Re: Bell's Spaceship paradox
- From: JmmWill@xxxxxxxxx
- Date: Sun, 2 Mar 2008 23:24:31 +0000 (UTC)
The links cited don't describe a paradox at all, just an incompletely
stated
question.
If the two ships accelerate but remain at rest in the same inertial
frame,
then the distance between them in that rest frame will not change.
If the frame (= both ships) is accelerated, then the distance between
them in
the frame with respect to which they are being accelerated will
decrease,
by the Lorentz formula. In their rest frame, the distance will not
change.
The "paradox" is because Newtonian absolute space is being assumed
without
thought of its relativistic implications. There is no such thing as
"distance",
unless one stipulates an inertial frame in which it is to be measured.
Adding energy to an object in an inertial frame causes that object to
be contracted in space and time in that frame, making general
relativity
an implication (integration) of special relativity.
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?).
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 = 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..
.
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