Consider the question below just as an example in order that the question I will ask makes a little more sense: enter image description here

In the case above it seems as though it would be the police ship frame where proper length is measured as in this frame they seem to be at rest relative to one another and in the earths frame they are moving past the observer and so must be length contracted.

However my confusion came about because in the frame of reference of the Solar system surely one can measure both points (nose/tail of both ships) simultaneously, (as they are a distance of 1 light second apart) in this frame and so why can this not be proper length?

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    $\begingroup$ You cannot be in two places at once, the measurement information from the two points must be combined to establish a length between them. The mechanics of doing this introduce length contraction. $\endgroup$ – JMLCarter Jun 2 '17 at 22:00
  • $\begingroup$ please elaborate $\endgroup$ – DJA Jun 2 '17 at 22:01
  • $\begingroup$ Try this en.wikipedia.org/wiki/Ladder_paradox $\endgroup$ – JMLCarter Jun 2 '17 at 22:14

An observer at rest relative to the solar system cannot measure the proper length of an object because if the object were constantly between the two vehicles, it would not be at rest in the frame of the solar system. One may try to argue that you could place a stick of appropriate length ($1\text{ ls}$) that when the vehicles pass, it will span their distance, but the vehicles will not agree that it fills this distance because their passing of the two ends opposite ends of the object will not be simultaneous in their frame.


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