A reference frame where Newton’s second law is valid is called an inertial frame of reference. Force is absolute, so is mass(for sufficiently small speeds), so if a frame is to measure an acceleration $a_1=\frac{F}{m}$, given a frame $F_1$ measures acceleration $a$, there will always be such a frame accelerating with respect to $F_1$ so $F=ma_1$. What I don’t understand is, why does this new frame have to be at rest or moving with a constant velocity. In other words, why is Newton’s second law only valid in non-accelerating frames? And this frame is to be non-accelerating w.r.t which frame?
I have studied this as a definition but couldn’t quite grasp the intuition.