1 MPH below the speed of light? Is that the next question?

[chris_uk_83]

Ooh, ooh, I know, that's an easy one!

It all depends on your frame of reference! As is the case with all of these lovely relativity questions, which is what makes them so bloody confusing!

A stationary observer would observe you travelling a little closer to the speed of light than the ship, but not actually at the speed of light.

You would observe yourself moving forward at 2 mph, but anything going backwards past the ship at, again, just below the speed of light.

The ship would see you go one way at 2 mph, and the water (I'm assuming a water ship, not a space ship here) go backwards at the speed of light - 1mph.

Now nobody's moving faster than the speed of light and nothing gets violated. There's some Lorentzian transformation that tells you exactly what speed you would see each go at from all of the frames of reference but I can't remember it off the top of my head.

[Spurius]

A stationary observer

The most hypothetical being imaginable....

[David Deas]

The most hypothetical being imaginable....

Hardly. But I think its weird how people can not know what happens when you try and accelerate something the speed of light in one scenario, but then know exactly what happens in another scenario where you essentially try and accomplish the same thing. The more energy you put into something, the more massive it becomes as it approaches the light barrier. It can get infinitely close but never go beyond. You obviously couldn't accelerate something beyond the point where time ceases. There is no way to somehow be clever and trick that process, which was the reason for my sarcastic commentary.

.....Unless you're a microscopic object, that is. But thats a subject for another day.


(*) And the speed that one end of a material reacts to the other end is limited to the speed of sound in that material. You can't strike a steel rod and get vibration on the other end happening at the speed of light.

[Spurius]

Hardly.

Oh? Then you must use another definition of 'stationary'. Even sitting in your office, you're not 'stationary', by a long shot.

'Assume a body at rest'. Newton's I believe.

[David Deas]

Ooh, ooh, I know, that's an easy one!

It all depends on your frame of reference! As is the case with all of these lovely relativity questions, which is what makes them so bloody confusing!

A stationary observer would observe you travelling a little closer to the speed of light than the ship, but not actually at the speed of light.

You would observe yourself moving forward at 2 mph, but anything going backwards past the ship at, again, just below the speed of light.

The ship would see you go one way at 2 mph, and the water (I'm assuming a water ship, not a space ship here) go backwards at the speed of light - 1mph.

Now nobody's moving faster than the speed of light and nothing gets violated. There's some Lorentzian transformation that tells you exactly what speed you would see each go at from all of the frames of reference but I can't remember it off the top of my head.

Not bad.

Now. What about when you have two space ships, A and B, each travelling in opposite directions at 99% the speed of light away from a common center point C. What is the relative velocity of spaceships A and B if it can't be 198% the speed of light?

Can you work that one?

[chris_uk_83]

The same Lorentzian Transformation applies. If it'll make you happy I'll dig it out and post it.

[Simetrical]

Diamond, maybe?

Uh, no.

Lets say for instance I try to spin the pole 1 degree right. Due to how long the pole is even if I try for instance to move the pole 1cm there already is a certain section of it (it only needs to be long enough) that would supposedly equal c and others that would surpass c. For instance I try to move the pole 1cm, but a certain section of the pole which is 1*10^7 Km away from me would already supposedly surpass the speed of light.

The answer is simple: no material object can be perfectly rigid. You don't need hypothetical light-second-long poles for this; take an ordinary meter stick. If you twitch the base, it will take at least a nanosecond or so for the end to even begin to move, because the end is over a light-nanosecond from the base. This absolutely requires that the stick must bend, no matter what it's made of and no matter how long or short it is.

In the case of an extremely long pole, as your friend (it seems) correctly notes, the pole must bend substantially if you accelerate the base by any substantial amount. But you're not really wrong either: if the pole were completely rigid, it would also be impossible for force to propagate through it (since it would have to do so instantaneously to maintain perfect rigidity). To move it, you would need to apply a force to each constituent particle simultaneously, and if you could only grab the end, no amount of force would budge it even a nanometer.

Of course, this is a straightforward violation of Newton's laws (and the variants thereof), so I'm led to conclude that no perfectly rigid object is possible for very fundamental reasons. You either need to violate Newton's Second Law, or light-speed constraints.

However, don't forget that v=w*r, so if I spin the pole 1 degree, although the section of the pole close to me will spin at a certain speed and without mass changes, if I look at another section of the pole 250000 Km away that section will have a speed close to C and it's mass would have increased significantly.

v = ωr always applies, but you're assuming that the angular velocity ω is constant throughout the entire pole at any given time. As noted, this is impossible if a non-uniform force is applied to the pole. For small objects that are relatively rigid we can neglect the momentary difference in angular velocity across the object, because it will propagate quickly enough that the difference between any two parts of the object will be negligible for any realistic purpose.

Ok, so the staff is 3*10^5 Km long. So, it would take about a second for the other end of the pole to move, however, due to the direct proportionality between the mass of the section of the pole and that section's distance from me, then I would be able to move the pole for less than a second.

Doesn't make sense to me. Whatever the scenario is, either you can move it or you can't (and the latter is impossible). If you can move it, you can do so for as long as you like; there will only be energy and speed constraints, not duration constraints.

[David Deas]

What? I am too stationary. I'm stationary relative to my computer. I'm stationary relative to my office. Why is that a long shot?

[Spurius]

relative to

Ah, the magic escape clause.

Both you and your pc travel with the rotation of the Earth, which is considerable, the Earth rotates pretty fast around the Sun which is moving to Hercules or Orion (I forgot) even faster. All in all a neck-breaking speed.

Not to mention the fact no single atom of either you or PC is really at rest.

Only relatively speaking.

[David Deas]

Ah, the magic escape clause.

Both you and your pc travel with the rotation of the Earth, which is considerable, the Earth rotates pretty fast around the Sun which is moving to Hercules or Orion (I forgot) even faster. All in all a neck-breaking speed.

Not to mention the fact no single atom of either you or PC is really at rest.

Only relatively speaking.

Motion is simply a change in position between two events. There isn't any other way to define motion so I'm really not sure what this business is about. With all of the talk about Relativity going on around here I'd expect you to know by now that you need at least two events to define motion.