If a person (free)falls into a black hole at some point or the other, he will be stretches by a 'force differential' between the two ends of his body. This is the process of spaghettification.
But, general relativity also tells us that any observer who falls into the black hole will be inertial, as he is just moving along a geodesic that leads to the interior of the black hole.
The Equivalence Principle surely cannot be wrong. But the observer also feels pulled and stretched by a force (which means he is accelerating for sure). So how do these tidal forces emerge (which clearly turn an inertial observer into an accelerating one, while he is in free fall)?
Not probably relevant to the question, but I thought up this explanation:
If we consider the observer to be like two spheres (one a the feet, other at the head) connected by a string (the rest of the body), and if we consider this object to be falling into a black hole, then du to the curvature of spacetime, the sphere nearer to the singularity will experience higher time dilation, and hence might take a different geodesic than the other sphere (which experiences lower time dilation).
In that case, as the two spheres travel in two separate geodesics toward the same singularity, maybe one of them accelerates faster (through time if not through space) than the other. The discrepancy in the accelerations causes the string to go taut, and eventually (as the discrepancy increases) to break, leading to the same effect of spaghettification.
Is this explanation correct, or at least am I thinking in the right direction?