sci.physics.research

"jacques" <@> wrote in message
news:0d23ec8d-8294-46f1-9a9f-c432a81ea9ea@...
> On 15 fev, 21:47, 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 in:
>>
>> /home/baez/physics/Relativity/SR/spaceship_puzzle....
> /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