A pole, 2 lightyears in length - conceptual question

[vorcil]

A pole in zero gravity, two light years in length

you push it 1m,

does it move instantly at the other end?
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its in my physics textbook but doesn't give an explanation as to why it doesn't move?

i know nothing can move faster the speed of light

 

[sylas]

A pole in zero gravity, two light years in length

you push it 1m,

does it move instantly at the other end?
-
its in my physics textbook but doesn't give an explanation as to why it doesn't move?

i know nothing can move faster the speed of light

No, it does not move instantly at the other end. Your final answer is the explanation; nothing moves faster than the speed of light. The "pole" is mostly empty space; a collection of atoms held together by electromagnetic forces. It takes time for movement of one atom to result in a force at another.

 

[vorcil]

No, it does not move instantly at the other end. Your final answer is the explanation; nothing moves faster than the speed of light. The "pole" is mostly empty space; a collection of atoms held together by electromagnetic forces. It takes time for movement of one atom to result in a force at another.

my reasoning for nothing going faster than the speed of light...

gamma(from special relativity) = 1/(squareroot ( 1-(v^2/c^2)))

if v > c, 1-X which would give a negative number
the negative number becomes a complex number upon square rooting it

-

and it's not really reasonable to have a complex number

is that why nothing can go faster than the speed of light?

 

[queenofbabes]

This "gamma" is used to calculate accelerations and times, we can't have them being imaginary >.<

As an object approaches the speed of light, it requires an infinite force to accelerate it any further, so it's impossible to go faster than that.

 

[Mentallic]

my reasoning for nothing going faster than the speed of light...

gamma(from special relativity) = 1/(squareroot ( 1-(v^2/c^2)))

if v > c, 1-X which would give a negative number
the negative number becomes a complex number upon square rooting it

-

and it's not really reasonable to have a complex number

is that why nothing can go faster than the speed of light?

Even if v=c, the denominator becomes 0 which isn't allowed either.

However, I wouldn't word it exactly in this way. I mean, the equation was "created" (for lack of a better word) to describe the effects of special relativity.

Sure, you could argue that the mathematics of this equation has been supported by experimental evidence, but the equation itself was derived with the intentions of relativity in mind.

I guess what I'm saying is that for e.g. it's not fair to say it's a square because its area is described as s² where s is a side length. The square came first, not the equation. It can be used as evidence to support it though.

 

[vorcil]

This "gamma" is used to calculate accelerations and times, we can't have them being imaginary >.<

As an object approaches the speed of light, it requires an infinite force to accelerate it any further, so it's impossible to go faster than that.

can you link me to some math of this? i looked around wikipedia but couldn't find anything, ended up reading about schrodingers cat lol

 

[queenofbabes]

Try this: http://en.wikipedia.org/wiki/Lorentz_transformation

 

[PhanthomJay]

Back to your original question:

A pole in zero gravity, two light years in length

you push it 1m,

does it move instantly at the other end?

The speed of light has nothing to do with the 'speed' of the force transmission through the pole (other than that the speed of light would be the absolute maximum limiting speed). The 'speed' of the force through the pole is more or less the speed of sound through that medium (material) , for reasons noted in sylas' earlier post. If the pole was made of steel, I expect it would take over 100,000 years for the movement to occur at the other end (relatively speaking ).

 

[turin]

The "pole" is mostly empty space; a collection of atoms held together by electromagnetic forces. It takes time for movement of one atom to result in a force at another.

This is irrelevant, and misses the point of Special Relativity. Special Relativity makes no claim whatsoever about the existence of such objects (i.e. atoms, and rods composed of atoms), and furthermore applies regardless of the composition of the rod. That is, while Special Relativity originated from electromagnetism, it is not limited thereto.

Suppose a perfectly uniform and continuous "mathematical rod" of length 2-lyrs. This is a continuum (wave) mechanics problem that applies to any hypothetical material. Special Relativity restricts the equations of motion (i.e. the wave equation). Then you must describe the "push" on one end in a covariant way (i.e. promote spatial vectors to Lorentz vectors). Assuming a longitudinal "push", you can do this in a single spatial dimension, so that you can draw a 2-D spacetime diagram of this process. From this, you can put a lower limit on the time delay between the "push" and the resulting motion at the other end.

 

[negitron]

That was easily the most ridiculous explanation for the mechanics involved I've ever seen. Sorry, but mathematically-correct or not, that post is virtually meaningless and lacking in any sort of educational value for the OP. Posts #2 and #8 had it.

 

[sylas]

That was easily the most ridiculous explanation for the mechanics involved I've ever seen. Sorry, but mathematically-correct or not, that post is virtually meaningless and lacking in any sort of educational value for the OP. Posts #2 and #8 had it.

I'll defer to #8 as my favourite, for a simple explanation at an appropriate level.

 

[negitron]

Agreed. However, I wanted to acknowledge your contribution, as well.

 

[Mentallic]

The speed of light has nothing to do with the 'speed' of the force transmission through the pole (other than that the speed of light would be the absolute maximum limiting speed).

ok they're both unrelated. But if we were wanting to make the transmission speed of the force through this pole move faster, what could we change? e.g. Composition of the pole; amount of force applied;??

 

[negitron]

Change the composition, specifically, the property sometimes called stiffness which is quantified by Young's modulus.

 

[Mentallic]

the property sometimes called stiffness.

and what would be the limit of the transmission speed if this stiffness were increased indefinitely? (Nearing perfect rigidity)

 

[negitron]

Presumably c, although this is wandering well outside of my expertise. And I suspect the molar mass of the material in question puts a smaller upper bound on it.

 

[PhanthomJay]

ok they're both unrelated. But if we were wanting to make the transmission speed of the force through this pole move faster, what could we change? e.g. Composition of the pole; amount of force applied;??

Since the molecules of the material make contact with each other at the speed of sound when the force is applied, and since the speed of sound in a solid medium is roughly equal to the sq rt of E/p, where E is the elasticity modulus of the material through which the force is transmitted, and p is its density, then the speed of sound, and the speed of the molecular collisions, would be fastest when E is maximized and p is minimized. E and p are properties of the material. Steel has a high elasticity modulus (doesn't deform very easily), so even though it is rather dense,the speed of sound thru steel is quite high. Aluminum is 1/3 less dense than steel, but also 1/3 less stiff, so the speed of sound in alum is on the same order of magnitude as steel. Now diamond will transmit sound the fastest amongst most common materials, but who can afford it, especially in the 2 light year length? So only by changing the composition of the material can you increase the force transmission speed. Increasing the force will incease the acceleration of the cm of the pole, but I do not believe it will affect the time it takes for the far end to start moving.

 

[PhanthomJay]

Presumably c, although this is wandering well outside of my expertise. And I suspect the molar mass of the material in question puts a smaller upper bound on it.

Agree. Try one of Einstein's rigid measuring rods.

 

[negitron]

Look, I'm not touching Einstein's rigid rod.

 

[PhanthomJay]

Look, I'm not touching Einstein's rigid rod.

And I'm not touching that response.

 

[Mentallic]

Look, I'm not touching Einstein's rigid rod.

lol

PhanthomJay, thanks, that was a very concise response.
And is E - the elasticity modulus - the same as Young's modulus that negitron mentioned?

 

[PhanthomJay]

And is E - the elasticity modulus - the same as Young's modulus that negitron mentioned?

Yes, it is.

 

[turin]

negitron, your response to my post was quite rude, and, since you claim in a subsequent post that the content of my post is well oustide your area of expertise, I don't understand how you qualify it.

Anyway, I don't want to hijack this thread with a some little dispute, so I would like to hear your explanation for E<ρc, where E is the elastic modulus of the rod, ρ is the density of the rod, and c is the speed of light.

My main point was the irrelevance of a discrete lattice for the explanation. Explanations that involve the speed of sound tend to lead the eager young minds to a misunderstanding about Special Relativity. (Of course, I will admit, I am simply assuming that the question is posed in the context of Special Relativity, and it may very well be a solid-state physics question for all I know.)

 

[PhanthomJay]

My main point was the irrelevance of a discrete lattice for the explanation. Explanations that involve the speed of sound tend to lead the eager young minds to a misunderstanding about Special Relativity. (Of course, I will admit, I am simply assuming that the question is posed in the context of Special Relativity, and it may very well be a solid-state physics question for all I know.)

If I may interrupt again, the OP needs to clarify the point of the question. I did not view it as a question on Special Relativity, but rather, a question about how long it takes for the far end of a long pole to move when a force is applied to the near end. Maybe I misinterperted it. Nonetheless, I would argue in the following manner: If the pole was say 6000 meters long and made of steel, and the speed of sound in steel is 6000m/s, and an axial pushing force is applied to one end, then it would take at least one second to see any movement at the other end. Movement would certainly not be instantaneous. I would further argue that if the material were completely rigid (that is, undeformable, with infinite stiffness (E modulus), a hypothetical case for sure), then although non relativistic formulas would yield the speed of sound as infinite for this case, implying instantaneous movement at the far end, that in reality, since nothing can go faster than light, the speed of sound would be limited to the speed of light in this hypothetical case. Now if the pole was 2 light years in length, the question of 'how long does it take the far end to move' may get into SR theory, and I'm no expert on that. But I'm guessing, without doing the math, a couple of hundred of thousand years for me to see it as measured by my clock, if steel; and if ideally rigid, 4 years (2 years for the force vibrations to get there and 2 more years for me to see the event thru my powerful telescope). What do you think? And what does Vorcil say about the original question??

 

[turin]

Movement would certainly not be instantaneous. I would further argue that if the material were completely rigid (that is, undeformable, with infinite stiffness (E modulus), a hypothetical case for sure), then although non relativistic formulas would yield the speed of sound as infinite for this case, implying instantaneous movement at the far end, that in reality, since nothing can go faster than light, the speed of sound would be limited to the speed of light in this hypothetical case.

It seems to be a contradiction, then. If E=∞, then doesn't that result in an infinite sound speed? Imagine a very simplified model: a lattice of a single spring connecting two masses at a distance of 2 lyrs. Wave propagation in the lattice is based on Newton's laws:

Law 3: Push on mass #1 and then the spring pushes back.

Laws 1 and 2: But the spring only pushes back because the spring itself is connected to another mass, which presents inertia (requires force to be accelerated).

Law 1: (only applicable for many lattice points) The lattice can sustain a wave because, after a given mass in the lattice is pushed, a force is required to return it back to some eq position.

Basically, the claim that "nothing can go faster than light" is simply vacuous, and this kind of thinking leads to confusion about what Special Relativity really says. For example, the concept of simultaneity "goes faster than light", meaning that the two ends of the rod can be said to exist at the same moment in time, even though they are separated by some distance. Granted, there is no single massive object moving faster than light w.r.t. any other massive object; however, note that the issue involves the temporal relation between the spatial position of two spatially separated objects (namely the two ends of the rod).

Now if the pole was 2 light years in length, the question of 'how long does it take the far end to move' may get into SR theory, and I'm no expert on that. But I'm guessing, without doing the math, a couple of hundred of thousand years for me to see it as measured by my clock, if steel; ...

Yes. Here is the distinction that I suggest. If the purpose of the question is to demonstrate material properties, such as the finite propagation of an impules in one part of a real material to another part of that material, then sure, there will be a delay. However, 2 lyrs is a rather exotic length for any material, and so I assumed that the this question regarded some distant future (in which humankind could actually construct such a rod). That being the case, I did not want to limit the consideration to known materials with such low stiffness-to-density ratios. In other words, if we're allowed to imagine the existence of a 2-lyr rod, then I think we should imagine a perfectly rigid material.

for me to see it as measured by my clock ... if ideally rigid, 4 years (2 years for the force vibrations to get there and 2 more years for me to see the event thru my powerful telescope).

Just a comment on this: if you set your watch to t=0 at the moment you push your end of the rod, and you know that the rod is 2 lyrs to the other end, then you would automatically know to subtract the 2-yr delay, and this is the idea of simultaneity. So, you would be able to say (assuming that Special Relativity is correct) that the other end of the rod moved 2 yrs after you pushed your end. Then again, if the speed of sound in the rod is infinite, then you would still have to wait 2 yrs to see the other end move. And that's the point. Simultaneity. And the other point is that simultaneity is relative. The problem with the infinite speed of sound is not some specific material property, it is a fundamental property of space and time. You have to ask yourself, "What would an observer in a boosted frame see?" The answer, according to Special Relativity, is that,

if a perfectly rigid rod (E=∞) is pushed at one end, then a boosted observer could actually see the other end of the rod move before the push.

 

[PhanthomJay]

It seems to be a contradiction, then. If E=∞, then doesn't that result in an infinite sound speed?

Yes, it does. That is why the formula for the speed of sound in a solid medium, v=sq root E/p, is not valid for hypothetical materials with high E/p ratios. Even the speed of sound in diamond (which is one of the stiffest materials known, transmitting sound waves at 12,000m/s), is only a tiny tiny fraction of light speed. I make no statements as to what the speed of sound would be in near rigid materials, except to say that its speed could nor exceed the speed of light.

Imagine a very simplified model: a lattice of a single spring connecting two masses at a distance of 2 lyrs. Wave propagation in the lattice is based on Newton's laws:

Law 3: Push on mass #1 and then the spring pushes back.

Laws 1 and 2: But the spring only pushes back because the spring itself is connected to another mass, which presents inertia (requires force to be accelerated).

Law 1: (only applicable for many lattice points) The lattice can sustain a wave because, after a given mass in the lattice is pushed, a force is required to return it back to some eq position.

Fine, but that does not answer the question as to what time elapses before the far end starts to move.

Basically, the claim that "nothing can go faster than light" is simply vacuous, and this kind of thinking leads to confusion about what Special Relativity really says.

Are you saying that sound waves in a near rigid material can travel faster than light??

For example, the concept of simultaneity "goes faster than light", meaning that the two ends of the rod can be said to exist at the same moment in time, even though they are separated by some distance. Granted, there is no single massive object moving faster than light w.r.t. any other massive object; however, note that the issue involves the temporal relation between the spatial position of two spatially separated objects (namely the two ends of the rod).

I don't know how you can assign a speed to simultaneity. That's like asking 'what is the speed of time?'. With Einstein as my guide, 2 spatially separated events occurring at points A and B are simultaneous if an observer standing midway between A and B sees both events at the same time. I claim that an observer standing at 1 ly away from points A(the left end) and B (the right end) of the 2 ly length pole, that is, at its midpoint, will not see the events (the application of the force at A, and the movement of the pole at B) at the same time.

Yes. Here is the distinction that I suggest. If the purpose of the question is to demonstrate material properties, such as the finite propagation of an impules in one part of a real material to another part of that material, then sure, there will be a delay. However, 2 lyrs is a rather exotic length for any material, and so I assumed that the this question regarded some distant future (in which humankind could actually construct such a rod). That being the case, I did not want to limit the consideration to known materials with such low stiffness-to-density ratios. In other words, if we're allowed to imagine the existence of a 2-lyr rod, then I think we should imagine a perfectly rigid material.

I think you'd have to consider a near rigid material, or else there would be no definitive answers.

Just a comment on this: if you set your watch to t=0 at the moment you push your end of the rod, and you know that the rod is 2 lyrs to the other end, then you would automatically know to subtract the 2-yr delay, and this is the idea of simultaneity. So, you would be able to say (assuming that Special Relativity is correct) that the other end of the rod moved 2 yrs after you pushed your end. Then again, if the speed of sound in the rod is infinite, then you would still have to wait 2 yrs to see the other end move. And that's the point. Simultaneity. And the other point is that simultaneity is relative. The problem with the infinite speed of sound is not some specific material property, it is a fundamental property of space and time. You have to ask yourself, "What would an observer in a boosted frame see?" The answer, according to Special Relativity, is that,

if a perfectly rigid rod (E=∞) is pushed at one end, then a boosted observer could actually see the other end of the rod move before the push.

Which I guess is why perfect rigidity, except in the case of Einstein's rigid rod, makes no sense.

 

[turin]

That is why the formula for the speed of sound in a solid medium, v=sq root E/p, is not valid for hypothetical materials with high E/p ratios.

And that is why I claim that discussion of material property is irrelevant.

I make no statements as to what the speed of sound would be in near rigid materials, except to say that its speed could nor exceed the speed of light.

Why do you claim that it cannot exceed the speed of light?

Fine, but that does not answer the question as to what time elapses before the far end starts to move.

I was never trying to answer the question of what time ellapses. However, I do claim that Special Relativity imposes an upper limit on the ellapsed time in terms of the spatial distance.

Are you saying that sound waves in a near rigid material can travel faster than light??

I make no claim about this.

I don't know how you can assign a speed to simultaneity. That's like asking 'what is the speed of time?'.

Yes, that was rather vague on my part. What I wanted to convey is that nothing stops you from dividing a spatial distance between events by the time between the events in a given frame of reference, and then labelling this as a speed. And, furthermore, that is what we're talking about. The two events are the push at the near end of the rod, and the motion at the far end of the rod. This issue deals precisely with the ratio of the spatial distance between these two events divided by the time between these two events. What Special Relativity actually says about this situation is that, if this ratio is greater than c, then the push could not have caused the motion (nor vice versa) - the events are not causally connected. So, the simple conclusion to draw from Special Relativity is that the far end will not move instantly in response to a push at the near end.

It is a common misconception (or oversimplification, at least) that Special Relativity prohibits speeds greater than c. Special Relativity separates speeds into categories: timelike, lightlike, and spacelike. The spacelike speeds are the ones that you might call unphysical or disallowed. (Special Relativity further implies that the category is invariant to Lorentz transformation.)

In fact, the travel of particles faster than light is quite commonplace in Quantum Field Theory (however, their interpretation is a different issue).

Which I guess is why perfect rigidity ... makes no sense.

That is exactly what I'm trying to convey. The reason has nothing to do with the fact that the material is composed of atoms connected by electromagnetic forces. The reason is based on a fundamental property of physics: causality.

 

[Count Iblis]

If you suddenly move one end, you'll create a shockwave that propagates faster than the speed of sound.

I agree with Turin about special relativity being irrelevant. This is also explained in this article:

http://arxiv.org/abs/gr-qc/0107091

 

[turin]

I agree with Turin about special relativity being irrelevant.

I think that's a contradiction (i.e. that you misunderstood).

 

[buffordboy23]

A pole in zero gravity, two light years in length

you push it 1m,

does it move instantly at the other end?

Wow! This thread makes me laugh. This seems like a simple conceptual question from a basic modern physics course, but it has been severely over-analyzed in this thread.

its in my physics textbook but doesn't give an explanation as to why it doesn't move?

i know nothing can move faster the speed of light

Your right. The other end does not move, because it would violate one of the postulates of special relativity; nothing travels faster than light speed. Problem solved.

Perhaps, it may help if the OP in the homework section of PF lists the course from which the problem is assigned.