Consider the following thought experiment. Two spaceships are initially floating in(adsbygoogle = window.adsbygoogle || []).push({});

a region of space far removed from other matter. They are at rest with respect to each

other, and with respect to some inertial reference frame F. There is a distance L between

them. At some time, t=0, as measured by this reference frame F, they both turn on their

engines and start accelerating very gently in the same direction (see the figure below).

The two spaceships have identical engines and are both programmed by identical

software to maintain this gentle constant acceleration for a long time T, until they

reach half the velocity of light, after which the engines are turned off simultaneously.

Furthermore, the rockets are initially connected by a fragile thread, just long enough

to cover the distance L between the two ships. (The material of which this thread is

made is heat resistant and will not suffer from the exhaust of the engines.) The

question is what will happen to this thread due to the relativistic length contraction.

Sketch a Minkowski diagram, clearly and completely labeled, of the world-lines

of both spaceships. (You are allowed to suppose their size is negligible.)

Here is what happens to the thread from the point of view of reference frame F: the

ships started accelerating from rest with the same acceleration at time t =0, and thus, at

all later times, gained the same speed. Hence the distance between them has not

changed: at time T, they are still a distance L apart. However, since they, and the

thread that connects them, are now moving at a very large velocity, relativity predicts

that thread will suffer length contraction. It will become shorter than the distance L it

needs to span, and build up tension and eventually break.

Sketch how the situation would look like from the perspective of a pilot in one of

the spaceships, say from the inertial frame in which he/she is at rest after time T. In this

frame, the thread is at rest too and there is no length contraction. Consider in particular

the questions whether in this frame of reference the moments their engines are turned

of is simultaneous, and whether the distance between the ships remain constant.

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# Homework Help: Bell Paradox Questions - Diagram help!

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