Re: Bell's Spaceship paradox


"jacques" <jacques.fric@xxxxxxx> wrote in message
news:0d23ec8d-8294-46f1-9a9f-c432a81ea9ea@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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.

Sure. It is customary in SR to do so.

The string would be stretched (according to SR
length measurement using simultaneity SR rules).
So the conclusion of Wiki looks correct..

Wikipedia is meant to only describe the opinions of the literature. The
literature's conclusion looks correct indeed.

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).

Interesting variant! And some adherents to SR considered motion as absolute.
However, me thinks you overlooked the simultaneity issue. Which reference
system do you use? That changes everything! There is no asymmetry.

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

OK, always simultaneous in the earth frame.

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).

Yes, that's SRT.

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 ?

In SR, the Lorentz contraction is supposed to be physical, all originators
of SR agreed on that. And the very purpose of Bell's Spaceship paradox was
to illustrate the "physical reality" of length contraction. Of course,
different people mean different things with "physical reality". :-)

Cheers,
Harald


.

Relevant Pages

  • Re: Ton of Bricks Paradox/Contradiction?
    ... As far as the rockets are concerned, ... The rockets are a distance D apart. ... If the metersticks are at rest in the moving frame, ...
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  • Re: A message to non-relativists
    ... the distance between the objects is seen to get shorter. ... > distance as determined in the rest frame between the rockets must remain the ... is a moving inertial frame rotated, ...
    (sci.physics.relativity)
  • Re: Bells Spaceship paradox
    ... me thinks you overlooked the simultaneity issue. ... In Minkowski diagram in the lab frame, I draw the 2 ... In the Wiki variant the rockets stopped their engine and inertial ... the distance between the 2 rockets decrease in the same ...
    (sci.physics.research)
  • Re: Bells Spaceship paradox
    ... In Minkowski diagram in the lab frame, I draw the 2 ... In the Wiki variant the rockets stopped their engine and inertial ... the distance between the 2 rockets decrease in the same ... You will enjoy the twin paradox (about proper time), ...
    (sci.physics.research)
  • Re: A message to non-relativists
    ... the distance between the objects is seen to get shorter. ... > you deliberately make the accelerations of the objects to be different ... > by 'stretching' the original proper distance in the moving frame. ... distance as determined in the rest frame between the rockets must remain the ...
    (sci.physics.relativity)