Equivalence Principle Problem

Question

Let's say there are two massive objects covered in a cloud of gas, and two observers with a mass comparable to the object.
One observer is free-falling to the object, there is no air resistance and it is a perfect free-fall. The other observer is floating in space and not affected by the spacetime curvature. As the free-falling observer gets closer to the object, the gas cloud starts to variate in shape and move towards the free-falling observer because of the gravitational pull. The parts of the cloud closer to the observer will start moving first, and as he gets closer it will be more distorted.
The other observer doesn't fall towards the gas cloud and the object because he is floating. Consequently the gas cloud doesn't deform and variate in shape, which allows the observer to infer he is floating. Furtheremore, there is no reason for the gas cloud to deform in this thought experiment as there aren't any other component that can cause the gas cloud to move in such way.
Does this break the equivalence principle and why?

Jonas · Accepted Answer

As already mentioned, the equivalence principle is only to be applied locally. Another example for this is the comparison between an observer in a rocket (in flat spacetime) and an observer in some box in free fall. As both observers release two balls, the balls in the free falling observer's frame of reference will slowly get closer as both accelerate towards the earth's center:

(very not to scale)
This situation is similar to the one you described in that the gravitational field of the body can only locally be approximated as uniform. In your situation, this causes gas to be more dense closer to the body.
I think one should also note that the equivalence principle is only about the equivalence of the gravitational field of two observers in free fall or in flat spacetime1 - It does not matter whether there is gas in one situation or not.
So no, this does not violate the equivalence principle since both observers experience the same gravitational "force", i.e. no force.

1 Of course, there is more to the equivalence principle, but this is a simplified description.

Equivalence Principle Problem

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