Faster than light information transfer

[1mmorta1]

I have what may be considered a rudimentary question, but one which I've actually never asked and have always wondered about.
Many people have posed the question as to whether or not a very long, rigid object could be "pushed" on one end and instantaneously transfer information across a vast distance by moving on its opposite end. I know that this will not work, but I have always wondered about the OPPOSITE scenario.

Picure a very long cord attached to two objects, one of which is spinning and exerting a tension on the cord, causing the other to move in a circular path around the central object. If this cord were cut, it seems intuitive that the object circling would HAVE to continue its perfect orbit until information had time to reach it. How would this happen, considering that the side cutting the cord would immediately witness its release, and this disconnected end would assume some of the "orbiting" ends velocity and beginning moving away from the central object?

 

[russ_watters]

If one wouldn't work, why would the other? Do you understand why the first didn't work?

 

[1mmorta1]

I do, but that is an exertion of pressure on one end that takes time to reach the other. It is easy to picture this, and it makes perfect sense. But by creating TENSION rather than pressure, it is more difficult. I suppose I'm just curious because I can picture the distant chord maintaining its rigidity until the information can reach throughout it, I just don't understand(if you were to frame one moment in time) what the RIGID part of the string adjacent to the now FREE portion would be moving with respect to.

 

[1mmorta1]

But twisted spark, using that logic would lead you to assume that pushing on one end of a lightyear long pole would cause it to instantaneously move on the other side. This is incorrect. Instantaneous information transfer is not possible

 

[Dale]

A pressure wave through material that is neither stretchable nor compressible would move instantaneously.

No such material exists, and it is, in fact, contrary to the fundamental laws of physics. The forces which one molecule exerts on another are electromagnetic, so they are fundamentally limited to the speed of light, which therefore puts a fundamental limit on the rigidity of any material.

 

[Dale]

1mmorta1, any mechanical disturbance in a material will propagate at the speed of sound in that material. It doesn't matter if the disturbance represents an increase or a decrease in the stresses within the material.

 

[1mmorta1]

So you are suggesting a hypothetical noncompressable material... I would like a second opinion on this, is there anyone out there that knows more about the physics governing electrons than I do that can speak on this? I know for SURE, twistedspark, that electrons do not move instantaneously through any conductor, even one with no resistance. Light IS energy and the upper bound for its velocity is C, as with all forms of energy(heat, radiation, etc. Well, maybe not neutrinos apparently...) So your first assumption is wrong, however I can't say why. As far as the hypothetical structure you propose, I'm not sure what the physics governing such an object would look like.
I know much more about quantum mechanics than I do this relativistic material, and I'm not sure how to apply what I know about electrons over such a large scale.

 

[1mmorta1]

Wow, we are so far off topic... Redirect: what would the RIGID part of the string adjacent to the now FREE portion be moving with respect to(instantaneously)?

 

[twistedspark]

... that electrons do not move instantaneously

You're misreading and misquoting me. I wrote that electrons do not have to move the entire distance so there is very little speed necessary. All the electrons in the circuit move a tiny bit at the same time throughout the entire circuit.

 

[Dale]

The force on molecule exerts on another is not electromotive force. Emf only deals with electrons and voltage.

That is not correct. Matter is made of atoms and molecules, and solid matter is formed because of strong interactions between neighboring molecules. These interactions are electromagnetic.

 

[Dale]

I would like a second opinion on this

twistedspark is wrong. There is no infinitely rigid material and even energy transfer is limited in speed to c.

 

[1mmorta1]

Twistedspark, every time one object moves another it is due to the interaction of electromagnetic forces. How these behave in the hypothetical pole we discussed is beyond me...

 

[1mmorta1]

twistedspark is wrong. There is no infinitely rigid material and even energy transfer is limited in speed to c.

Haha, thank you for clarifying the obvious. I was wondering more as to WHY, and naturally I should have used my brain and thought of the electromagnetic nature of the interaction between electrons. I guess I felt thrown off by all the hypotheticals...

 

[DaveC426913]

Haha, thank you for clarifying the obvious. I was wondering more as to WHY, and naturally I should have used my brain and thought of the electromagnetic nature of the interaction between electrons. I guess I felt thrown off by all the hypotheticals...

Note though that, while the theoretical upper limit on propagation of forces is limited to the speed of light (the EM forces between atoms), the real upper limit is the speed of sound of the object (the mechanical movement of the atoms themselves).

No real material will ever have a speed of sound any more than a small fraction of c. Diamond, the hardest substance conceivable in our periodic table of elements, has a speed of sound of 12km/s - a mere 1/25000th of c.

 

[Integral]

How would this happen, considering that the side cutting the cord would immediately witness its release, and this disconnected end would assume some of the "orbiting" ends velocity and beginning moving away from the central object? t to see this effect.

I suspect the loss of tension in the rope would be seen as pulse traveling along the rope.

Haven't you ever stretched a rope and waggled the end up and down to create a pulse traveling along the rope? That pulse is changes in position and time of the rope's tension. Clearly the idea that tension must be constant through out the entire length of a rope is incorrect.

 

[1mmorta1]

I think you've misunderstood my question. I know what would happen, I'm looking for a mathematical, or at least detailed description of the instantaneous change in the orbital velocity of the cable. I don't need an explanation of WHAT, but HOW.

 

[Dale]

actually working out the motion in detail would be a real pain in the neck. The highlights are that the outer end of the cord would continue it's circular orbit since it is still under tension, but the center of mass of the cord would move inertially since the cord is no longer subject to any external forces. These two effects are both possible because the shape of the cord changes, and the cord begins to spin about it's own center of mass.

 

[DaveC426913]

I think you've misunderstood my question. I know what would happen, I'm looking for a mathematical, or at least detailed description of the instantaneous change in the orbital velocity of the cable.

1mmortal, I see two phrases, the use of which I do not understand in the context of your scenario, since neither apply.

1] instantaneous change - why do you think any change here is instantaneous? Wherever the cable is cut (btw, you do not specify where), it will begin moving away from that point. But the cable is not "assuming any characteristics of the moving body" - it is simply recoiling. It was under tension - being stretched. Every inch - even the inch next to where it was cut - is under tension, and will recoil (shrink). This has nothing to do with any distant orbiting body; it is entirely explainable with local effects - within inches/feet from the cut point, not miles.

2] orbital velocity - nothing here is in any orbit. The cable is keeping the object in a circular path. And it is doing so by being under tension, which is what is making it stretch in the first place.

 

[1mmorta1]

When I say instantaneous change, I mean the literal instantaneous rate of change of velocity(speed and direction) of the chord at any given point. If you were to cut the cord and then freeze time, and zoom in and examine the point where the information "IS".(i.e. if the chord were a single strand of carbon nanotube, looking at the atom adjacent to the atom that has just changed velocity, the atom "next in line" to receive the information that the chord has been cut) Is it fully unaware that there has been a change? Is it moving exactly as it had been, still circling the central object, though it is unattached?
The reason this question seems more complicated to me is that, though the initiating action is completed at the center(by cutting the chord) the change in the system occurs because of the angular velocity(which is the term I should be using instead of orbital) of the circling object. You cut the cord, the force exerted by the circling object causes the chord to pull away. Yes, if your chord is made of rubber, the tension causes a recoil. I am aware that this recoil exists even in rigid materials, but my confusion comes from the fact that it seems information comes from both ends of this system. You cut the cord, the pull from the outer object, which is what causes the tension, begins to pull the cord away.
What would someone standing out of frame witness?

 

[sophiecentaur]

Work this out by assuming a really bungee piece of rubber cord.
It will be moving along a tangent with velocity ω^2 r as soon as it is released.
The very end of it will be pulled radially, by the piece adjacent to it by a force equal to the tension T in the cord, so it will accelerate in the direction of the string at T/δm. (δm is the mass of the end piece) That's the easy bit. Now what happens after time t? The sections of the rest of the string will only 'know' about the cutting when the ''changing tension wave reaches them so I think they will all continue in a circular path until the tension wave reaches them. They can't know about the cutting as there will still be a radial centripetal force on them until the wave reaches them.

The shape of the string after a given time would be interesting to know. It would, presumably form a spiral of some sort? But I can't decide which way the thread would go.

Having a 'rigid' material in this model is pointless.

 

[1mmorta1]

Thank you! That is the sort of thing I'm looking for. I'm not so curious as to WHAT happens, I know that. I'm curious as to HOW it happens and WHAT it looks like. What does the connecting material do? (Even a rigid material is going to behave like rubber over such distances, because of our lovely universal speed limit) And what exactly causes it.
You've been the most helpful thus far.
Any relativity masters able to tell me what someone standing far enough out of frame to witness the entire event would see? Would it appear natural, instantaneous? (IE would it look like the outer mass changed course immediately, as if there weren't a vast distance between the inner and outer masses)

 

[sophiecentaur]

How could it look, to any outside observer, like the outer mass changed its motion if the force change hadn't reached it yet? For someone on the axis of rotation and at a great distance, they would see it more like how you'd describe it - time delays to the observer would not come into it.
Someone on the outside mass would see the tether moving oddly long before they were aware of a change of course, of course (haha), even though the light took a year to reach them. What would they see, looking down along the tether?

 

[1mmorta1]

Well, I know someone on the outer mass would feel the motion as soon as they could see the tether being cut(due to the fact that it would take light just as long as information to arrive at the outer point). I'm not sure what someone looking from the center out would see... However i do know that if they wanted to shoot the outer mass after cutting the cord, they would have to calculate for a time delay between what they see and what is "actually" happening. It would seem that an observer sitting along the axis of rotation far enough away to witness the entire event would witness an "instantaneous" change in course. (Which is okay because it takes light so long to reach the observer)

 

[sophiecentaur]

I don't follow your reasoning on this one. Have you read that story of Einstein's cows on the electric fence?
He observes a row of cows with their noses on an electric fence. The farmer turns on the current at one end. The observer, at one end, sees them all lift their heads at once and an observer at the other end sees them lift their heads in sequence.
I think this is a modification of his story but with a slow signal moving along the fence. Things wouldn't appear simultaneous from either end, I reckon. We are assuming that the tension wave in the string only travels at sonic speeds rather than light speeds, surely.

 

[1mmorta1]

Right, but relativity still maintains causality. So, if your standing in the middle of a field, swinging a ball around over your head by a long rubber band, when you release the cord the ball doesn't continue to circle you until the ripple reaches the ball. It is circling you BECAUSE your holding the cord, and, once you let it go, the ripple and release are simultaneous...you stop holding the cord, the ball stops spinning around you. Cause and effect
An outside observer could never witness an unattached outer mass circling an inner mass, because there is no cause for it to do so. The distant observer SHOULD see the same thing that a person in a helicopter looking down on you in your field swinging the ball would see, if only to maintain causality.
The only purpose of the relativistic reasoning is to determine what "actually" happens. The hypothetical scenario shouldn't APPEAR unnatural to anyone involved. It is only when looking at physical limitations of a system that we can determine the nature of the event, which is what I'm trying to do :)

 

[1mmorta1]

I think I've got it. Assume the distance separating the two masses is one light year:
If your standing on the central mass and cut the cord, you immediately witness the cords release. Looking through your telescope, you know the light coming from the outer mass is a year old, so you realize that you will see it coninue in orbit for a whole year. One year later, you see its course change exactly as it should. Which would indicate to you that the change happened instantaneously, and the light took a year to reach you. To the observer on the outside mass, you see a man approach your cord and cut it. As soon as this happens, you feel a change in your velocity, but realize that the light you saw was a year old and that the cord has been cut for some time. The outside observer would witness no delay, only the "helicopter" situation I mentioned above.
Does this seem to hold up?

 

[sophiecentaur]

Re. earlier of the two posts
I can't agree. You have to ask why the mass on the end is going in a circle. It's not 'because your are pulling it in' so much as because there is a central force on it. How can that central force change until something changes it. Only the tension wave can change it? That must take time to occur and can't be instantaneous.
Your causality idea is not relevant here. There are plenty of events that occur long after their cause. If you observe someone hit a rod, the object on the other end will not move until the shock wave reaches it. If a mass is hanging on a long spring and you let go, the mass won't start falling until the end you let go has moved downwards far enough to reduce the upwards force on the mass. This, again, takes a time which depends on the mass per unit length of the spring and its modulus. For a massive spring with a low modulus, it could be a long time.

 

[sophiecentaur]

Re Second post
This, again, is not right. How can the distant mass be affected 'instantly'? If we were using gravity (or a mega pulse of laser energy), instead of a string, it would still take one year for the gravitational change (or laser energy) to reach there and yet another year for the light to reach us to tell us what had happened.

Why are you thinking in terms of 'instantaneous' effects? Nothing is instantaneous. It takes 1ns for light / information / an effect to move through one foot.

 

[Dale]

I think I've got it. Assume the distance separating the two masses is one light year:
If your standing on the central mass and cut the cord, you immediately witness the cords release. Looking through your telescope, you know the light coming from the outer mass is a year old, so you realize that you will see it coninue in orbit for a whole year. One year later, you see its course change exactly as it should. Which would indicate to you that the change happened instantaneously, and the light took a year to reach you. To the observer on the outside mass, you see a man approach your cord and cut it. As soon as this happens, you feel a change in your velocity, but realize that the light you saw was a year old and that the cord has been cut for some time. The outside observer would witness no delay, only the "helicopter" situation I mentioned above.
Does this seem to hold up?

This is not correct. Assume that the speed of sound is .5 c in the cord and the cord is a very massive material. The inner guy cuts the cord, the outer guy continues on a circular path, at year 1 outer sees inner cut the cord, and still outer continues on a circular path, at year 2 the tension wave hits outer and outer begins to deviate from the circular path, at year 3 finally inner sees outer deviate from the circle.

This assumes that the cord is sufficiently massive that the tension does not accelerate the cord faster than .5 c. Those details are very tricky.

 

[sophiecentaur]

That's a good scenario to explain it.
It's essential to chuck out any idea of simultaneity.

 

[DaveC426913]

You cut the cord, the pull from the outer object, which is what causes the tension, begins to pull the cord away.

No, it doesn't matter what force originally caused the tension. The simple fact is that the tension is there in every molecule of the cord, even the ones right next to the cut.

If you cut the cord simultaneously at centre-sphere and at orbiting-sphere the cord would still recoil even at the centre-sphere's surface, even though, ultimately every far away, the original force of the orbiting-sphere pulling is no longer there.

 

[DaveC426913]

I think I've got it. Assume the distance separating the two masses is one light year:
If your standing on the central mass and cut the cord, you immediately witness the cords release. Looking through your telescope, you know the light coming from the outer mass is a year old, so you realize that you will see it coninue in orbit for a whole year. One year later, you see its course change exactly as it should. Which would indicate to you that the change happened instantaneously, and the light took a year to reach you. To the observer on the outside mass, you see a man approach your cord and cut it. As soon as this happens, you feel a change in your velocity, but realize that the light you saw was a year old and that the cord has been cut for some time. The outside observer would witness no delay, only the "helicopter" situation I mentioned above.
Does this seem to hold up?

No. The delay between cutting at ground-level and change in movement of the small body is quite real and will be observed by all in real time.

They would actually be able to watch the wave of tension-release travel up the cord at .5c.

 

[1mmorta1]

Okay I get it. Is it even possible for the two ends to cut "simulataneously" on both ends considering that this is relative?

 

[Dale]

See a new FAQ on a closely related topic:
https://www.physicsforums.com/showthread.php?p=3537287#post3537287

 

[Dale]

Okay I get it. Is it even possible for the two ends to cut "simulataneously" on both ends considering that this is relative?

With some advanced planning it is certainly possible, but if they are cut simultaneously in one frame they will not be cut simultaneously in other frames.