An inertial frame of reference is described as being a frame of reference in which the first law of Newton (the law of inertia) holds. This means that all events as described with respect to this frame of reference must have a zero net force acting on it and therefore traces a straight line with a uniform non-translatory motion. But, I have read in some books, especially "Introduction to Special Relativity" by the well-known Robert Resnick, wherein his definition of an inertial frame of reference also refers to such a frame of reference as being an unaccelerated system. This is where I am confused.
How can we describe a frame of reference as being unaccelerated if we occupy the frame of reference itself? No mechanical experiment conducted solely confined to a single frame of reference can determine the absolute motion of the frame of reference relative to another frame of reference. All that can be understood is that there is a certain uniform relative motion between frames of reference and no more. Is Robert Resnick saying that the inertial frame of reference is unaccelerated with reference to another frame of reference?
Best Answer
Yes, the (any) inertial frame is unaccelerated relatively to any other inertial frame. The previous sentence, if it were the only thing we could say, would be a circular definition of the inertial systems of a sort. But given one inertial frame, it would still be enough to find all the other inertial frames.
You should view the situation as follows: Newton's theory or, analogously, Einstein's special theory of relativity postulates that there exist inertial frames. We may also say that it's those in which all the objects that are unexposed to any forces remain in a uniform motion in the same direction. One may see that the previous sentence implies that there exist infinitely many inertial frames; and they're in uniform unaccelerated motion with respect to each other.
All other frames, those that are not in uniform unaccelerated motion in the same direction relatively to an inertial frame, are non-inertial and according to these frames, objects may move along curved or accelerated paths even if no forces act upon them.