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center o bass
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Previously, before getting into relativity, I've always thought of a 'reference frame' of basically an "observer carrying a coordinate system" - where I thought of an observer as anything which could record information of positions and velocities of particles etc. Now, however, I'm reading a book about SR and GR (Øyvind Grøn - Einstein's general theory of relativity) where these concepts are defined precisely in a way that at least is new to me. The definitions are as follows
Coordinate system: "A coordinate system covering a region of spacetime, is a continuum of four variables ##\{x^\mu\}## that uniquely label every event in the region."
Reference frame: "Is a continuum of non-crossing time like or light like curves in spacetime. We may thus think of a reference frame as a continuum of particles, called reference particles or observers. These reference particles need not move freely."
Comoving Coordinate system: "A comoving coordinate system in a reference frame is defined by the requirement that the reference particles have constant spatial coordinates."
Thus, by these definitions, it seems like one can think of a reference frame of being constructed out of particles. So, I wonder, what is the usefulness, in relativity, of thinking of reference frames in terms of particles moving along world-lines? Is there somehow a necessity, in relativity, to take this view?
I also note that particle worldlines never can be space like, so while coordinates can label events which lie on space like curves, the curves of a 'reference frame' can not, according to the above definition.
Any insight on these concepts would be appreciated.
Coordinate system: "A coordinate system covering a region of spacetime, is a continuum of four variables ##\{x^\mu\}## that uniquely label every event in the region."
Reference frame: "Is a continuum of non-crossing time like or light like curves in spacetime. We may thus think of a reference frame as a continuum of particles, called reference particles or observers. These reference particles need not move freely."
Comoving Coordinate system: "A comoving coordinate system in a reference frame is defined by the requirement that the reference particles have constant spatial coordinates."
Thus, by these definitions, it seems like one can think of a reference frame of being constructed out of particles. So, I wonder, what is the usefulness, in relativity, of thinking of reference frames in terms of particles moving along world-lines? Is there somehow a necessity, in relativity, to take this view?
I also note that particle worldlines never can be space like, so while coordinates can label events which lie on space like curves, the curves of a 'reference frame' can not, according to the above definition.
Any insight on these concepts would be appreciated.