Which best explains how an object at rest deep in space and far from any massive body behaves compared to an object in free fall in earth’s gravitational field?

they behave differently because, according to the principle of equivalence, the laws of physics depend on frames of reference.
they behave differently because, according to gravitational redshift, the laws of physics depend on frames of reference.
they behave the same because, according to the principle of equivalence, the laws of physics work the same in all frames of reference.
they behave the same because, according to gravitational redshift, the laws of physics work the same in all frames of reference.

They behave the same because, according to the principle of equivalence, the laws of physics work the same in all frames of reference.

Explanation:

According to the equivalence principle postulated by Einstein's Theory of General Relativity, acceleration in space and gravity on Earth have the same effects on objects.

To understand it better, regarding to the equivalence principle, Einstein formulated the following:  

A gravitational force and an acceleration in the opposite direction are equivalent, both have indistinguishable effects.  Because the laws of physics must be accomplished in all frames of reference.

Hence, according to general relativity, gravitational force and acceleration in the opposite direction (an object in free fall, for example) have the same effect.  This makes sense if we deal with gravity not as a mysterious atractive force but as a geometric effect of matter on spacetime that causes its deformation.

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