restraining orders for physicists

Restraining orders for physicists.

Someone was telling me about restraining orders yesterday. Specifically, the fact that this bird had a restraining order imposed on this bloke who worked in the same building as her. Which made it a tad difficult for the bloke to get about his daily life.

This got me thinking. When they say that one cannot approach within 100 mts (ok, yards, in this unmetricised backwater called the US of A), do they mean scalar distance or vector displacement. I mean, X may have a restraining order against Y. Its fine when they are on level ground, but what if X happens to occupy offices or an apartment which are one floor above that of Y. what then? Do we measure straight vectorial displacement through the roof/floor, or do we measure scalar distance measured by walking through the corridor and through the stairwell? Do judges think about that? This appears to be a serious loophole in the law.

There are several other cases which must be considered. What if X and Y have cabins on the opposite ends of a spaceship 110 mts long. Fine, the 100 mts restraining order is not being violated. But when the spaceship is moving at a speed 'v' wrt any inertial frame (say, the Earth), then following the Lorentz length contraction formula, the apparent distance seen between X and Y is 110/(sqrt[1-v^2/c^2]), where 'c', of course is the speed of light in vacuum. The speed at which the restraining order will be violated ACCORDING TO EARTHBOUND OBSERVERS can be easily calculated as 1.35146 times c. Thus, common civil law will have to subject to substantial correction as and when (if) hyperluminal flight is achieved. A brief caveat: X and Y will not observe the length contraction in their own reference, i.e, that of the spaceship.

There could be other situations where 'straight line distances' simply do not apply. What if X and Y were in the immediate vicinity of a huge gravitational sink (such as any ordinary, or garden variety black hole)? There are no straight lines left!!


I am not sure that the law will take cognizance of such obvious lacunae, but any self respecting physicist will think about all of these if ever subject to a restraining order.