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Thread: Yet Another Relatively Confused Newbie

  1. #1
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    Yet Another Relatively Confused Newbie

    If I had a ruler that reached the moon and it suddenly started moving away from me towards the moon its length would contract. If the moon suddenely started moving at the same time with the ruler then the distance to the moon would contract. If there was a beacon on the moon sending me light pulses then the signals sent after it started moving would have less far to go than the ones beforehand. If the speed of light is constant then the initial signals sent after the moon started to move away would reach me (although redshifted) before some of the signals sent just before it started to move!

    You don't need to tell me I'm confused, but I would like to know why.

  2. #2
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    Re: Yet Another Relatively Confused Newbie

    You've confused me!

    Are you staying where you were, with the ruler and Moon moving away from you, or are you hanging on to your end of the ruler so you move, too?
    Sometimes you win, sometimes you learn

  3. #3
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    Re: Yet Another Relatively Confused Newbie

    Quote Originally Posted by SeanF
    You've confused me!

    Are you staying where you were, with the ruler and Moon moving away from you, or are you hanging on to your end of the ruler so you move, too?
    Me staying on earth watching the moon (and ruler) suddenly depart.

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    Re: Yet Another Relatively Confused Newbie

    Quote Originally Posted by worzel
    Quote Originally Posted by SeanF
    You've confused me!

    Are you staying where you were, with the ruler and Moon moving away from you, or are you hanging on to your end of the ruler so you move, too?
    Me staying on earth watching the moon (and ruler) suddenly depart.
    Okay, then the distance between you and the moon would increase, not contract. You would see the length of the ruler contract (and the moon itself would contract), but the distance from the moon to you would do nothing but increase.
    Sometimes you win, sometimes you learn

  5. #5
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    Re: Yet Another Relatively Confused Newbie

    Quote Originally Posted by SeanF
    Okay, then the distance between you and the moon would increase, not contract. You would see the length of the ruler contract (and the moon itself would contract), but the distance from the moon to you would do nothing but increase.
    But if the moon and the ruler were attached to each other and started to move off together then they are both in the same inertial frame so if the lenght of the ruler contracts in my FoR then surely that means the same thing as the moon getting closer in my FoR too :?

  6. #6
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    Re: Yet Another Relatively Confused Newbie

    Quote Originally Posted by worzel
    Quote Originally Posted by SeanF
    Okay, then the distance between you and the moon would increase, not contract. You would see the length of the ruler contract (and the moon itself would contract), but the distance from the moon to you would do nothing but increase.
    But if the moon and the ruler were attached to each other and started to move off together then they are both in the same inertial frame so if the lenght of the ruler contracts in my FoR then surely that means the same thing as the moon getting closer in my FoR too :?
    No.

    Think of it this way - the ruler is moving away from you, but the "near end" of the ruler moves away faster than the "far end." Thus, the ruler itself gets shorter from your FoR (the distance between the two ends shrinks), but both ends, and the entire ruler, are moving away from you.

    The moon is always located at the far end of the ruler, so it is also moving away from you. The near side of the moon moves away faster than the far side (just like the ruler), so the moon gets smaller along that direction, but the entire thing moves away.
    Sometimes you win, sometimes you learn

  7. #7
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    "Simultaneous" is relative. So if the moon and the end of the tape measure started to move at the same time relative to the moon, an earth observer would disagree--instead, he would think that the end of the tape measure that was touching the earth would start to move before the moon started to move.

    Instantaneous acceleration is a bit confusing in SR (because instantaneous depends on the reference frame).

    You might try reformulating the problem with a moving moon and tape measure from the very beginning. The observer on the moon and the tape measure thinks that a foreshortened earth passes the end of the tape measure 300,000/v seconds after the earth passed the moon; the observer on the earth thinks that the moon is 300,000 * sqrt(1-(v/c)**2) km away when the end of the tape measure passes the earth, and that it took 300,000 * sqrt(1-(v/c)**2)/v seconds to get there, but that since the clocks on the moon are running more slowly, that an observer on the moon would think that only 300,000 * (1-(v/c)**2)/v seconds would have elapsed.

    Note that the earth observer and the moon observer disagree about what the time on the moon clock reads when the end of the tape measure passed the earth. If you want to continue the calculations, though, you can assume that the earth observer sent a light pulse to the moon when the end of the tape measure cleared the earth, and calculate the time both reference frames think the moon clocks show when that light pulse reaches the moon (I'll give away the ending--both reference frames give the same answer).

  8. #8
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    3 problems:

    1. The ruler is not infinitely rigid - it will not all start to move at the same time.

    2. The ruler and the moon don't accelerate infinitely fast - it will take quite a while to accelerate to relativistic speed.

    3. For the second signal to beat the 1st signal to the earth, the moon must have been traveling above C toward the earth in the interim. And length contraction won't ever beat the recession velocity.

  9. #9
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    Thanks guys, I think I sort of have it now. That twin problems of tacitly assuming absolute simultaneosity and instantaneous velocity changes.

    On the way home I was wondering what would happen if I poked the moon with my ruler. Of course it could not all move at the same time or I'd be able to tap out morse code on the lunar surface and transmit messages faster than light!

    Would it be true to say that if both ends of the ruler accelerated uniformly from my FoR then both ends would see each other move apart (I'm guessing this would have something to do with them being at diffent heights in their psuedo gravitional fields) and so the ruler would break. And from my FoV I would see them remain at the same distance apart and interpret the ruler breaking as a result of the lenght contraction?

    Still a bit confused about what it means to set a rigid body in motion. When I think of how complicated classical physics can get despite the initial simple and intuitive laws, I can only yawp in bewilderment at what it must be like to deal with real world problems in GR given that understanding a moving a ruler feels like trying to achieve zen enlightment.

  10. #10
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    Quote Originally Posted by worzel
    Would it be true to say that if both ends of the ruler accelerated uniformly from my FoR then both ends would see each other move apart (I'm guessing this would have something to do with them being at diffent heights in their psuedo gravitional fields) and so the ruler would break. And from my FoV I would see them remain at the same distance apart and interpret the ruler breaking as a result of the lenght contraction?
    =D>

    Absolutely. You should've been involved in the Rockets and Rope discussion three years ago!

    The reason the ruler's FoR would see the two ends move apart is because simultaneity is relative. When you say they "accelerated uniformly" from your FoR, that basically means that they will both reach any given velocity (say, 0.5c) at the same time. This means, from a FoR in relative motion to yours (in the same direction as the ruler is moving), the front end of the ruler will reach that velocity first - hence it is accelerating faster and moving away from the back end.
    Sometimes you win, sometimes you learn

  11. #11
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    Quote Originally Posted by SeanF
    Absolutely. You should've been involved in the Rockets and Rope discussion three years ago!
    yeah I just saw it resurface earlier. Cool, I feel smug all over now, won't last though, thinking about the ruler to the moon has confused me again

    If I pushed on the earth end of the ruler, and assuming the ruler is perfectly rigid, how fast from earth's FoV does the acceleration propagate up the ruler? It can't be instant. I'm guessing c and wondering if this is intimately related to the length contraction and whether or not it puts an upper constraint on the maximum acceleration you can impart on the ruler like this that is somehow related to its proper length. And what happens from earth's FoR if I tug on the moon end and there's a delay before the earth end starts to move :-?

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