does that affect the equivalence principle?
Yes you can .
You feet will feel 9.80627m/s acceleration on earth and your head will feel 9.806264773m/s2
Because your head is farther from the centre of the gravity. But there's no such thing on elevator.
Okay, seriously. No!
That's the concept of Einstein Elevator. Light, everything works the same as on earth.
But not everything!
In Einstein Elevator the acceleration from your head and your feet is the same!
On earth there's a very-very little different.
And I might add, your head is older than your feet, because your feet ages more slowly than your head.
But just ignore my number. See the answer of the staffs in my post.
The whole post is based on the assumption that your feet-head axis is parallel to the radius of the source, which must no necessarily be the case.
But the point is not the a on your head or feet, the issue is that, whatever the difference, you can always tell when the F (or a) is coming from a push/pull i.e. on the inertial mass and not on the gravitational mass.
If Einstein knew that, what is the purpose of the example? More in general, how can our subjective perception or objective measurement of a phenomenon influes the actual state of the world?
In a small enough region you cannot tell why you are in an accelerating frame. If the region is large enough that the non-uniform nature of the gravitational field is measurable that will give the game away, but the equivalence principle does not apply to such a large region.
Let's put it this way. Assume you are comparing someone in Einstein's elevator to someone in small room on a rotating space station. Both feel a "force" holding them to the floor. Careful experiment can show that conditions in the two are not exactly identical, however, this does not mean that, fundamentally, they are not the same( both are cases of acceleration). If we keep increasing the radius of the space station while maintaining the same g-force in the room, the conditions in the room become a closer and closer match to that in the elevator and it becomes harder and harder to tell them apart. They begin to converge. The same thing happens if you make the size of the elevator and room smaller and smaller.
The same is true for gravity and the elevator. As you make the elevator smaller and smaller, the differences become harder and harder to measure and they tend to converge. On a fundamental level, they are equivalent.
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