Throughout my life I've been told that an inertial frame is one that is not accelerating and I was satisfied with that. Well up to this day, until I asked: accelerating with respect to what ? Now this seems as a flawed definition to me.
Another definition states that an inertial frame is one in which a body remains at rest or moves at constant velocity unless acted upon by forces. This definition seems to be flawed too, don't we usually tell whether or not a force is acting on a body by measuring its acceleration ? How can we switch to doing the opposite so quickly ?
Wikipedia defines an inertial frame as:
In classical physics and special relativity, an inertial frame of reference (also inertial reference frame or inertial frame, Galilean reference frame or inertial space) is a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. The physics of a system in an inertial frame have no causes external to the system.
Well this looks too complicated for me, can any one help explaining it in simpler terms please ? How can time and space be "homogeneous", "isotropic", and "time-independent" ?
Finally, can we define an inertial frame as the one in which Newton's three laws of mechanics hold?