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Lorentz contraction 
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#19
Nov1509, 07:57 AM

P: 687

I gave both sides to the problem, one by doing the integral in the instantaneous frame of the rockets and rope here http://www.mathpages.com/home/kmath422/kmath422.htm And, the other by viewing the problem from the launch frame using the constant acceleration equations of SR here http://math.ucr.edu/home/baez/physic...SR/rocket.html http://arxiv.org/PS_cache/physics/pd.../0411233v1.pdf http://www.ejournal.unam.mx/rmf/no521/RMF52110.pdf Then, I began analyzing the problem but Jesse does not want me to so I am going to stop. 


#20
Nov1509, 08:16 AM

P: 1,060

I can asure you that my remarks were not aimed at you personally. I was commenting generally on the confusion amomg people, many of which I assume, are well versed in relativity. My position is that from what I have read I believe that the correct answer is that the string breaks. However, I am as yet not confident in my ability to explain the reasons to anyone else, which of course is the acid test of understanding. I am also aware that there are variations on the scenario and so we may not all be singing from the same songbook. Matheinste. 


#21
Nov1509, 08:29 AM

Sci Advisor
P: 8,470

If you think there is any dispute among modern physicists about what would happen in this thoughtexperiment, you need to post some actual peerreviewed literature, not a reference to an informal poll taken back when the idea was totally new. I am quite confident that there is no actual dispute about the fact that the stress increases, although as I said there could be types of accelerations where the stress increases but the string doesn't break (maybe because in certain types of accelerations the stress would approach a fixed limit rather than increasing without bound). 


#22
Nov1509, 08:40 AM

P: 1,060

The reason I asked for confirmation of this is that some commentators on the paradox claim that the break/nonbreak outcomes are a result of the two differing approaches. I believe that the differing outcomes are due to faulty reasoning on the part of one side or the other. If the claims of those commentators are correct, then there would be an experimental method to decide between the formulations. If the two formulations are generally accepted, by proponents of both formulations , to be experimentally induistinguishable I would consider such claims for the reasons of the differring outcomesto be invalid. Matheinste. 


#23
Nov1509, 09:42 AM

P: 687

Neither I nor anyone else on this thread has disputed the claim that the distance will remain constant in the launch frame if both ships have the same coordinate acceleration in this frame. Again, the point is that the stress in the string will be continually increasing even though its length in the launch frame is remaining constant. This peer reviewed paper proves the string contracts and that is the reason for the string to break. See theorem 3. http://arxiv.org/PS_cache/arxiv/pdf/...902.2032v2.pdf 


#24
Nov1509, 10:05 AM

P: 89

Imagine two rockets separated by d=1 lightsecond, whereby the rockets are connected by a rope. In the launch frame the rockets accelerate simultaneously up to a velocity of 0,8c and therefore the distance between the rockets will remain the same. However, because of length contraction the rope (not the distance between the rockets) tends to get contracted to [tex]d/\gamma=0,6[/tex] lightseconds. This generates stresses within the rope, so it will break. On the other hand, the observers within the rockets will note that the acceleration of the rockets was not simultaneous, so the calculation shows that after the acceleration the distance between the rockets is increased to [tex]d\cdot\gamma=1,67[/tex] lightsecond. Now, because the proper length of the rope is still 1 lightsecond, the rope will also break in the (new) rocketframe. So in both frames the rope will break. Regards, 


#25
Nov1509, 10:42 AM

P: 687

Bell’s paradox was that his intuition told him the cable would break, yet there was no change in the distance between the ships in system S. He suggested resolving the paradox by stating that a cable between the ships would shorten due to the contraction of a physical object proposed by Fitzgerald and Lorentz, while the distance between the ships would not change. This resolution however contradicts special relativity which allows no such difference in any measurement of these two equal lengths. Conclusion: For two spaceships having equal accelerations, as in Bell’s spaceship example, the distance between the moving ships appears to be constant, but the rest frame distance between them continually increases. http://arxiv.org/PS_cache/arxiv/pdf/...906.1919v2.pdf 


#26
Nov1509, 10:59 AM

P: 89




#27
Nov1509, 11:05 AM

P: 687

How do you tell if they are not reviewed? 


#28
Nov1509, 11:47 AM

Mentor
P: 17,330

If they don't also show up in a peerreviewed journal.



#29
Nov1509, 12:05 PM

Sci Advisor
PF Gold
P: 1,848

In the case of the article in question
http://arxiv.org/abs/0906.1919 shows the article has been submitted to the European Journal of Physics http://www.iop.org/EJ/journal/page=forthart/01430807 shows it has been accepted for publication and is "provisionally scheduled for October 2009"(!) 


#30
Nov1509, 01:23 PM

P: 687

From what I have seen, all calculations agree the launch frame observer believes there is no distance differential between the two ships. Is this correct as far as you know? 


#31
Nov1509, 03:04 PM

P: 1,060

Also the fact that he describes the apparent relativistic contraction of length as illusory is a bit unusual."And, just as the “shortening” of a stick that is rotated in three dimensions is an illusion, we now can see that the “shortening” of a stick that is rotated in four dimensions by a Lorentz transformation is also illusory." I have not read the rest of the article closely yet but the above points disturb me a little. Of course it may just be my reading of the text that is in error. Matheinste. 


#32
Nov1509, 03:08 PM

Sci Advisor
P: 8,470




#33
Nov1509, 03:19 PM

Sci Advisor
PF Gold
P: 1,848

There is no doubt about this. In the launch frame the distance between the ships is constant. You gave a valid explanation at the end of post #18. If the string was attached to the front ship only, trailing behind it, it would initially be touching the back ship, but as soon as the acceleration begins, the length of the string contracts as measured in the launch frame (assuming its "rest length" remains constant i.e. its length in any frame in which it is momentarily at rest). Therefore if you had attached the string to the back ship, if the string was elastic it would stretch and if it couldn't stretch it would break. I think this agrees with what everyone else has been saying in this thread and what the quoted paper says. There is certainly no disagreement amongst experts that the string will break (despite the fact that long ago some experts initially got it wrong when they heard of the problem for the first time; even experts can make mistakes occasionally but now there is consensus as to what the correct answer is). 


#34
Nov1509, 03:40 PM

P: 687

In other words, does the launch frame conclude the distance does not change yet the string contracts? 


#35
Nov1509, 03:49 PM

Sci Advisor
P: 8,470




#36
Nov1509, 03:59 PM

P: 687

From the POV of the rest observer, what is the math to indicate the space remains constant but a rod will contract if allowed between the two ships. All these links show what happens from the POV of the accelerating ships. I want to concentrate on the math from the rest/launch frame's POV. Also, this paper seems to say something different. 4 Conclusion We have seen that the physical length of an object is the rest frame length as measured in the instantaneous rest frame of the object. For two spaceships having equal accelerations, as in Bell’s spaceship example, the distance between the moving ships appears to be constant, but the rest frame distance between them continually increases. This means that a cable between the two ships must eventually break if the acceleration continues. http://arxiv.org/PS_cache/arxiv/pdf/...906.1919v2.pdf 


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