4 ms·

Very long string vs speed of light

12 points by pchristensen 15y ago

noonespecial 15y ago
I always heard the paradox as a light-year long tube filled with pingpong balls. Stick a ball in at one end, how long does it take the one at the other end to fall out. From the other perspective (space) its often called the "ladder through the garage" paradox. The answer, of course, is that simultaneity is observer relative as well. What if you and I are at each end of this string, and I pull on it (or I have an incredibly powerful machine do it for me). How fast would you feel the pull? I would feel the pull at the instant I saw the string get pulled by your machine with my giant telescope. This ought to help: http://en.wikipedia.org/wiki/Relativity_of_simultaneity http://en.wikipedia.org/wiki/Relativity_of_simultaneity
- rlpb 15y ago
  Your ping pong ball example sounds very much like the car in the garage problem which is explained well here: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Reciprocity/index.html http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Rec... I suppose that's the same as the "ladder through the garage" paradox you mention?
- dspillett 15y ago
  I've heard a variant where the tube is curved such that the other end is also at your location, so no giant telescope is needed to see the end that inserts the new ball (or pulls the string) from the end where you are waiting for the action to have the consequence you are looking for. This adds the complication of you being both observers despite the effect needing to travel a huge distance, so one observer has two relativistic frames of reference.
runaway 15y ago
There is a physical limit to rigidity. You basically cannot have a giant string that doesn't deform. Still limited by the speed of light.
archgoon 15y ago
All physical objects are made up of atoms. To a first approximation, this means everything is connected by springs, which means the assumption of zero elasticity is impossible. 'Inelastic' objects just have very large spring constants, they don't deform much, but they still deform. By the way, long before we talk about speed of light considerations we run into the speed of sound. This is material dependent, true, but that'll again be dictated by the physics of atoms. Or alternatively (if you want to start imagining crazy ass materials made of dark matter), zero elasticity is defined by invariants of length. Length is not something which is preserved by the symmetries of special relativity (Lorentz Transformations), so a rigid object is not a compatible notion with the idea that the laws of physics are invariant under Lorentz Transformations.
- noonespecial 15y ago
  I think maybe you can have a perfectly inelastic object in a "spherical chicken of uniform density" type thought experiment. The catch is that space is deformable(1) so it makes the experiment not especially useful. And that might be the point. (1) Unless you assumed that your material did not deform with the space that contained it, which would make the experiment nonsense.
  - archgoon 15y ago
    No you can't have an inelastic object and at the same time say that "Special Relativity is Correct". They are incompatible definitions. It's like talking about all even primes greater than 2. Or green objects that aren't green.
- geon 15y ago
  Exactly. To clarify: When you tug the string, you create a shockwave of tension traveling along it. Since this is a wave of actual moving matter, it is an acoustic wave, moving at the speed of sound (whatever it is for the string material).
mikegreenberg 15y ago
I'll repeat the question I asked on the site... how do you pull on a frictionless string? (Not that any other part of the question was very plausible.)
- shubber 15y ago
  Tell you what: assume it's a loop, and I'll hook it to something that does have friction. Or, we could just nail it to something. I mean, if we're talking about inelastic megastructures, the logistics of manipulating a frictionless string seems a little silly to worry about.
ggchappell 15y ago
What this really is, is a nice proof by contradiction, that objects with absolutely no elasticity, cannot exist.
tomelders 15y ago
Assuming the most obvious obstacles were solved (rigidity, how you tug on a frictionless string [great point mike] etc), and you had the perfect string for this experiment: Nothing would be moving faster than the speed of light. Every single inch of the string would be moving at the same speed, which would be a lot slower than the speed of light. But every inch would move in unison. I don't see how the "faster than the speed of light" thing has any bearing. That said, it's still a physically impossible experiment.
magicbv 15y ago
What if the sun was to magically disappear. how much time would it take for us here on earth to feel the effects of it. approximately 8 (light) minutes. which is the distance between sun to earth. my point is, nothing can travel the speed of light. not even information.

12 points by pchristensen 15y ago

I always heard the paradox as a light-year long tube filled with pingpong balls. Stick a ball in at one end, how long does it take the one at the other end to fall out. From the other perspective (space) its often called the "ladder through the garage" paradox. The answer, of course, is that simultaneity is observer relative as well. What if you and I are at each end of this string, and I pull on it (or I have an incredibly powerful machine do it for me). How fast would you feel the pull? I would feel the pull at the instant I saw the string get pulled by your machine with my giant telescope. This ought to help: http://en.wikipedia.org/wiki/Relativity_of_simultaneity http://en.wikipedia.org/wiki/Relativity_of_simultaneity

rlpb 15y ago
Your ping pong ball example sounds very much like the car in the garage problem which is explained well here: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Reciprocity/index.html http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Rec... I suppose that's the same as the "ladder through the garage" paradox you mention?
dspillett 15y ago
I've heard a variant where the tube is curved such that the other end is also at your location, so no giant telescope is needed to see the end that inserts the new ball (or pulls the string) from the end where you are waiting for the action to have the consequence you are looking for. This adds the complication of you being both observers despite the effect needing to travel a huge distance, so one observer has two relativistic frames of reference.

runaway 15y ago

There is a physical limit to rigidity. You basically cannot have a giant string that doesn't deform. Still limited by the speed of light.

archgoon 15y ago

All physical objects are made up of atoms. To a first approximation, this means everything is connected by springs, which means the assumption of zero elasticity is impossible. 'Inelastic' objects just have very large spring constants, they don't deform much, but they still deform. By the way, long before we talk about speed of light considerations we run into the speed of sound. This is material dependent, true, but that'll again be dictated by the physics of atoms. Or alternatively (if you want to start imagining crazy ass materials made of dark matter), zero elasticity is defined by invariants of length. Length is not something which is preserved by the symmetries of special relativity (Lorentz Transformations), so a rigid object is not a compatible notion with the idea that the laws of physics are invariant under Lorentz Transformations.

noonespecial 15y ago
I think maybe you can have a perfectly inelastic object in a "spherical chicken of uniform density" type thought experiment. The catch is that space is deformable(1) so it makes the experiment not especially useful. And that might be the point. (1) Unless you assumed that your material did not deform with the space that contained it, which would make the experiment nonsense.
- archgoon 15y ago
  No you can't have an inelastic object and at the same time say that "Special Relativity is Correct". They are incompatible definitions. It's like talking about all even primes greater than 2. Or green objects that aren't green.
geon 15y ago
Exactly. To clarify: When you tug the string, you create a shockwave of tension traveling along it. Since this is a wave of actual moving matter, it is an acoustic wave, moving at the speed of sound (whatever it is for the string material).

mikegreenberg 15y ago

I'll repeat the question I asked on the site... how do you pull on a frictionless string? (Not that any other part of the question was very plausible.)

shubber 15y ago
Tell you what: assume it's a loop, and I'll hook it to something that does have friction. Or, we could just nail it to something. I mean, if we're talking about inelastic megastructures, the logistics of manipulating a frictionless string seems a little silly to worry about.

ggchappell 15y ago

What this really is, is a nice proof by contradiction, that objects with absolutely no elasticity, cannot exist.

tomelders 15y ago

Assuming the most obvious obstacles were solved (rigidity, how you tug on a frictionless string [great point mike] etc), and you had the perfect string for this experiment: Nothing would be moving faster than the speed of light. Every single inch of the string would be moving at the same speed, which would be a lot slower than the speed of light. But every inch would move in unison. I don't see how the "faster than the speed of light" thing has any bearing. That said, it's still a physically impossible experiment.

magicbv 15y ago

What if the sun was to magically disappear. how much time would it take for us here on earth to feel the effects of it. approximately 8 (light) minutes. which is the distance between sun to earth. my point is, nothing can travel the speed of light. not even information.