Physics experts: Cosmic speed limit the cause of momentum?

[alt_f13]

1) If you had a lightyear-long pole made of some sort of exotic, super-strong material that would not bend under any circumstances, would it be impossible to move due to the fact that the far end would have to react faster than the amount of time it would take for the information from you to reach it?

 

2)Would a voluminous material strong enough to hold its shape perfectly be impossible, or would it be impossible to move?

 

3)Would something strong enough to hold its shape perfectly have to be infinate in density?

 

4.1)Singularities can move. Is this because they are infinately small in volume?

4.2)Something with volume and infinate density would be infinate in mass, and impossible to move, correct?

 

5) Is the mechanism that causes matter that is moving at near to light-speed hard to accellerate further the same mechanism that causes more momentum in dense masses compared to less dense masses?

 

6) Is 5) due/related to the fact that denser objects hold their shape better than objects of less density?

 

 

If 5) and 6) are true, could someone show me the formulae that compare them?

[Ragib]

1) No. If would resemble a compression wave. The material would compress from the direct force applied, and it will expand again.

2) Holding its shape exactly perfectly in everyway is impossible, it difies Heisenbergs Uncertainty Principle. The electrons would have to be at a temperature where they don't move. That doesn't Exist.

3) As Said above, impossible.

4.1) Well, really, who said they can't move..

4.2) Something like that is impossible, but yes.

 

5) Mechanism that accelerates matter moving near the speed of light..do you mean force?.. And, More momentum in dense masses than less dense masses? Well if they are the same mass and same force is applied, Momentum should be the same. I guess if you mean air resistance, a less dense medium would be resisted more, made slower, less velocity means lower momentum.

 

6) No.

And no, they aren't true.

[swansont]

Infinite rigidity is incompatible with special relativity. The forces between atoms and molecules are electromagnetic, and propagate at the speed of light.

 

As for #6, you haven't demonstrated that more dense objects hold their shape better. Mercury is denser than many metals, yet it is a liquid at room temperature, i.e. it doesn't hold its shape at all. Lead, a very soft and malleable material is much more dense than most, too, including titanium. The premise is false.

[alt_f13]

1) No. If would resemble a compression wave. The material would compress from the direct force applied' date=' and it will expand again.

2) Holding its shape exactly perfectly in everyway is impossible, it difies Heisenbergs Uncertainty Principle. The electrons would have to be at a temperature where they don't move. That doesn't Exist.

3) As Said above, impossible.

4.1) Well, really, who said they can't move..

4.2) Something like that is impossible, but yes.

 

5) Mechanism that accelerates matter moving near the speed of light..do you mean force?.. And, More momentum in dense masses than less dense masses? Well if they are the same mass and same force is applied, Momentum should be the same. I guess if you mean air resistance, a less dense medium would be resisted more, made slower, less velocity means lower momentum.

 

6) No.

And no, they aren't true.[/quote']

 

I think you misread the last 2 questions, or I misworded them. The first 5 questions were really only explaining my thought process, and you answered 1 and 2 the way I expected anyone to.

 

I'll post again in statements.

 

1)

Assuming a completely and utterly unmalleable magic object could exist, moving such an object would be impossible due to the fact that it would require that the molecules on the other side of the object move at the same instant that molecules on the near side do.

 

and

 

One end of a super-dense, super-long pole would be hard to move in a direction perpendicular to the direction of the length of the pole, partly because you would be required to bend it. It bends because the effects of the force would have to move along the pole at a speed at or under the speed of light, even if it were close to unmalleable.

 

2) I don't mean frozen in time, but completely unmalleable. I'm asking if it would be impossible to move an object that could not experience a compression wave, assuming such an object could exist. I think it would be impossible to move such an object, because the force applied would have to affect the entire object at once. The object would have to be super-dense, impossibly dense, I imagine.

 

A super-dense object that could possibly exist would be hard to move, as you have to initiate a compression wave in a material that really resists it. In this case you have to influence alot of matter in one go, compared to something that was not so dense. This is really hard to visualise, I know, because it sounds obvious... (duh, the object has mass, so it's hard to push)

 

What I am saying is that the denser an object is the more of it is acted upon at the same time when a force is applied... therefor, the closer an object gets to infinately dense, the closer the force being distributed through it gets to the speed of light.

 

Sound moves faster in denser materials, right? What I'm asking is if the reason that sound moves faster in dense materials is the same reason that dense materials have more inertia, because more matter moves/time?

 

Damnit, I'm sure this is circular logic somehow... Still like to know where though...

 

Infinite rigidity is incompatible with special relativity. The forces between atoms and molecules are electromagnetic, and propagate at the speed of light.

 

Awesome, that was my point! Sorry, I'm finding it really hard to explain what I mean, so I'm forced to use examples, and hope someone can extrapolate what I mean. Erg...

 

As for #6' date=' you haven't demonstrated that more dense objects hold their shape better. Mercury is denser than many metals, yet it is a liquid at room temperature, i.e. it doesn't hold its shape at all. Lead, a very soft and malleable material is much more dense than most, too, including titanium. The premise is false.[/quote']

 

"Hold their shape" was the wrong term. I think I made my point better above.

[swansont]

You can't make an assumption that is physically impossible, and then ask what physics predicts. Once you violate physical law, you can't use physics to give you a valid answer. (i.e. any conclusion drawn from a false premise is invalid)

[alt_f13]

Highschool physics does it all the time with 100 percent efficiency scenarios.

 

Anyway, I don't believe the following violates any laws, and is my main point anyway. I just want to know if I got it right or not. And if not, where I went wrong.

 

A super-dense object that could possibly exist would be hard to move, as you have to initiate a compression wave in a material that really resists it. In this case you have to influence alot of matter in one go, compared to something that was not so dense. This is really hard to visualise, I know, because it sounds obvious... (duh, the object has mass, so it's hard to push)

 

What I am saying is that the denser an object is the more of it is acted upon at the same time when a force is applied... therefor, the closer an object gets to infinately dense, the closer the force being distributed through it gets to the speed of light.

 

Sound moves faster in denser materials, right? What I'm asking is if the reason that sound moves faster in dense materials is the same reason that dense materials have more inertia, because more matter moves/time?

[swansont]

Can't comment without an example of 100% efficiency, but I suspect it is used when that's a limiting, or ideal case, like the limit of zero friction.

 

Infinite rigidity is a limiting case in classical physics, but the solutions are only valid for a range of problems, i.e. if you have a collision, you assume the collision itself takes zero time, so your answers won't be valid for extremely small values of t after the collision (characteristic time would probably be d/c, where d is the size of the object colliding); solutions are valid only if t is large compared to that.

 

But your scenario requires relativity, and is also in the range where the solution would not be valid, i.e. you want to know what happens in a time short compared to d/c.

[Klaynos]

*sigh* read swansont's post again about the propergation velocity of the interactions between atoms.

 

Highschool physics does it all the time, and gets things wrong all the time.

 

The reason the sound moves faster in denser objects is because the interactions are over smaller distances...

 

There are limits to the denseness of matter. Wander - Vaals forces and the pauli exclusion principle....

 

But please reread Swansonts post...

[JustStuit]

Highschool physics does it all the time with 100 percent efficiency scenarios.

Yes it is done but the answer is not exactly correct. It is done so that problems can be worked out and the answer still be very close without involving advanced techniques. Without doing this, phsyics 1 would be virtually all conceptual.

[alt_f13]

*sigh* read swansont's post again about the propergation velocity of the interactions between atoms.

 

Highschool physics does it all the time' date=' and gets things wrong all the time.

 

The reason the sound moves faster in denser objects is because the interactions are over smaller distances...

 

There are limits to the denseness of matter. Wander - Vaals forces and the pauli exclusion principle....

 

But please reread Swansonts post...[/quote']

 

I don't think "wrong" is the correct word to use in this case. Highschool physics arrives at approximations of what accurate physics would arrive at. Swansont explained what I meant by that comment perfectly with "I suspect it is used when that's a limiting, or ideal case, like the limit of zero friction.

"

 

There are many instances where highschool physics are completely wrong, like you say, but these are usually for the benefit of the students who need to wrap their minds around ambiguous concepts. But why don't we leave that subject.

 

So far I've been using completely nonsensical scenarios, and comparing only loosely related concepts (ie propogation of sound waves and propogation of EM force between atoms :S) so I'll try explaining my example again. I have a feeling swansont already answered it sufficiently, and I'm just not clear on it.

 

I understand that a reaction along an object can only propogate at the speed of light, that's what my whole post is about.

 

 

You have a very strong, long metal pole in space. The pole is 100% possible, made of non-exotic matter, and of a density compatible with physical law.

 

One end is situated directly in front of you, and the other end is a lightyear off to your right.

 

Stick Fig. 1

______________________________________ _ _ _ _ _ _ _ _ _ _ _ _

O

/|\

/ \

 

You push foreward on the pole.

 

Stick Fig. 2

 

^

^

|

________________________________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

\O/

|_|

/ \

 

 

Q1)Now, in this scenario, the entirety of the pole would not move in apparent unison* because the reaction would not propogate quickly enough to the other end for it to rotate along the axis vertical to you. It would bend, however, at a rate dictated by the speed at which the reaction can propogate, c. Correct?

 

*I say "apparent unison", because I'm highlighting the fact that a pencil moves in apparent unison, but doesn't actually move in complete unison, due to the limiting factor of the propogation of the reaction its atoms can have with eachother. A case similar to the pole, but without the distances involved

 

Q2)In this situation, it would be impossible to rotate the pole along the axis of the poles length*, but it would twist at the rate as described above, correct?

 

*In a manner perceptable at the time at least.

 

Q3)Would twisting or pushing this pole be harder than twisting or pushing a pole with the exact same mass, higher density and a length of 20m, because of the limiting factor of the speed of the propogation of the force?

 

Q4) Is it possible to come up with a formula that would compare "F" (the amount of force it would take push or rotate the object) to "d" (how far you rotate or bend it), taking into account "c" (the speed of the propogation of the forces acting along the objects length)?

 

I am suggesting that inertia is a function of the propogation of the force acting on the object, and is in that way related to mass and density.

 

 

I think I worded my questions perfectly here and will understand your answer based on the scenarios given :z

[JustStuit]

 

 

Q3)Would twisting or pushing this pole be harder than twisting or pushing a pole with the exact same mass' date=' higher density and a length of 20m, because of the limiting factor of the speed of the propogation of the force?

 

[/quote']

It would not be harder to twist because the formula for rotational inertia of a cylinder is [math] I = \frac{1}{2}MR^2 [/math]. The radius is the distance from the outer point of circle to the axis of rotation which stays the same in both cases and so does the mass. The problem would be creating a pole with a density low enough to be that long and still rigid and stable. It would be impossible.

[swansont]

You keep using density, but as I had previously pointed out, this does not correlate well with mechanical properties you are discussing. Some of the stronger/stiffer materials are low density (and very useful as a result), e.g. titanium alloys.

 

The connection to density simply isn't there.

[alt_f13]

The problem would be creating a pole with a density low enough to be that long and still rigid and stable. It would be impossible.

Why? What about a pole that is 75 000 000 000 m long? You think that is impossible? A spacship spitting the pole out while making it as it moves in a strait line with negligable gravitational forces acting apon it should be able to do it.

 

In this case it would still take 3 or so minutes for the other end of the pole to start rotating.

 

 

It would not be harder to twist because the formula for rotational inertia of a cylinder is [math] I = \frac{1}{2}MR^2 [/math']

 

How do you take into account the fact that much of the mass has no bearing on the immediate part of the pole, until the far end of the pole feeds back that it is rotating? I want to know if there is a way to factor that amount of time into it.

 

Or to reverse the question, is it possible to measure the mass of a pole that is longer than a light minute, by measuring how hard it is to rotate?

 

(not that it matters how long it is, but a light minute would produce a perceptible difference, whereas in a metre long pole, the time it takes for the force to be felt throughout the pole would be negligable)

[JustStuit]

Why? What about a pole that is 75 000 000 000 m long? You think that is impossible? A spacship spitting the pole out while making it as it moves in a strait line with negligable gravitational forces acting apon it should be able to do it.

No, making a pole that long that weighs the same amount as the 20m pole.

[alt_f13]

No, making a pole that long that weighs the same amount as the 20m pole.

Heh, you always answer the least pertinent question. Any idea about the others?

[JustStuit]

I answer the ones I know . I know that is the equation for rotational inertia but it may be like newton's gravity and not work in some cases. I don't know if this is one of them. I think that is a pertinent question because being able to create such a senario would be an important part as the rest is null if it initially defies current law of physics.

[alt_f13]

You keep using density' date=' but as I had previously pointed out, this does not correlate well with mechanical properties you are discussing. Some of the stronger/stiffer materials are low density (and very useful as a result), e.g. titanium alloys.

 

The connection to density simply isn't there.[/quote']

 

The only reason I mentioned density in the latest example was because a shorter pole would have to be denser in order to remain the same mass.

[edit]Density has no bearing on the questions. I'm just trying to avoid confusion :S Seems that I was unsuccessful.

 

If you would please reread the post with the stickmen, and ignore any coment made about density alltogether, I would be grateful.

 

I'm really only concerned about the length of time it takes for the entire object to "realise" a force is acting on it, and how that affects its apparent inertial mass, especially on very large distance scales.

 

It seems obvious to me that very long distances would affect measurement of inertial mass, and I am trying to understand the math behind it...

 

Of course I could be wrong, but I don't see how, when the mass of the object is unmeasurable for a certain amount of measurable time, for sure.

 

Time is an issue, merely because of the time it takes for the propagation of force along the poles length. I want to come up with a formula for the time, or a formula for measuring mass, that takes the time into account.

 

If this is not possible, how?

 

I answer the ones I know . I know that is the equation for rotational inertia but it may be like newton's gravity and not work in some cases. I don't know if this is one of them. I think that is a pertinent question because being able to create such a senario would be an important part as the rest is null if it initially defies current law of physics.

 

Touché. Unfortunately it was a detail I could have changed to make the scenario possible.

[swansont]

So is this representative of the scenario?

 

A small object of mass m and speed v strikes a large rigid object of mass M. The assumed elastic collision itself takes a time t, but the large object has a diameter that exceeds ct, so that the force exerted during the collision, the small mass can't possibly "sample" the entire mass M of the large object. So the usual conservation of momentum results can't possibly give the right answer.

[alt_f13]

Yes! Nice paraphrase, too. The other scenario would be a continuous force attempting to rotate the mass M object around the axis that follows its >ct length. The idea is the same, so let's not continue with the rotation scenario; its purpose was to better explain what I was trying to get accross to anyone who didn't understand the first scenario.

 

The way I see it, the conditions of this scenario aren't that different from the average collision, because in neither situation does the event take place in zero time, so there has to be a fairly simple formula that gives either t, based on v, M and m, or gives M based on t, m and v. [edit] I guess t would be the same, but would the inertial mass M then be infinate? That's the part I don't understand.

 

Will the large object ever move, assuming the energy isn't lost as heat before it is realised by the entire object, or if a constant force is applied to the large object?

 

Can we calculate the mass of the large object knowing the force that was applied to it in an elastic collision?[/edit]

[swansont]

It's an interesting problem. The body would recoil, but not according to the standard formula — it would not depend on M; you'd have to model some sort of "reduced mass" of the large object. Essentially you have to consider it's not one object, but a series of connected smaller objects. IOW, rewrite the terms so that the original assumptions would hold.

 

The rotation case might be easier to model, because you have a much better defined torsion propagation, and in only one direction.

[alt_f13]

This is tough.

 

To me it seems like object_m could only get information about object_M up to a distance of ct/2 into it. If this were true, mass M cannot be calculated for an object that has a length of >ct/2, because the energy will have already passed further down the line.

 

I have a gut feeling this isn't the whole picture though, so let's use two new objects for another situation.

If we have object_L strike object_l, object_l having a length of ct/2, and object_l with a negligable length for the time being, a compression wave is formulated for the entirety of t, and since object_l is so small, it has all of t to transmit its energy. Object_L, however, has exactly one pass of a wave from the beginning of the collision to the end to transmit its energy.

 

The problem is this. If you launch a spring at a wall, you'll observe a wave that continues to move from one end of the spring to the other, even after collision takes place. If this type of thing is happenning during a collision between object_l and object_L, wouldn't it take many passes of a wave moving at c to transmit the energy from object_l to object_L and vice versa? The wave, for example, may only be transmitting p/2 for each pass. So even if object_L is below ct, even ct/2, and even ct/300,000,000 (!) there are probably waves (or even just one part of the original compression wave, as I could be wrong about there being more than one wave in a collision scenario) of small magnitudes not reaching object_l.

 

It looks like the amount of energy being transmitted is a function of the length of the smaller object, object_l, versus t of the collision, and all the momentum not transmitted in both objects remains within the objects, possibly reducing the end velocities of the objects, as the momentum is not fully transmitted. That remaining energy would be negligable in almost all measurable collisions.

 

Does this make sense? It sounds like a collision that is less than 100% elastic, where the resulting velocities aren't quite representative of an obvious p=mv scenario.

[organ]

It's useful for me!

[alt_f13]

organ: how?

 

swansont: How does special relativity deal with this problem?

[CanadaAotS]

You can't make an assumption that is physically impossible, and then ask what physics predicts. Once you violate physical law, you can't use physics to give you a valid answer. (i.e. any conclusion drawn from a false premise is invalid)

 

What about the "If you could travel at the speed of light, it would seem like time stopped" or many other examples like this. Like the guy said, people (at least try) to make physical assumptions on impossible scenarios all the time

[swansont]

swansont: How does special relativity deal with this problem?

 

I don't recall seeing an analysis where it mattered. c is a pretty big number, so d/c is a very short time for reasonably-sized objects. Perhaps it comes up in nuclear/particle physics, where there are some very short interaction times, but that's outside of my area.