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Many textbooks state the principle of equivalence as such: There is no experiment that can be done inside a small closed space, such as a box, that would allow an observer inside the box to distinguish between being in a uniformly accelerated box or being in a box that is at rest on the surface of a planet. (Assume the radius of the planet is large enough such that there is no detectable convergence of the gravitational field lines at the surface of the planet.) But this assertion about the principle of equivalence is not true.
Suppose initially there is a box made of aluminum in inertial space, far away from any gravitational fields. In the box is an observer with a measuring rod made of a diamond. One interior side of the box is painted blue and the opposite interior side is painted red. The remaining interior sides are painted yellow.
The observer places the measuring rod against one of the yellow sides with one end of the rod flush against the blue side. The observer draws a line on this yellow side, one meter in length, perpendicular to the blue side.
After drawing the line, the observer sends a radio signal to begin the first test, takes a sleeping pill, and goes to sleep. An hour later, the observer awakes. Relative to an outside observer at this time, the box is resting on the surface of a planet. At the surface the gravitational constant is equal to g. The inside observer takes the measuring rod and measures the length of the line.
After making the measurement, the observer sends a second signal to begin the second test, takes a sleeping pill again, and goes to sleep. An hour later, the observer awakes. At this time a cable attached to the outside of the box, opposite the interior red side, accelerates the box at a uniform acceleration g. The observer measures the line again.
The observer sends a radio signal, announcing correctly that the box is accelerating and that in the first test the box was resting on a planet. This disproves the assertion there is no experiment possible within a closed box to distinguish between being in a gravitational field or being uniformly accelerated. Anyone would like to guess how the observer knew this?
Suppose initially there is a box made of aluminum in inertial space, far away from any gravitational fields. In the box is an observer with a measuring rod made of a diamond. One interior side of the box is painted blue and the opposite interior side is painted red. The remaining interior sides are painted yellow.
The observer places the measuring rod against one of the yellow sides with one end of the rod flush against the blue side. The observer draws a line on this yellow side, one meter in length, perpendicular to the blue side.
After drawing the line, the observer sends a radio signal to begin the first test, takes a sleeping pill, and goes to sleep. An hour later, the observer awakes. Relative to an outside observer at this time, the box is resting on the surface of a planet. At the surface the gravitational constant is equal to g. The inside observer takes the measuring rod and measures the length of the line.
After making the measurement, the observer sends a second signal to begin the second test, takes a sleeping pill again, and goes to sleep. An hour later, the observer awakes. At this time a cable attached to the outside of the box, opposite the interior red side, accelerates the box at a uniform acceleration g. The observer measures the line again.
The observer sends a radio signal, announcing correctly that the box is accelerating and that in the first test the box was resting on a planet. This disproves the assertion there is no experiment possible within a closed box to distinguish between being in a gravitational field or being uniformly accelerated. Anyone would like to guess how the observer knew this?
