Hi all, I am struggling with the following problem, and so far I have not found a satisfying solution. The problem is that the definitions of "Inertial" and "Non-Inertial" in relativity appear to me as being at opposites with the ones in Classical Physics (and of course I am probably missing something but my question is what?). The definition of an inertial frame in which the principle of relativity takes place is defined in classical relativity text books (see "Spacetime Physics" by Taylor and Wheeler 1966 and many others) to be an object falling in gravity (such as a rocket, airplane or ship) in which according to the principle of equivalence it should be considered to be an inertial frame. (Why can we not use directly a true inertial frame without any gravity at all? The answer on that appears to be that such ideal frame is not actually possible [or at least common] because there is gravity all around and any two object in existence will exert gravity on each other.) On the other hand for the most part in relativity a gravitational frame is considered to be non-inertial (even if the frame is not in orbit or rotation) just because the gravitational force itself, again this is based on the principle of equivalence. So far for relativity, let us see what general mechanics says on this matter. In general mechanics any object falling in gravity have gravity as a force acting on it and therefore the object will accelerate towards the source of the gravity (provided that there is no air resistance) and as such the object must be considered non-inertial! If the gravitational force is actually in orbit or rotation (such as the earth or other planets and even stars) this is yet another reason for it being non-inertial. Such objects are non-inertial themselves and can of course not be used as an "inertial frame of reference", since besides the requirement to be inertial it has another requirement and that is that all other inertial frames will appear to the frame as obeying the inertial law of motion, but in this case different objects falling in gravity will see each other as accelerating, and objects on earth will see similar objects on the moon in rotation. On the other hand for an object at rest on earth, although there is gravity acting upon the object but there is also an equal and opposite force (the third law of motion) that the earth is causing on the objects, which balances out the gravitational force and as such the net force equals zero, and the objects remains at rest relative to the earth, thus the objects are inertial (in case of a gravitational field not in orbit). So how do we relate the two definitions? Here are I will list my attempts to solve this. First I attempted to answer that the inertial definition of relativity is only for an object that meets two requirements, 1) that it is in terminal velocity (since the air resistance is balancing out the gravitational force) 2) that the gravitational field is not in orbit or rotation. However I am not currently satisfied with such an answer for the following reasons: 1) In such case the problem with the objects at rest in the gravitational field remains. 2) There is no way to distinguish with an internal experiment between an object in terminal velocity and an object that is not. 3) More over since objects in terminal velocity and objects that are not in terminal velocity are obeying the same physics laws (and similar can be said that object that the gravitational field is orbiting are also obeying the same physics laws), and as such it will follow that inertial and non-inertial frames are equivalent, something that does not comply with the principle of equivalence. On the other hand I attempted to answer that the definition for non-inertial for a gravitational frame is only when the gravitational field is in orbit or rotation. However I am not currently satisfied with such an answer for the following reasons: 1) In such case the problem with the objects falling in the gravitational field remains, as they cannot be considered as inertial. 2) Since objects in a gravitational field in orbit and objects in a gravitational field that is not in orbit are obeying the same physics laws, and as such it will follow that inertial and non-inertial frames are equivalent, something that does not comply with the principle of equivalence. But recently I started to think that the principle of equivalence does not necessarily have to be interpreted as saying that equivalent behavior must also be considered to have the same inertial and non-inertial status, and we might able to say that although gravity and acceleration behave equal and have similar laws of physics they are still not the same when considering the inertial status. In fact there are ways to distinguish between gravity and acceleration such as tidal gravity, and it might be that the same is with the inertial status. However if this is the case then we can no longer use the principle of equivalence to say that an object falling in gravity is considered inertial since we just interpreted the principle of equivalence of not saying this at all. If so then the question remains what is the inertial frame of relativity? and why do the classical relativity textbooks consider object falling in gravity to be inertial? We may again try to use terminal velocity in a gravity field that is not in orbit, but if so why not use objects at rest in the gravity field? But the real problem is that since there is gravity everywhere there is no gravity field that is not in orbit and if we are to claim that we can find one then why not go back to the simple definition of relativity in which objects are just moving in uniform motion without any gravitational field involved at all? Help is needed, and satisfying answers are appreciated. Thanks in advance.