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Why is the Wikipedia article about Bell's spaceship paradox disputed at all?

  1. Jan 30, 2007 #1

    Fredrik

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    Why is the Wikipedia article about Bell's spaceship "paradox" disputed at all?

    Link to the article

    This problem is ridiculously simple. The condition that the spaceships experience the same acceleration implies that their world lines will have the same shape. (The acceleration doesn't have to be constant. It's sufficient that both spaceships accelerate the same way). This implies that the length of the rope will remain constant in the launcher's frame. Think about that for a second. After a while, the rope is moving at a high velocity in the launcher's frame, and must therefore be Lorentz contracted, but it's still the same length! That means that it must have been stretched. If it was already stretched to its maximum length when the acceleration began, it must break. It's as simple as that.

    This is all very basic stuff that belongs in an introductory level class about special relativity. So why is this article disputed at all?

    Is it because of the common (but silly) misunderstanding that you can't solve a problem involving any kind of acceleration entirely in SR? (It's really weird how many people who have studied SR still believe that you need GR for problems like this).

    Or is it because some people who understand that the rope gets stretched are arguing that SR somehow also implies that the rope gets stronger, so it can handle getting stretched?

    I can't think of a third reason.

    I know that some people here have been working on this article. Perhaps one of you can explain this to me.
     
  2. jcsd
  3. Jan 30, 2007 #2
    Perhaps as one poster said, there is no stretching at all - just a matter of siumultaneity.
    To measure length, you need to know two points at the same time.
     
  4. Jan 30, 2007 #3
    Bell's spaceships is didputed because Bell was wrong !

    You're right about the problem being simple but it is rather important to use special relativity and not Lorentz's pre-1905 theory, which postulates actual physical contraction of solid lengths in the direction of motion. It should be remembered that Einstein's SR is a fundamentally different theory even though it leads to the same Lorentz transformations.

    Einstein's theory involves a purely kinematical approach involving no physical "shrinkage" but achieving contracted measurements by means of the relativity of simultaneity. That is to say, the shift in simultaneity causes the front end to be measured first with respect to the rear end a moment later, resulting in a reduced measurement.

    What this means is that a rod initially at rest with respect to an observer does not, in SR, change its length with respect to that same observer, as it is accelerated to some fraction of c. What happens is that the length of the rod defined by another observer moving with it will appear to get longer with respect to the "stationary" observer who sees the rear end marked increasingly before the front end, as the moving observer's simultaneity shifts.

    Einstein's 1905 paper only concludes that a length defined in K' appears shorter in K by the Lorentz factor, and vice versa, where K' and K are in relative uniform motion. It does not say nor suggest that a body would change its physical length during acceleration.

    The idea of a rod "shrinking" as it accelerates is an unfortunate anachronism - a "hang-over" from Lorentz's earlier theory that still lingers on a century later and even finds its way into textbooks now and then.

    If you read Bell's original article you will see that he makes it clear throughout that he is using Lorentz's theory in preference to SR. He was a quantum physicist with no track record in relativity and it's not clear whether he disliked Einstein's SR or whether he didn't realise the significant difference between the two approaches.
     
  5. Jan 30, 2007 #4

    Fredrik

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    Boustrophedon, you're wrong. I don't know how you got the idea that everyone who's making correct claims about SR is actually wrong because they're using some pre-SR theory that we've barely heard about, but I can assure you that's not what I'm doing, and it's not what the people in the other thread are doing either.
     
    Last edited: Jan 30, 2007
  6. Jan 30, 2007 #5

    Fredrik

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    If someone said that, he or she was either talking about Lorentz contraction in general, or hasn't understood SR at all. Lorentz contraction can be said to be "just a matter of simultaneity", but in this case the rope is clearly being forcefully stretched. Otherwise its length wouldn't remain the same when it gets Lorentz contracted.

    That obvious. What's your point?
     
  7. Jan 30, 2007 #6

    Ich

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    The problem has nothing do with whether you choose Einstein or Lorentz. When people here are speaking of actual stretching/compression, they mean actual stretching.
    There is confusion about what exactly "accelerating a rod" means. I can think of 4 substantial different scenarios:
    1. The rod is being pulled. It will first get stretched, stay so during acceleration, and finally come to "rest" at its initial proper length when the acceleration ceases. There are no internal stresses then.
    2. The same with a rod being pushed; just replace "stretched" with "compressed".
    3. The rod is being pushed and pulled in a way that the proper accelerations of both ends are the same. It will experience stretching and compression (depending on the position) during acceleration. It will come to "rest" with a greater proper length, actually stretched.
    4. Every single point of the rod is being accelerated with a carefully chosen proper acceleration such that no internal stresses occur. Its length, as measured in in a suitable comoving frame, will stay constant. It will come to rest with its original proper length an no stresses.[
     
  8. Jan 30, 2007 #7
    OK.
    I see the problem here.
    There is a rigid rod to the co-moving observers.
    But the lab observers see a contracting rod.
    So shall I say that the spring constant has also got be relativistically transformed.
     
  9. Jan 30, 2007 #8

    Fredrik

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    Just adding to the list...

    5. Every point of the rod is instantaneously (or near instantaneously) boosted to a new velocity, all at the same time in the frame where the rod was at rest before the boost. This stretches the rod to a longer proper length.
    6. Every point of the rod is instantaneously (or near instantaneously) boosted to a new velocity, all at the same time in the frame where the rod will be at rest after the boost. This compresses the rod to a shorter proper length.
     
  10. Jan 30, 2007 #9

    Ich

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    If you measure the rod contracted according to Length Contraction, you know that it has not changed at all. No need to consider spring constants.
     
  11. Jan 30, 2007 #10

    Fredrik

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    I think he's trying to argue that the string/rope/rod in the Bell's spaceship scenario won't break even though it's getting stretched. Any such argument would have to say something about the properties of the material.
     
  12. Jan 30, 2007 #11
    Both 5 and 6 are not possible. Forces travel at finite speed (the speed of sound) in rigid materials. This is a pretty slow speed , so you cannot have "instantaneous (or near instantaneous) velocity boost". This is what Born rigidity is all about.
    So, the rear of the rocket , where the engine is, is boosted earlier than the front.
    So, the rear of the leading rocket is boosted earlier than the front of the trailing rocket.
    So, the rod anchored between the rear of the leading rocket and the front of the trailing rocket gets STRETCHED (if the two rockets motors exhibit the same uniform acceleration) .
    If you would like the mathematical tratment that goes with it, you can check wiki on the "Bell's paradox" or I can add a reference to a college course notes on hyperbolic motion/Born rigidity. They show the conditions under which the rod breaks.

    Now, why is the wiki article disputed? I am sure CH can explain this a lot better, the short of it is that it takes one kook (Rod Ball in this case) to slap the "NPOV disputed" on any wiki article. If you click on "discussion", you will find the never ending argument with Rod Ball.
     
    Last edited: Jan 30, 2007
  13. Jan 30, 2007 #12

    Fredrik

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    They're possible. You just have to find a way to push every atom at the same time. :rolleyes:

    I'm not saying it's easy. 5 and 6 are not reasonable ways to accelerate objects, but they have a pedagogical value.
     
  14. Jan 30, 2007 #13
    Physics says that the above is not possible. (unless you decide to attach a miniature rocket motor to each atom)


    If you use absurd premises don't be surprised to get absurd conclusions.
     
  15. Jan 30, 2007 #14

    Fredrik

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    So it is possible. What's interesting is what's possible in principle, not what's easy.

    5 and 6 are interesting mainly because thinking about those only for a few seconds is by far the easiest way to understand the claim that there are no rigid bodies in SR.
     
  16. Jan 30, 2007 #15
    Sounds like an attempt to justify why you got the solution wrong at post #1
     
  17. Jan 30, 2007 #16

    Fredrik

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    Are you one of those guys who just tries to deliberately misunderstand everything?
     
  18. Jan 30, 2007 #17
    No, not at all. I tried to help you see your own mistakes. Look at your initial post and at your persistence that all atoms in a rigid object can be accelerated in sync.
     
  19. Jan 30, 2007 #18

    pervect

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    You are assuming that the reason articles get tags is based on logic and an actual substantial objection. It's actually more of a political process.

    It's disputed mainly because of Rod Ball, although the detailed history of how it got that tag is a little more complicated. If you're really curious, and have enough time, you can see the history of the evolution of the article, and the talk pages for the article.

    I believe that I actually tagged the article with an NPOV tag when it was in a significantly different form - the history page shows my September 2006 edit below as adding the tag.

    http://en.wikipedia.org/w/index.php?title=Bell's_spaceship_paradox&oldid=76280528

    I don't feel that there are any NPOV problems with the current article either, but as a very involved party in writing the current version of the article, I don't feel it's appropriate for me to remove the NPOV tag. In fact, I'm not quite sure what the wikipedia process for reomving a tag is (if there is one).

    From my POV, the biggest open question with some (small) amount of merit was the debate over whether or not a man named Petkov and his opinions should be mentioned. AFAIK Rod Ball is the only one who feels this particular author's contributions are notable.

    I'm happy to have what I think is a reasonably good article with a NPOV tag stuck on it, as opposed to having a very bad article with a NPOV tag stuck on it, so I haven't really investigated closely what it would take to get the tag removed.
     
  20. Jan 30, 2007 #19

    disregardthat

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    How about gravity, are the atoms not accelerated equally (or nearly equally because of longer distances from back to front of the object to the pulling object) The atoms are equally gaining acceleration, but the atoms are organizing themselves so the object will be compressed, but if the atoms did not interact with eachother, the object would be stretched in a frame equal to the original frame before the objects starts moving. This is making these points real:
    The only difference is that it is looked upon at a different frame of movement.



    Anyway, I don't see the reason why the rope is not being snapped.

    If one spaceship is being pulled from behind by it's rocked engine, it is contracted, and observed as compressed in a rest frame. But this is only if it is accelerated from one point, or plane of the object. If it was pulled from the front, it would also get a compressed form.
    If each atom now were accelerated equally with respect to the REST frame the object would indeed be the SAME size in the rest frame, but larger in the moving frame. (Each atom has a greater distance to eachother in the moving frame) This makes it true that if an object were pulled by two or more points of the object, the object would appear larger.

    Now, if we see the two spaceships as ONE object, it would be true that the object "stretches". Because both ships are simoultaneously accelerated in the rest frame. As the acceleration continue, the distance in the rest frame will appear un-changed (although each spaceship will look contracted). In the moving frame however, the distance will be enlargened.
    The rope that is tied together between these ships (assuming that the ships are accelerating the same direction, but the one slightly ahead of the other, with respect to the direction of acceleration) will be accelerated equally in both front and back in the rest frame. As the distance between the ships remain unchanged in the rest frame, the distances will, as said, increase in the moving frame. The same applies for the rope. It is accelerated at the same time equally in the rest frame, which means it will be larger in the moving frame. (If you apply te atoms interaction with eachother, they will make the object stretch, but as acceleration continue, the object will inevitably snap, since the atoms cannot hold the stretching. This will happen at the place where the atoms hold on eachother least. (a weak spot in the rope for example)

    This explanation is only true if the spaceships are NOT accelerating in a directioin showed here:

    "S"=spaceship
    "-"=rope
    ^=direction of acceleration
    "_"=empty space(no effect on the situation, only added because of to make the direction sign be in the correct position)

    ____^____
    S---------S

    It must be something like this, (actually, anything except the situation above)

    "S"=spaceship
    "."=rope
    "-"=rope
    "^"=direction of acceleration
    "_"=empty space(no effect on the situation, only added because of to make the direction sign be in the correct position)

    ______^________
    S---...
    ______ ---...
    ____________---S


    I just want to say, that I have given a lot of thought into this, and find it correct. If you believe I am wrong, please elaborate why. But please make sure which frame I am basing my statements on, before you argument over it...
    I am relatively new to the concept of general relativity :tongue:
     
    Last edited: Jan 30, 2007
  21. Jan 30, 2007 #20
    Your post is not understandable, are you asking for the GR treatment of the problem instead of the treatment under SR with accelerated motion? Of course we can treat it using GR but the gravitational field difference between the two ends of the rockets is so small that we can neglect it wrt the much higher effect due to the thrust acceleration. Would you care to repost such that your question is more understandable?
     
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