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A pole, 2 lightyears in length - conceptual question

  1. Jul 16, 2009 #1
    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 dosen't give an explanation as to why it dosen't move?

    i know nothing can move faster the speed of light
     
  2. jcsd
  3. Jul 16, 2009 #2

    sylas

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    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.
     
  4. Jul 16, 2009 #3
    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?
     
  5. Jul 16, 2009 #4
    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.
     
  6. Jul 16, 2009 #5

    Mentallic

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    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.
     
  7. Jul 16, 2009 #6
    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
     
  8. Jul 16, 2009 #7
  9. Jul 16, 2009 #8

    PhanthomJay

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    Back to your original question:
    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 :wink:).
     
  10. Jul 16, 2009 #9

    turin

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    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.
     
  11. Jul 16, 2009 #10

    negitron

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    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.
     
  12. Jul 16, 2009 #11

    sylas

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    I'll defer to #8 as my favourite, for a simple explanation at an appropriate level.
     
  13. Jul 16, 2009 #12

    negitron

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    Agreed. However, I wanted to acknowledge your contribution, as well.
     
  14. Jul 16, 2009 #13

    Mentallic

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    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;??
     
  15. Jul 16, 2009 #14

    negitron

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    Change the composition, specifically, the property sometimes called stiffness which is quantified by Young's modulus.
     
  16. Jul 16, 2009 #15

    Mentallic

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    and what would be the limit of the transmission speed if this stiffness were increased indefinitely? (Nearing perfect rigidity)
     
  17. Jul 16, 2009 #16

    negitron

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    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.
     
  18. Jul 16, 2009 #17

    PhanthomJay

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    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?:eek: 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.
     
  19. Jul 16, 2009 #18

    PhanthomJay

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    Agree. Try one of Einstein's rigid measuring rods.
     
  20. Jul 16, 2009 #19

    negitron

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    Look, I'm not touching Einstein's rigid rod.
     
  21. Jul 16, 2009 #20

    PhanthomJay

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    And I'm not touching that response. :rofl:
     
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