I Reference frame vs coordinate chart

[cianfa72]

The standard inertial frame with Einstein synchronization convention where such and such body is at rest.

So that does mean: take a family of free bodies (zero proper acceleration) at rest w.r.t. the given (free/inertial) such and such body in a region surrounding it (just to fix ideas we can imagine a wristwatch attached to each of them).

Note that 'at rest' does actually mean that the round-trip time of 2-way light signals exchanged between those bodies does not change. Then, as pointed out in a recent PF thread, we can consistenly apply the Einstein synchronization convention to synchronize such wristwatches (the resulting one-way speed of light in the frame being defined is the universal constant value c).

Label every wristwatch (or body) with fixed different spatial coordinate values and take the proper time of each of them as the coordinate time of the frame being defined.

The map defined as above is the standard inertial frame you were talking about. Btw we're aware of we can do that just in a limited spacetime region in the context of GR. In flat spacetime instead (SR) there is no limit in principle to extend such standard inertial frame to the entire spacetime.

Make sense ? Thank you.

 

[Dale]

Make sense ? Thank you

Yes, that makes sense.