Can someone explain what Einstein meant by the distinguish in his equivalence principle? Did he meant that it's impossible to distinguish between an elevator lying on earth and an elevator going at 1G? (As long as there is no tidal force involved and the experiments are inside).
I don't have this clear, Is there really no experiment that could distinguish between that two cases?
 A: Yes, the two things really are absolutely equivalent so there would be no way that anyone could distinguish whether they were in a lift car at rest on Earth or one being accelerated at g in deep space. You say "lying", but the equivalence is of course between a lift car standing on Earth and one being accelerated in the direction from floor to roof.
See the answers to the related questions.
A: Not exactly as you stated. If elevator goes up at $1g$ then your body will effectively feel $2g$, because earth gravity is already pushing you to the floor with $1g$. If elevator goes down with $1g$, then you will feel $0g$ - weightless when floating in the air due to elevator free fall. What Einstein did have in mind is that you can't distinguish by any physical experiment inside a rocket if it goes at $1g$ acceleration in space, under no influence or at least no strong gravitational fields OR if this rocket sits at rest parked at NASA rocket takeoff place (however experiencing same $1g$ due to Earth gravity). That was the point.
Again, in short, acceleration can be due to object placement into gravitational (or technically in any other field - consider a metal attached to a permanent magnet, this metal constantly feels pressure towards magnet) or simply due to being in a non-inertial reference frame, such as when you suddenly push a car pedal and it "jumps" forward with acceleration. Though in this case car is not in any specific field which attracts with that acceleration, car propels itself. Those two situations are physically symmetrical, because not any single experiment can show somehow that you are in one scenario, but not on the other. (Looking trough car window doesn't counts, and it can be faked anyways). Hope that makes it more clear.
