Relativistic rolling tank

Discussion in 'Physics & Math' started by Pete, Jul 20, 2006.

  1. Pete It's not rocket surgery Moderator

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    I posted this in CANGAS's excellent [thread=56170]Next to last relativity thread[/thread], but the discussion has drifted beyond the thread's main topic. To avoid further hijacking, I'm making a new thread. It's also an instructive illustration of what Special Relativity does and doesn't say.

    I've drawn up animations of a tank rolling along at 0.866c It gives interesting insights into the problem of the relativistic rotating disk, specifically that the outer rim of the disk (or in this case, the tank tread) must be physically stretched by a factor of gamma (unless the supporting structure is physically compacted). Notice how the portion of the track in contact with the ground is stretched to twice its proper tread spacing.

    Macromedia Flash player required.

    This animation simulates what a distant camera moving parallel to the tank sees:
    <object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="500" height="100" id="RollingTank" align="middle"><param name="allowScriptAccess" value="sameDomain" /><param name="movie" value="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTank.swf" /><param name="quality" value="high" /><param name="bgcolor" value="#ffffff" /><embed src="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTank.swf" quality="high" bgcolor="#ffffff" width="500" height="100" name="RollingTank" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer" /></object>

    This animation simulates what a camera fixed to the ground sees:
    <object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="500" height="100" id="RollingTankGroundFrame" align="middle"><param name="allowScriptAccess" value="sameDomain" /><param name="movie" value="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTankGroundFrame.swf" /><param name="quality" value="high" /><param name="bgcolor" value="#ffffff" /><embed src="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTankGroundFrame.swf" quality="high" bgcolor="#ffffff" width="500" height="100" name="RollingTankGroundFrame" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer" /></object>

    Note that both cameras are filming at the same time, so they are recording exactly the same events. They look different because (according to Special Relativity), the relationship between events depends on the reference frame chosen to describe them (ie on the motion of the observer).

    This weekend, I will add clock readings in both frames to the animation. This will make the time dilation of ground clocks in the tank frame easier to see.

    Feel free to criticise, question, or comment.

    Pete
     
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  3. DaleSpam TANSTAAFL Registered Senior Member

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    Hi Pete,

    Excellent animations. 2inq is correct in one of his points. We can certainly consider the striking the ground of the front tread to be a clock tick. This is a single clock, not multiple simultaneous clocks. This clock is plainly stationary in the tank's frame and moving in the ground's frame. This clock is correctly time dilated in the ground frame, and length contraction is correctly applied in both frames.

    -Dale
     
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  5. Pete It's not rocket surgery Moderator

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    Thanks Dale. I was focusing on comparing clocks in the two frames... and you're right - it doesn't need to be that complicated.
     
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  7. Vern Registered Senior Member

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    Did you need to say that the camera moving along with the tank in its frame does not see the stretching?
     
  8. DaleSpam TANSTAAFL Registered Senior Member

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    Actually, the tread does contract in the tank's rest frame. It just contracts the same amount on the top and bottom. The only tread without length contraction is the bottom tread in the rest frame of the ground.

    -Dale
     
  9. imaplanck. Banned Banned

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    Nice one, you concluded this yourself or was this secondhand?
    It seems obvious when you know: that the bottom of the tracks time will not be contracted as it's velocity is 0 in the ground frame of referrence.
    My brain isn't in first gear at the moment, but should'nt the top animation show the bottom tracks time also contracted as from the parallel observation at the 0.86c frame of referrence isn't the ground(and therefore also the bottom of the track) travelling a 0.86c in the oposite direction and therefor its time would be contracted by a factor of gamma?
     
    Last edited: Jul 20, 2006
  10. Neddy Bate Valued Senior Member

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    That is a good point. If Pete were to make a drawing of the tank at rest on the embankment, I think the tank should be twice as long as it appears in the top animation, and the tread spacing would be exactly as it appears on the bottom tread of the bottom animation.

    (I was wondering where that "stretching" of the bottom animation's bottom tread was coming from...)

    Edit:
    On second thought, the length of the tank would not be twice as long, but the length of the drive-belt would change. This goes back to a point I raised a while back about pi not applying to calculating the circumference of a spinning disk. Apparently there is a similar problem with spinning belts.

    I will make a drawing of the tank at rest...
     
    Last edited: Jul 21, 2006
  11. 2inquisitive The Devil is in the details Registered Senior Member

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    You are correct in what you stated, Dale. Now, would you care to state if the clock moving with the tank is correctly dilated? Notice the clock in the tank frame (the first animation) also ticks once to each of the grounds two ticks. According to Special Theory, the clock in the tank frame should 'see' only one tick on the ground to each of own clock's two ticks. Pete's animations depict the tank clock beating slow in both frames of reference. The time interval between 'ticks' is longer on a slow clock. The 'fast' clock ticks twice to each of the slow clocks one tick. Now does everyone understand what I was speaking of when I said Pete's animations showed a tank moving away from a ground frame? If the animations started with the ground moving away from the tank tracks (the tank's preferred frame of reference), the ground clock would tick once for each of the tank clock's two ticks.
     
  12. imaplanck. Banned Banned

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    So I am saying the same as Dale? sorry I didn't mean to steal his thunder but Dale didn't make it clear there was an error.

    So everyone agrees that the track spacing in the mutual 8.66c frame of referrence is incorrect?
     
    Last edited: Jul 21, 2006
  13. Neddy Bate Valued Senior Member

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    This might seem crazy, but here is what I think the tank looks like when it is at rest with the embankment.

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    If you apply the same reasoning to a disk instead of a belt, you can see that the circumference

    CIRC=2&pi;r

    only holds when the disk is not rotating. It may seem nuts, but as the disk rotates, we would have

    CIRC=2&gamma;&pi;r

    where gamma is calculated based on the angular velocity of the edge of the disk.

    Much later, by edit:
    This drawing turns out to be wrong, although it sparks off some interesting discussion over the next few pages. Then I finally post the corrected drawing, along with my reasoning for changing my mind, in this post:

    http://www.sciforums.com/showthread.php?p=1103430#post1103430
     
    Last edited: Aug 2, 2006
  14. Neddy Bate Valued Senior Member

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    You brought up an excellent point. Since there was no drawing of the tank and the embankment both at rest, I made one which shows that the tread spacing is length-contracted in Pete's top animation. This verifies a point I made earlier (in the other thread) that there is something strange happening to the circumference of the spinning wheels, and also the length of the belt.

    Please refer to my drawing above of the tank at rest.
     
    Last edited: Jul 21, 2006
  15. imaplanck. Banned Banned

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    Yes indeed, I would agree.
     
  16. Pete It's not rocket surgery Moderator

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    That right.

    Do you mean the tank rest frame?
    In the tank's rest frame, the distance between the axles is not contracted, but the track is. So, the track must physically stretch to reach around the uncontracted axles, and the spacing ends up remaining unchanged.

    Neddy's picture of the tank at rest is correct.

    EDIT -
    I've just noticed that Neddy's picture of the tank at rest is not correct. The tank at rest will look like a freeze-frame of the rolling tank in the tank frame.
     
    Last edited: Jul 26, 2006
  17. imaplanck. Banned Banned

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    Yes. I thought it was you that phrased it different to begin with though.
    My mistake, for some reason I was thinking you were using the track notches to represent a tick of a clock(as it were), not length.

    My mistake, I didn't participate in the other thread so I didn't get the point of this.
     
    Last edited: Jul 21, 2006
  18. DaleSpam TANSTAAFL Registered Senior Member

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    Yes, the clock is correctly dilated.


    Huh? The ground is not a clock in either frame. If you want to time when the tread-marks occur in the ground frame then you will need to use multiple synchronized clocks.


    I think you are confusing rods and clocks here. The distance between two marks on the ground would be measured with a rod. The time between the formation of two marks on the ground would be measured with a clock. You are essentially trying to equate a rod in the ground frame with a clock in the ground frame.

    -Dale
     
  19. CANGAS Registered Senior Member

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    If a tiny little reality check may be interjected:

    The seeming failure of MM 1880s was explained by Fitzgerald and Lorentz proposing a REAL length contraction. Although he never directly addressed the MM issue, Einstein's adoption of the REAL length contraction gave his theory the needed credibility in the face of the lingering spectre of the experiment.

    And, Einstein's adoption of Lorentz spacetime therefore gave his signature to the REAL reality of real time dilation in conjunction with real space contraction.

    MM 1880s cannot be explained away without REAL space contraction. And Lorentz spacetime is just a bad joke if it is supposed to be REAL space contraction intimately conjoined with VISUAL ILLUSION time dilation.

    If grave doubt is cast upon the reality of time dilation, then its conjoined sibling space contraction must bear intense suspicion also. And grave doubt has indeed been successfuly cast upon time dilation.
     
  20. imaplanck. Banned Banned

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    Or grave doubt on some peoples understanding?
     
  21. 2inquisitive The Devil is in the details Registered Senior Member

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    How do you measure a rod, Dale? In SI units, the official measurement system, a meter (rod) is measured by the the distance light travels in a specific time (clock) in any inertial frame of reference. Light travels exactly 299,792,458 meters in one second, by definition. How long is a 'rod'?
    Pete and I were discussing clocks in the other thread when he said he would continue the discussion in a new thread. I didn't notice he was back to rods. The time between two marks on the ground would be measured with clocks, and the distance between two marks on the ground would also be measured with a clock. The time it takes light to transverse that distance.
     
  22. DaleSpam TANSTAAFL Registered Senior Member

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    No, the distance between two marks on the ground would be measured with a light signal sent between two synchronized clocks (or with a rod). You cannot possibly use a single clock to measure distance nor can you use two unsynchronized clocks. Unless you explicitly add other clocks you are still looking at only a single clock which is stationary in the tank frame and which is correctly time dilated.

    You keep erroneously claiming that the distance between two tread marks is a clock and that therefore the front-axle-clock runs slow in both frames. This is simply wrong. If you want to use light propagation to equate distances and times (which is perfectly reasonable to do) then you need to put a synchronized clock at each tread mark. These clocks will only be synchronized in the ground frame, not in the tank frame.

    -Dale
     
    Last edited: Jul 23, 2006
  23. 2inquisitive The Devil is in the details Registered Senior Member

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    DaleSpam,
    Dale, are you claiming the cleats that make the marks on the ground are a different distance apart than the marks made on the ground? We aren't talking about 'front axels', only marks on the ground made by the tank tracks. So, is the tank thread shorter than the tank itself in the tanks 'rest frame'?

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