Frame of reference of any observer

[paweld]

Let's consider flat 4D Minkowski spacetime. Is it possible to define (local) coordinate
system for any observer (its natural reference frame) so that these coordinates
posses interpretation of time and spatial position measured by this observer?

It can be done in two dimensional Minkowski spacetime. One coordinate is time
measured by the observer - the length of its world line, the second is the spacetime
distance from the world line measured along the line of constant time (for the comoving
inertial the observer). I proved that there always exist an open set containing
observer world line in which these coordinates have sense. An good example of
such coordinates are Rindler coordinates for uniformly accelerated observer.

I wonder if it's possible to generalize my construction to four dimensional spacetime.

 

[atyy]

http://arxiv.org/abs/gr-qc/0104077

Maybe also see Fermi normal coordinates
http://relativity.livingreviews.org/Articles/lrr-2004-6/

I think there may be a problem with observers on a rotating disk, but I don't remember the resolution of that. Fredrik and Demystifier had good answers sometime ago.

 

[paweld]

Thanks for answer.
Could you give me a link to post by Fredrik and Demystifier.

 

[Fredrik]

Atyy probably means posts 138-144 here. I'm not sure how useful those posts will be for you. This post that deals with the synchronization procedure might be better.

In GR, I think my description is a bit ambiguous and that Fermi normal coordinates is what should replace it.

 

[starthaus]

Thanks for answer.
Could you give me a link to post by Fredrik and Demystifier.

Demystifier is the author of this very useful paper.