Gravity vs Inertia: Einstein's Simple Experiment Explained

[Reuben Smith]

Einstein stated that “there is no experiment that a person can conduct in a small volume of space that would distinguish a gravitational field and an equivalent uniform acceleration”.
He proposed that if you had two elevators, one on the Earth and the other far out in space away from any gravitational body and it was accelerating at 9.8 meters per second per second that there would be no way to tell if you were in the one in space or the one on earth.
Now he also stated that if someone who is outside each of these imaginary elevators shines a beam of light through the window of the elevator that is accelerating the person shining the light will see the beam traveling in a horizontal path, while the person in the elevator will perceive the beam of light as having a curved path.
Now according to his equivalence theory which is the backbone of his general theory of relativity, a person in the elevator on Earth will perceive a beam of light shone through the window of his elevator as following a curved path.
Now if he allows for one to observe close enough perceive this curve in the light beam, I will propose an experiment that will differentiate gravity from an inertia field due to acceleration of gravity in a small closed space.
If you were to fill these elevators with enough water to cover the floors and shine a beam of light from the center of each of these two elevators outward horizontally the beam of light would be closer to the water at the edge of the elevator in the inertial field than the one in the gravitational field of the earth, because the water in the gravitational field will have a curvature equal to the curvature of the earth. The reason for this curvature is that the force of gravity between two objects varies inversely with the square of the distance as shown by the formula and gravity works as we know works idepentaly on each atom. . The reason we know that gravity works indepenantly on each atom is the fact that a feather will fall at the same rate as a lead ball in a vacuum


. This simply means that gravitational force decreases with distance.
Therefore if the floors in these two elevators were perfect planes and did not have the same curvature of the earth, the center of the elevator in the gravity field of Earth would be closer to the Earth than the outside edges, therefore the water would be deeper in the middle where the force of gravity is stronger, because the water would have the same curvature as the Earth and the floor being a perfect plane would not follow the curvature of the earth.
While the water in the inertial field would be at the same depth at the center as it is at the edges.
This is the tidal effect and it would not be present in a field due to pure acceleration

 

[JesseM]

If you were to fill these elevators with enough water to cover the floors and shine a beam of light from the center of each of these two elevators outward horizontally the beam of light would be closer to the water at the edge of the elevator in the inertial field than the one in the gravitational field of the earth, because the water in the gravitational field will have a curvature equal to the curvature of the earth. The reason for this curvature is that the force of gravity between two objects varies inversely with the square of the distance as shown by the formula and gravity works as we know works idepentaly on each atom.

As you say later in your post, this curvature is a "tidal effect", and it's understood that the equivalence principle is only supposed to work in the limit as the size of the elevator (and the time interval in which you are making your measurements) becomes small enough that tidal effects also become arbitrarily small (too small to measure by whatever instruments you're using, say). See the discussion of this in the last section of this article about the equivalence principle.