Re: Bell's Spaceship paradox

jacques 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.html
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?).

Which is correct depends on what you mean by "correct". That is, what
are you trying to do? Or more directly: what are you MEASURING?

There is no "correct" in the abstract here, there is only a set of
different possible measurements which obtain various different results
for "proper distance" in non-inertial coordinates. Because, as you
mentioned above, there is no definitive simultaneity in such coordinates.

I thought that, in SR, the Lorentz "contraction" between two inertial
systems was not physical and would not involve the string to break.

Yes. Length contraction is purely observational, and the fact that some
other observer moving past your rocket sees it as shorter than you do
does not affect the rocket at all. Just like looking at a building from
different points of view changes how you see it but does not affect the
building itself.

The difference between that and the Bell paradox is that in the latter a
PHYSICAL SITUATION was constructed (well, imagined) that breaks the
string. It is not some other observer measuring the string, it is two
rockets PULLING on it.

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

One can imagine the two rockets stopping (briefly) in successive
inertial frames. Thus one sees that the string breaks as they are
accelerating, and there is no need to stop in any inertial frame for it
to break.

Tom Roberts

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Relevant Pages

  • Re: BELLS PARADOX FOR DUMMIES
    ... problem statement relies on the fact that the rockets STOP ... accelerating simultaneously in the launcher frame (i.e. asynchronously ... relying on classical intuitions. ...
    (sci.physics.relativity)
  • Re: BELLS PARADOX FOR DUMMIES
    ... problem statement relies on the fact that the rockets STOP ... accelerating simultaneously in the launcher frame (i.e. asynchronously ... in the co-moving frame) and this leads to the fact that the lead ...
    (sci.physics.relativity)
  • Re: Bells Spaceship paradox
    ... then the distance between them in that rest frame will not change. ... accelerating rockets starting from rest from an inertial lab frame. ...
    (sci.physics.research)
  • 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, ...
    (sci.physics.relativity)
  • Re: Paradox in need of resolution.
    ... In Minkowski spacetime consider inertial frame A and inertial frame B moving rapidly along a common X/X' axis relative to A; the point X'=0 is at rest in B and moves to increasing values of X in frame A. Their Y and Z axes are parallel (everything happens in the ... At any time t>0 in frame A, both rockets have identical values of Y, and their clocks both display the same time. ... Moreover, each of these rockets is moving differently relative to frame B, in a complicated and changing direction (initally along -X', but increasingly pointed toward Y', and asymptotically parallel to Y'; the different rockets approach the asymptote differently as a function of frame-B time t'). ...
    (sci.physics.relativity)