I have seen the mathematical concept of the pseudo force exerted to a mass in a non-inertial reference frame. But I did't find any theoretical idea that explains it. When I read the books, it says "to make adjustments for a non-inertial reference frame to apply Newtonian mechanics on it", "we assume a force from a invisible provider opposite to the direction of the frame's acceleration", "we can predict it by Mathematics". But could we give a physical interpretation of it which explains us why we feel such force in the accelerating frame?
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$\begingroup$ The physics is that objects are obeying Newton's laws in the usual way; that is, they have inertia. That's why they are sometimes called "inertia pseudoforces". $\endgroup$– dmckee --- ex-moderator kittenCommented Nov 20, 2015 at 16:32
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$\begingroup$ Hint: The physical law and its explanation, when expressed in terms of an accelerated frame, is going to be much more cumbersome than the equivalent law/explanation in an inertial frame; and that is pretty much the whole reason for the bias toward expressing physical laws in terms of inertial frames. The "real" vs. "pseudo" nomenclature, is just an expression of that bias. $\endgroup$– Solomon SlowCommented Nov 20, 2015 at 18:25
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$\begingroup$ NB: attention, there are plenty of other pseudoforces in physics than the one you are mentionning here. $\endgroup$– Fabrice NEYRETCommented Nov 20, 2015 at 22:02
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If you accelerate relative to other objects, you will see them accelerate towards you. according to Newtons laws if a object is accelerated some force must be acting on it. but this acceleration is not causes by a real force, it is only caused by your own acceleration. Newtons laws then should no longer valid if you are accelerating. However, you can make a trick to make them work: You invent a fictitious force that causes the acceleration of the objects, and then newton's laws become applicable again in your accelerated frame of reference.