# How can a person inside from a veiled and free-falling elevator distinguish whether he is in an inertial or non-inertial frame?

From wikipedia: "A non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame", according to that statement, I would say that an elevator that is in free fall under a gravitational field is a non-inertial frame, and anyone at rest on the ground can tell that, but how could the person inside the elevator tell what kind of frame the elevator is? Assume that the elevator is veiled, and there will also be no form of acceleration in the elevator, thus disregarding Einstein's Equivalence.

• What is the source of that definition of non-inertial? Dec 28, 2021 at 14:40
• @BillN Text taken from wikipedia: "A non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame". So if a person is situated at infinity free of any gravitational force and other types of forces, and therefore free of acceleration, he is an inertial frame, so he would see the elevator falling rapidly, so if this elevator is accelerated relative to a inertial frame, so it must be a non-inertial frame, as defined above. Dec 28, 2021 at 14:46
• Observer would see the elevator accelerated relative to the earth, which is not an inertial frame. You are making an incorrect assumption that the elevator would accelerator relative to the observer. Dec 28, 2021 at 15:33
• @BillN So a frame of reference accelerated relative to a frame of reference, which is guaranteed to be non-inertial, could possibly be inertial or non-inertial, in which case the free-falling elevator is inertial? Dec 28, 2021 at 18:26

Within the frame of the free falling elevator the reading on an accelerometer always matches the acceleration with respect to the frame. Therefore the free falling frame is inertial.

In the frame of the ground an accelerometer at rest reads an upward acceleration of $$g$$ despite having no acceleration with respect to the ground. Therefore the ground’s frame is non-inertial.

Each frame can determine if they are inertial or not by looking at their own accelerometers and their own frame, without reference to any other frame. But the inertial vs non-inertial designation is exactly backwards from what you had indicated. A free falling frame is inertial and the ground frame is accelerating upwards at $$g$$.

• I can't understand this, the definition of a non-inertial frame is a system that is subject that is different from zero. A free-falling elevator has net force proportional to acceleration g, how can it be an inertial frame then? And the same goes for him on the ground, the weight force is contradicted by the normal force, in the end the net force is null, how then can it be a non-inertial referential in this case? Dec 28, 2021 at 13:52
• @userN see physics.stackexchange.com/questions/685601/… as explained there “If the acceleration relative to the reference frame is not equal to the acceleration measured by the accelerometer (for all accelerometers) then the frame is non-inertial.” We simply apply that rule here. Doing so shows that the ground is non inertial and the free falling elevator is inertial
– Dale
Dec 28, 2021 at 13:58
• As an aside, Einstein’s two great intellectual accomplishments were to take measurements seriously. Special relativity came from taking the speed of light measurements seriously and general relativity came from taking accelerometer measurements seriously. The speed of light really is c, it is not some trick or failure of our measuring devices. A free falling frame really is inertial, it is not some trick or failure of our measuring devices
– Dale
Dec 28, 2021 at 14:03
• So if you have these two situations, an elevator on the floor with a person falling from the ceiling, both subjected to a gravitational field; and an elevator accelerating upwards with the person standing on the ceiling, both without a gravitational field. By the Einstein's Equivalence principle, locally for the person inside the elevator, both situations are the same (which a third outside observer could no longer assert). (...continuation is the next comment) Dec 28, 2021 at 14:36
• @userN yes that is correct. In both the cases you mention the person is inertial (accelerometer reads 0) and the elevator is not (accelerometer reads “upward” acceleration of g)
– Dale
Dec 28, 2021 at 16:03