Isn't the Equivalence principle not quite true, technically speaking? A gravitational acceleration and an inertial acceleration are communicated very differently. A gravitational acceleration is communicated throughout your body and its stress is spread out in your body, whereas an inertial acceleration is communicated by points of contact and its stress is focused on these points of contact. And the different types of acceleration will also affect the fluid in your inner ears different, which means you will not be able to balance as easily in an acceleration caused by inertia as one caused by gravity.
Am I missing some caveat or rule or disclaimer, that makes these things irrelevant?
For instance in the classic elevator example, the walls of the elevator will communicate the acceleration to you. If the elevator is moving towards your head, the acceleration is communicated through your feet, and due to inertia your body is compressed. Whereas if you are on Earth and step off a building, your feet will fall first, and then the rest of your body, so you get stretched slightly.
And if you had a constant space elevator acceleration to match Earth's gravitational acceleration rate, your skeleton should be under more stress in the elevator because the acceleration has to begin at your feet and then overcome the inertia of your body, and the fluid in your inner ears would not give you the same sense of balance perception as if you are standing still on Earth. If you are standing still on Earth the acceleration is communicated simultaneously throughout your skeleton since your whole body is in Earth's gravity well.
What is it that the way the forces are communicated, and the different stresses they place on your body and skeleton, not considered a violation of the Equivalence principle? What am I missing?
Best Answer
What you are pointing out is in fact one of the key insights of the equivalence principle: if every atom in your body is accelerated in the same fashion then there is no differential acceleration across your body and therefore no force in your body and therefore no way of "feeling" the acceleration or experiencing it in a way that can be distinguished from free fall. Similarly if a scale you are standing on is accelerating at the same rate as you, then you will exert no force on it and you will be weightless. Since gravity results in the same acceleration on all atoms in your body and on any nearby scale (locally, i.e. ignoring tidal effects) freefall in gravity is therefore the same as being in an inertial frame that is not in a gravitational field.
In the case of acceleration, say in a rocket, yes, indeed the force is communicated via the points of contact with the chair or floor or whatever, and this is indeed different from the above description of gravity in free fall or an inertial frame. We call it a non-inertial frame. And indeed the point is that if you are standing on, say, Earth, the floor is similarly exerting a force that is communicated via the points of contact with the floor, and the result is a physical situation identical to the rocket accelerating. We also call this a non-inertial frame: you are not in free-fall, because the Earth/floor is preventing you from being in the inertial reference frame of a freely falling observer.