# Question on Newton's first law

In our physics course, Newton's first law was given as a definition of inertial reference frame. Now in order to use it we need to take some object which has zero interaction with other objects. But now in order to check it, we need to know which forces are acting on an object. But how can we be sure that the fact that an object, with zero net force on it, is accelerating because we are in a non−inertial reference frame and not because of the fact that we haven't accounted for some "real" (as opposed to those called "fictitious") forces. And in general, how can we determine that the force that acts on an object is "real" and not "fictitious" ? E.g. how can we determine that electromagnetic force is "real" and not "fictitious" ?

Very good question. You would do many experiments with many different bodies and you would find that, for all of them, you would have to account for a mysterious force given in terms of a constant vector $$\boldsymbol{f}_i=-m_i\boldsymbol{A}$$ that must characterize your system kinematically, because it affects all moving bodies equally in proportion to their inertia. Your version of Newton's law would be, $$m_{i}\boldsymbol{a}_{i}=\boldsymbol{F}_{i}-m_{i}\boldsymbol{A}$$ You would conclude --or it would be reasonable to conclude-- that $$\boldsymbol{A}$$ is something kinematical characterizing your frame.
• @DerHutmacher, I think you're right that in a very general case you would be hard-pressed to give a simple argument like the above. One example I can think of is if you had strong gravitational fields and the $\boldsymbol{A}$ acceleration field were non-homogeneous. Then you would have strong tidal forces that would be very difficult to tell apart from a plausible $\boldsymbol{F}_{i}\left(\boldsymbol{x}_{i}\right)$ force law. Please, let me keep thinking about it. Feb 26 at 9:59