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From: harald on 18 May 2010 17:07
On May 18, 7:13 am, nobody1357 <nobody1...(a)operamail.com> wrote:
> Hi, please consider this setup
>
>       A        B
> ______________
>
> ______ is the lab frame, A and B are identical cars
> carrying same amount of fuel.
>
> They start their engines at the same time and accelerate in
> the same direction until they run out the fuel.
>
> Now, according to the lab frame, the distance between A and B has not
> changed, it's same as when they started, since there is no
> reason for identical cars would have moved differently.
>
> Now, If A and B were connected, they would have lorentz contracted as
> a system, but since they are not connected, according to them, the
> distance must have increased (as opposed to the contracted
> state which their distance would seem the same to them).
>
> So far so good...

Yes:
http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox

> However, suppose A sends a light pulse to B, which
> gets reflected back to A, and A measures the duration of this. Since
> their clocks are slowed down, A must now find that this duration has
> decreased, compared to the beginning of the experiment, and
> therefore concludes their distance have decreased.

No. Probably you mixed up reference frames. In the lab frame they are
measured to be moving, with slowed down clocks - that includes light
clocks! The typical "according to them", is just such a measurement
with light!

Remember Michelson-Morley*: by means of light, they would only measure
in the moving frame that the distance remained the *same*, if in the
stationary frame the distance along the line of motion was measured to
be *contracted*. As that did not happen, they will measure that the
distance has increased.

* If you don't know the essential details of MMX, see:

- bottom of http://www.bartleby.com/173/16.html
- http://en.wikisource.org/wiki/On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether

> So there is the paradox, was the distance increased or
> decreased according to A?
> Thanks for your help in advance.

Increased.

Regards,
Harald
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