Relativity: Inertial vs. Coordinate Systems Explained

[gdpudasaini]

Can anyone explain me what is the difference between inertial system and coordinate system in relativity? Please make me understand.

 

[HallsofIvy]

A coordinate system is a mathematical concept- just a way of assigning values to each point so you can "tell them apart". In physics those are normally position and time.

An "inertial system" is a physical system that is not accelerating: in particular there are no external forces acting on it.

 

[neutrino]

Also, all inertial coordinates systems at rest with respect to each other belong to the same inertial frame.

 

[JesseM]

A coordinate system is just a way of assigning 3 position coordinates and 1 time coordinate to every point in spacetime in the region the system covers, so you can identify the coordinates of particular events, like "this event happened at position x=5 meters on the x-axis, y=3 meters on the y-axis, z=10 meters on the z-axis, and time t=12 seconds." An inertial coordinate system is just one where, if an object's position coordinate stays the same over time relative to this coordinate system, that automatically means the object is moving inertially. I'm not sure if there's a difference between "inertial system" and "inertial coordinate system"--it may be that "inertial system" is meant to imply something like an actual physical apparatus for defining the coordinates of an inertial coordinate system. In SR we imagine that coordinates can be assigned using a grid of inertially-moving rulers with synchronized clocks placed at each marking, and then the coordinates of a given event would correspond to the ruler-markings and the readings of the clock that were right next to the event as it happened.