Einstein, following his usual æsthetics of simplicity, assumed the ``dilemma'' was its own solution - namely, you can't tell an accelerated reference frame from a reference frame in a gravitational field. This is known as the equivalence principle:
No experiment performed in a closed system can tell whether it is in an accelerated reference frame or a reference frame in a gravitational field.
If you wake up in a closed box and you experience ``weight''
(as one normally does on Earth), there is no way
to be sure you are actually being attracted by gravity,
as opposed to being in a spaceship (far from any stars or planets)
which is accelerating at one ``gee.'' What's more,
if Einstein is right, no matter how clever you are
you will not be able to measure any phenomenon
from which you can tell the difference.
The two cases are perfectly equivalent,
hence the name of the Principle.
So far this Principle agrees with experiments, which has led people to look for ways to make the statement, ``A gravitational field is the same thing as an accelerated reference frame,'' sound reasonable. To make any progress along these lines we have to turn to an analysis of our notion of ``acceleration'' - i.e. of the nature of space and time, and therefore of geometry.