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B Relativity of simultaneity and the balance of the systems

  1. Feb 14, 2016 #1
    Hi everybody,
    Glad to be with you, in the most popular physics forums on the Internet.
    First of all, I'm not a physicist and the problem I hope to get the answer from you, is part of the work I'm writing in another field.
    To cut it short, I don't quite understand how the relativity of simultaneity works without braking the laws of physics.
    My understanding is that one system must be in balance in all frames of reference, meaning that the chain of cause and the effect cannot be broken in any of the reference frames.
    Do I make sense :smile:

    I'll give an example with the ladder paradox.
    Mentioning the balance word, let us balance the garage on a triangle, and it will go out of balance in the ladder reference frame, which will make it impossible for the ladder to go through.
    ladder_paradox1.png

    If you think, we can create many such cases (not only with balanced on triangle garages), where the cause and effect chain will brake in the frames of reference where the simultaneity is not seen. The funniest of all such cases would be the flight of a bird :biggrin:

    Please help me with this.
     
  2. jcsd
  3. Feb 14, 2016 #2

    andrewkirk

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    Why do you think that will happen? Are you imagining the ladder contacting the floor of the garage as it slides through, and applying a downwards force? If so then the overbalancing is basic physics and doesn't have anything to do with relativity.
     
  4. Feb 14, 2016 #3

    PeterDonis

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    It will also go out of balance in the garage frame, because the ladder's center of mass is not directly over the balance point at all times.
     
  5. Feb 14, 2016 #4

    Dale

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    The cause and effect chain is limited to c. So causes always preceed effects in all reference frames.
     
  6. Feb 15, 2016 #5
    Thank you for your answers, guys.
    The garage will go out of balance in the ladder reference frame, because the doors are not moving simultaneously thus moving the center of gravity left and right.
    Or if we imagine how the flight of a bird will be seen, it will be against laws of physics.
    Or perhaps you could imagine that simultaneous events from one frame are sending signals to another in order to keep it in motion.
    If that events are the simultaneously closing garage doors, the ladder shouldn't move, according to its own pint of reference.
     
  7. Feb 15, 2016 #6

    PeterDonis

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    Just to be clear: you are assuming that the ladder never actually touches the garage floor? So the ladder itself will not throw the garage out of balance in the garage frame?

    Assuming that's the case, then a correct SR analysis would have to take into account that the garage is not moving inertially, so what we have been calling the "garage frame" is not an inertial frame. Neither is the "ladder frame". Non-inertial frames don't work the same as inertial frames, so your reasoning, which assumes that the "ladder frame" is an inertial frame and that the transformation between the "garage frame" and the "ladder frame" is a Lorentz transformation, is not correct.
     
  8. Feb 15, 2016 #7
    Yes, Peter,
    I'm assuming that the ladder does not touch the garage, and will not throw it of of balance.
    It is the doors that will do it, because they don't open simultaneously to keep the center of gravity in one point.
    And with your answer you left me completely confused.
    Are you saying that two moving airplanes are not inertial frames?
    Would you explain, please, why the garage wouldn't be inertial frame if the ladder doesn't touch it?
     
  9. Feb 15, 2016 #8

    A.T.

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    Seems like the ladder is completely irrelevant to your question, and just makes it confusing. Can we boil down your scenario to the relevant bit:

    An object is in a unstable balance under gravity, and extends symmetrically in both directions, simultaneously as measured in it's initial center of mass rest frame.

    The object is not in free fall, so it's not inertial in the relativistic sense. An neither is a frame moving horizontally relative to it. So you have to consider two non inertial-frames, and the mechanical signal propagation delays within the object.
     
  10. Feb 15, 2016 #9
    If I consider the garage and the ladder as two non inertial frames, how would the ladder go through the garage?
    And if the garage-ladder does not make sense in connection to my question, I'll give another example. One can think of countless examples.
    We have a train moving with fast speed on a track. It only moves on the tracks because on the side of the tracks simultaneously opening and closing doors are keeping the rails inline (or producing power for the train, or sending signals to keep the engine running .e.t.c.)
    These simultaneity is not present in the train. Should it move?
     
  11. Feb 15, 2016 #10

    andrewkirk

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    If the scenario has doors that open and close - which I note are not present in the drawing - then there are crucial details missing from the problem specification. When and how do the doors open?
     
  12. Feb 15, 2016 #11
    Hi Andrew,

    The scenario is presented in Wikipedia, and I gave the link to it in the OP.
    Here it is again. You can find there graphics of the way the doors open.
    It's well known problem of a long ladder going through short garage which is solved with relativity of simultaneity.
    And my question is how that relativity of simultaneity works, if the system is going out of balance in one of the reference frames.
     
  13. Feb 15, 2016 #12

    A.T.

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    Yes, but usually the frames are assumed to be free falling and thus inertial. You are introducing gravity or non-inertiality, but also the dynamics of an extended deforming object.
     
  14. Feb 15, 2016 #13

    andrewkirk

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    This problem is similar to the 'Gravity on Einstein's Train' thread from a few months back, for which Peter did lots of interesting calculations. The key point is that both reference frames are non-inertial, so none of the usual SR expectations are valid.

    The frame that matters for the question of whether the garage is balanced is the garage's own frame - as we would expect. If the doors open simultaneously in that frame then it remains balanced and doesn't topple. The garage is analogous to the rocket in the older thread.

    In the frame of the ladder (which is analogous to the train) the doors may or may not open simultaneously. The calculations are complex so we can't easily assume either as we would in SR. However another effect of the gravity/speed combo is that, in the ladder's frame, the garage is tilted (not horizontal). That may offset issues involving the garage doors, as regards balance.
     
  15. Feb 15, 2016 #14
    I am sure the garage does not tilt.

    Why does it not tilt? I guess the doors weigh different amounts during the opening process, in that frame where the doors do not open simultaneously.
     
    Last edited: Feb 15, 2016
  16. Feb 15, 2016 #15
    Guys, as I already mentioned I'm not a physicist and my knowledge in that field is limited.
    The "ladder paradox" in Wikipedia starts with the statement: "The ladder paradox (or barn-pole paradox) is a thought experiment in special relativity."
    If the ladder paradox is explained with special relativity, why do you say that "none of the usual SR expectations are valid".
    My question concerns the simultaneity which gives the solution of the ladder paradox.
    I already gave another example. Here it is again. Does it make any difference to the ladder example?

    Please help me understand it, as I need the right understanding for my work.
     
  17. Feb 15, 2016 #16

    andrewkirk

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    Because in the situation that you are describing, the garage is stationary in a gravitational field. In the ladder paradox scenario, as described in the page you linked, there is no gravitational field. The situation you are envisaging is completely different from the ladder paradox.
    Your other example is insufficiently specified to allow any analysis. We don't know what shape the track is, what the velocity of the train is, what's happening to the sides of the tracks etc etc. Thought experiments need to be very simple in order to be amenable to analysis. That one does not sound simple at all.
     
  18. Feb 15, 2016 #17
    Thank you Andrew.
    Now I understand :smile:
    I didn't know that the gravity defines a frame as non inertial.
    If we put back the garage in an inertial frame and set the simultaneously closing and opening doors to send signals to the ladder/rocket in order to keep it moving, should I also provide all the information about the speed of the ladder, the speed of the doors and so on. Or the information in the initial thought experiment should be sufficient for your answer?
     
  19. Feb 15, 2016 #18

    A.T.

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    If the ladder doesn't always move at constant speed it's non-inertial as well. And different parts of the ladder will be moving at different speeds in some frames.
     
  20. Feb 15, 2016 #19
    How about this version of the thought experiment:

    There are two counter rotating flywheels at opposite ends of a space station. The flywheels are stopped simultaneously in the space station frame, this operation does not tilt the space station in the space station frame. Does the space station tilt in a frame where the stopping of the flywheels was not simultaneous?
     
    Last edited: Feb 15, 2016
  21. Feb 15, 2016 #20

    A.T.

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    I don't think bringing in rotation makes it easier to analyze.

    But it will twist the space station. The propagation of that twist through the structure will be different for different frames. The final orientation will be the same.
     
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