My head is spinning

With distances and times defined this way, the speed of light is just one. In more familiar language, if our unit of time was the second, the corresponding unit of distance is the light-second, and by definition light travels one light-second in one second of time. It is only when we choose different, more arbitrary distance units, like the meter as one-ten millionth of the distance from the equator to the pole, that we get the more familiar "speed of light equals $3\times 10^8\text{ m/s}$ ". We will stick with the speed of light being numerically equal to one in this discussion.

We now have a family of observers for which we can define position $x$ and time $t$ coordinates. As you can see from the previous question we can now define the velocity of an object by the simple relation $v=\Delta x/\Delta t$ . Let's toss a little more physics in. We ignore gravity for the moment and define an "inertial observer" as an observer for whom Newton's first law of inertia holds. In other words, if Finn is carrying along an apple and lets it go the apple stays next to Finn - it does not move off. If we have a family of such inertial observers that also maintain the same distance from each other always then we have an "inertial reference frame".

One frame is rotating relative to another. Is it possible for both frames to be inertial reference frames?