Proper Distance, Rest Length: What to Know

[JD96]

Hello,

Could someone check my following statement: The proper distance between two spacelike separated events can be thought of as the rest length of a rod that connects both events in an inertial frame in which both events happen simultaneous.

Thanks in advance!

 

[vanhees71]

That's correct, and you can always find this frame of reference, by choosing the spacelike vector as one of the basis vectors of an inertial reference frame in Minkowski space.

 

[JD96]

Okay, that makes sense :) Thanks for the quick reply!

 

[Matterwave]

One should note that this does not necessarily work in GR. In SR where there are global inertial frames, one can always define a rest frame for such a rod, in GR if the two space like points are too far apart, there may not be a unique way to measure the distance between them (different "straight line paths" may connect the same two points).

 

[sardar]

Yes, your statement is correct. The proper distance between two spacelike separated events is the distance measured by an observer at rest in the same inertial frame as the events. It can also be thought of as the rest length of a rod connecting the two events in that frame. This distance is independent of the relative motion of the observer and the events, making it an important concept in understanding the geometry of spacetime.