# How time-like unit four-vector is tangent to the observer's world-line?

I just have started studying special relativity and moving to general relativity

Special relativity only deals with inertial frame (non accelerated frame) but there are no inertial frame in the curved space time so we consider local inertial frame from the global (which is accelerating) like earth is accelerating but you can measure things (time, distance) by considering a laboratory on earth. In a local laboratory an observer carries along four orthogonal unit four-vectors which define a time direction and 3 spatial coordinates But then the book says "time like unit four vector will be tangent to the observer's world line since that is the direction a clock at rest in the laboratory moving in spacetime"

I don't get how Time like unit four vector is tangent to observer's world line!! The example is from gravity by James.hartle Can someone please explain

• If you draw the space time diagram of stationray observer, then it will be vertical line. Now vertical direction the vector is time, so yeah Jun 7, 2022 at 12:07
• Special relativity can handle non-inertial frames (although the simple equations in introductory treatments of special relativity can't handle non-inertial frames). What special relativity can't handle are curved spacetimes. Jun 7, 2022 at 14:46