Lorentz contraction

cfrogue

Obviously, I was talking about the instantaneous frame of the rockets. And, these are not my ideas. The description of the rope I as talking about was from this link.

Consider a uniform distribution of particles at rest along some segment of the x axis of an inertial coordinate system x,t at the time t = 0. Each particle is subjected to a constant proper acceleration (hyperbolic motion) such that, with respect to its instantaneously co-moving inertial rest frames, the distances to each of the other particles remain constant
http://www.mathpages.com/home/kmath422/kmath422.htm


Well, the article did not state that CERN changed its mind. Further, I am not in a position to claim that CERN would look at a problem casually.

Finally, there is no literature that I am aware of that says CERN backed away from its decision on the rope.

Here is the x for constant acceleration.
It is in the links I posted.
x(t) = c^2/a ( sqrt( 1 + (a t/c)^2 ) -1 )

Now, by adding 0, ie choosing the back back to initialize at 0 and x0 for the front rocket, you can readily see the x(t) is based only on a and t from the launch frame. Thus, the launch frame will not see a deviation with the distance between the rockets.

cfrogue

I was aware of the fracture for solving this problem.

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.

matheinste

Hello cfrogue,

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.

JesseM

That wasn't too obvious, because earlier you had suggested you wanted to focus on the launch frame when you said: "But, the launch frame in and of itself presents a problem." And "instantaneous frame of the rockets" is still too vague, the instantaneous frame at any given instant is an inertial frame so there will be no gravitational force in this frame, I think what you really mean is an accelerating frame whose definitions of distance and simultaneity at each moment match those of the instantaneous inertial frame at the same moment.
I never suggested the idea of gravity in an accelerating frame was "your idea", but it is your own reasoning that leads you to the conclusion there is some doubt about whether the string breaks, since you have not pointed to any papers that mirrored your argument that the original paper failed to consider the "back side" (and you still haven't explained what you meant by that phrase), or that there is any disagreement among physicists that the string will break in the standard version of the problem.
You're talking as though "CERN" as an institution issued some official position about the rope not breaking, but this is obviously not the case--the article clearly states that Bell just took an "informal and non-systematic" poll of his colleagues at CERN, and that most of them thought it wouldn't break. He adds that many of them changed their mind (i.e. 'backed away from their decision') after further reflection, and I also quoted a paper that said "Though many of Bell's CERN colleagues originally thought the thread would not break, it is now universally agreed that it, indeed, will."

If you think there is any dispute among modern physicists about what would happen in this thought-experiment, you need to post some actual peer-reviewed 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).
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.

matheinste

I think that the in LET the space between solid objects is considered not to contract and the contraction of solid objects is due to stresses or other effects between the interatomic forces. There are of course all the other complications with local time etc. required to make the theory work. In Einsteins' formulation everything contracts.

The reason I asked for confirmation of this is that some commentators on the paradox claim that the break/non-break 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.

cfrogue

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

Histspec

No - the point is that the stress in the string will be continually increasing because its length in the launch frame is remaining constant.

Imagine two rockets separated by d=1 light-second, 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] light-seconds. 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] light-second. Now, because the proper length of the rope is still 1 light-second, the rope will also break in the (new) rocket-frame.

So in both frames the rope will break.

Regards,

cfrogue

Here is a peer reviewed paper just published Oct 18, 2009

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

Histspec

Arxiv preprints are not necessarily "peer reviewed".

cfrogue

Oh.

How do you tell if they are not reviewed?

DaleSpam

If they don't also show up in a peer-reviewed journal.

DrGreg

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/0143-0807 shows it has been accepted for publication and is "provisionally scheduled for October 2009"(!)

cfrogue

I have a question.

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?

matheinste

On page 3 the author seems to be using the fact that Lorentz transforms (coordinate transforms) do not induce stress in an object as proof that Lorentz contraction, in the original Lorentzian use of the term, do not either.-----"-One other point to be considered is whether strains and stresses can be induced by Lorentz contraction, as is contended in Refs. [1,2,4,5]. Our answer to this is clear from the previous discussion. Just as a 3D rotation of an object does not induce strain, a 4D rotation (Lorentz transformation) will not induce strain and consequent stress."--------

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.

JesseM

I don't know what you mean by "theorem 3"--what page are you looking at? In any case, looking over the paper, in equation 3.12 at the bottom of p. 11 they explicitly show that the length of the string does not change in the frame where the ships have identical coordinate accelerations (and started accelerating simultaneously). I'm sure you won't find any physicists who dispute this very obvious and trivial point.
This paper does not dispute Bell's claim that the cable would break! Instead it calls for a rethinking of the reason the cable breaks...the author's argument seems to be that the only physical way of defining an object's length is by looking at its own rest frame, so that treating "length contraction" as a change in length is overly confusing...from p. 3:
The author then points out that the "rest frame length" of the cable or string does grow as the ships accelerate, even though the distance between them in the observer's frame does not change, and that this should be seen as the true reason a cable or string would break, not length contraction:

DrGreg

Yes.

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).

cfrogue

OK, would the rest frame/launch frame conclude the string will break given the distance does not change between the ships from the POV of the rest frame?

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