Re: Bell's Spaceship paradox

On 15 fev, 21:47, jacques <jacques.f...@xxxxxxx> wrote:
This famous paradox is about the distance between two identicaly
accelerating rockets starting from rest from an inertial lab frame. It
is described i.e in:

http://math.ucr.edu/home/baez/physics/Relativity/SR/spaceship_puzzle....
http://en.wikipedia.org/wiki/Bell's_spaceship_paradox

It illustrates the problem of defining a "physical"distance (something
we would call"proper distance") in non inertial frames due to the
breakdown of simultaneity.

There is not only one definition and they do not give always the same
result:(which one is correct?).

In the Wiki article, one tries to avoid the difficulty in considering
that the two rockets will stop their engine after the same ellapsed
proper time continuing flight in inertial frames. So one can perform
easily the distance "d" between rocket 1 and 2 in lab frame and this
distance "D" in rocket 1 frame using plain Lorentz transform group.
The result is that (D ppp d* gamma) which looks fine, but the conclusion
looks quite odd to me, as it is said that a string linking the 2
rockets should break according to this formula.
I thought that, in SR, the Lorentz "contraction" between two inertial
systems was not physical and would not involve the string to break.
Can someone help me to understand whether and in case where I am
wrong?

Notice also that this solution does not describe the situation when
the 2 rockets are accelerating, but the result of such situation when
freezed..

Forget my first post, Meanwhile, I found my error . "D" is the
"proper" distance measured between rocket in their boosted rest
frame (at the end of acceleration), and "d" was the "proper"distance
between rockets measured before to start motion in the lab frame (rest
frame at that time). So the relation is between two measures in their
respective rest frames. The string would be stretched (according to SR
length measurement using simultaneity SR rules).
So the conclusion of Wiki looks correct..

But I guess that if from this status, the two rocket now deccelerate
at the same rate for the same time this stretch would be cancelled
which shows some antisymetry in the process depending on relative
directions of motion and acceleration, which looks quite odd in SR
(motion is usually considered as not absolute).
If we close the loop ( by proceeding the reverse operation) to get
back in the lab frame at rest, the distance between rockets would be
the original distance but obviously the proper time of the rocket
observers would be different from the proper time of static observers
remained in the lab frame (twin paradox). I find this disymmetry
between distance and time intriguing and I wonder how physical is a
distance (therefore this stretch) in Relativity. The only physical
thing in relativity including SR looks to be "length" of worldline of
observers, the "s^2" as measured by clocks carried by the observers.
So I still wonder how physical is this stretch ?

.

Relevant Pages

  • Re: Bells Spaceship paradox
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    (sci.physics.research)
  • Re: Bells Spaceship paradox
    ... accelerating rockets starting from rest from an inertial lab frame. ... easily the distance "d" between rocket 1 and 2 in lab frame and this ...
    (sci.physics.research)
  • Bells Spaceship paradox
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  • Re: A message to non-relativists
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