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Thought experiment about Simultaneity

  1. Dec 1, 2009 #1
    My 9 year old son made an interesting observation, and I couldn't explain it. Maybe you can help. He interlocked several gears on his Lego set, all in a straight line. He then put a handle on the first one and turned it. Simple enough. Then he said to me, "Dad, when I move the first gear, the very last gear moves at the exact same time. How is that possible?"

    So you can imagine a thought experiment along these lines. Let's say you machine 93,000,000 1 mile wide gears precisely so that the teeth mesh exactly. You arrange the gears out in space in a line from earth to the sun, then turn the first one. Again, assuming the gears are precise, wouldn't the very last gear move simultaneously with the first? In a sense, NOW is "universal" in the context of the gears/earth/sun. Or rather, this seems to be an example of action at a distance.

    Thoughts? Thanks in advance!

    - Kane
  2. jcsd
  3. Dec 1, 2009 #2


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    The last gear does not start moving at the same time as the first one. Mechanical disturbacnes propagate through an object at the speed of sound in the material, not instantaneously.
  4. Dec 1, 2009 #3
    What do you mean by "mechanical disturbances"? I'm assuming the gear is perfectly solid.
  5. Dec 1, 2009 #4


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    Yes, if the gear were perfectly solid, then there could be action at a distance.

    In real life, nothing is perfectly solid, and disturbances will move through at some finite speed, as DaleSpam said. When the distance is short, the speed is fast enough that the time it takes to propagate through the gears is so short that it appears instantaneous to your eyes. If you were to build the huge gear system stretching from the sun to the earth, the time difference would be more noticeable. It's similar reasoning as teh case where the light seems to reach your eyes instantaneously when you flip the light switch in a room, but from the sun to the earth it takes 8 minutes.
  6. Dec 1, 2009 #5


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    This page explains in a little more detail why perfectly rigid/solid are impossible in relativity.
  7. Dec 2, 2009 #6


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    To amplify on what atyy said, if there was such a thing as a perfectly rigid body (which there can't be in relativity), you wouldn't be able to change its state of rotation. Changing its state of rotation would cause a Lorentz contraction in the transverse direction, which means that the body would have to distort ... but it can't.
  8. Dec 2, 2009 #7
    Ok, I get it. And thanks for that link...talk about to the point! So on somewhat of a tangent, my thought experiment is evidently different from say the elevator in space thought experiment. In what way though? I can certainly say, "In real life you can't have an elevator in space that accelerates to near c...". So what's the difference?
  9. Dec 6, 2009 #8
    I know I switched gears to Philosophy of Science, but aren't there any takers on this one?
  10. Dec 6, 2009 #9
    Sure you could say that, but you would be wrong. Just because there isn't currently an elevator in space doesn't mean it couldn't happen,

    Certainly we have accelerated objects at 1G, which is equivalent to gravity at earth's surface.
  11. Dec 6, 2009 #10
    Just because there isn't currently a perfectly rigid body doesn't mean it couldn't happen. I.e. you've just moved the ball a little closer to the goal without explaining anything. I DID read in the link above about how perfectly rigid bodies aren't allowed in SR. But aren't there also explanations as to why we can't "really" accelerate elevators to c? Now I admit I don't quite understand the math in the rigid bodies article, but conceptually it seems odd talking in a vague way about "effects" that can't propagate. What's the physical effect that propagates to the end of the rod when all I'm doing is holding the top of it vertically, and drop it?
  12. Dec 6, 2009 #11
    Absolutely, but that's not what you said. You said near c. Every elevator that exists is moving near c in some reference frame.
    None after you drop it. There is a force propagating through the rod while you are holding it, accelerating the rod at 1 G, assuming you are near earth's surface, holding the rod stationary relative to earth's surface.
  13. Dec 6, 2009 #12


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    If you tap the rod at one end, the vibration travels at infinite velocity to the other end. If you assume SR plus causality, then you can't have signals traveling at >c.
  14. Dec 6, 2009 #13


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    This is very similar to the argument "if i had a perfectly rigid rod that was 1 light year across and pushed on it over here, wouldn't someone 1 light year away be able to instantaneously see that I pushed it?"

    The answer is that there isn't a perfectly rigid rod, which was expounded on before. Now, to your other question.

    Think about what a Rod really is, it's a collection of atoms. If you pushed on one side of the rod, how would the atoms on the other side of the rod know? The answer is, you push the atoms on your side, the atoms on your side pushes adjacent atoms, and those adjacent atoms push on more adjacent atoms, and so on and so forth until this propagation gets to the other side of the rod. Thus, there is no instantaneous transfer of information because it takes a finite amount of time for one atom to push on another.

    Rods cannot be perfectly rigid because they are made of atoms. The universe has no such mechanism to create a perfectly rigid rod.

    So, while it may be practically impossible to build an elevator that accelerates in space, it is actually impossible to build a perfectly rigid rod. There is a difference because one may be practically impossible (i.e. the technology isn't there), while the other is PHYSICALLY impossible (i.e. the laws of physics forbid it).

    If you argue using the first one (the elevators) you can make thought experiments that may illuminate some nature of the universe. If you argue with the second one (physically impossible objects) all you end up doing is setting up new laws of physics that do not apply.
  15. Dec 6, 2009 #14
    Cool idea.

    What I found even cooler was how people ripped it apart.
  16. Dec 8, 2009 #15
    You've been listening to too much politics in the news. No one "ripped apart" my thought experiment. All the posters gave thoughtful answers that addressed it, especially Matterwave who gave a perfect answer.
  17. Dec 9, 2009 #16
    No. I'm pretty sure they ripped it apart.
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