# Inertial and Non-inertial frames of reference

I'm really beginner in physics and I recently started to study the concept of frames of reference, inertial and non-inertial ones.

In the end, I thought I had understood it: frames of reference have coordinate acceleration (dependent on other frames of reference) and proper acceleration (universal) .
Proper acceleration is measured by accelerometers, and we can detect how non-inertial a frame of reference is by detecting its proper acceleration via accelerometers.

But then someone talked to me about Principle of Equivalence and not possibly being able to identify what is proper acceleration and what is coordinate acceleration with an accelerometer. Is it true ?

Is there any constraint situation under which we can identify between those, or similarly, can we talk about degrees of accuracy in distinguishing between those two ( a degree of accuracy or a constraint situation in which we can detect the other degree of accuracy in which a frame is non-inertial ? )

If there is such constraint situation or degree of accuracy, then I'd be safe to know that all the talking about frames of reference, non-inertial and inertial would have a use ( inside that constraint situation/degree of accuracy ) .

But if there is no such constraint situation/ degree of accuracy measurement , that is, if we can NEVER distinguish between the proper acceleration and coordinate acceleration and there is not a concept of degree of accuracy of the distinguishment, it seems to me that all this talk about frames of reference, inertial and non-inertial ones, is a bit useless.

As I said, I'm really beginner in physics and I'm not aware of more advanced physics ( general relativity, principle of equivalence, etc ) , i just wanted to know if in fact i should drop all this notion of frames of reference, inertial and non-inertial ones, because in fact this is all universally flawed, or if there are degrees of accuracy or constraint situation in which it is valid/reasonable.

But then someone talked to me about Principle of Equivalence and not possibly being able to identify what is proper acceleration and what is coordinate acceleration with an accelerometer. Is it true ?

That's not true. By definition, an ideal accelerometer measures proper acceleration.

It appears you (and possibly the acquaintance who talked to you) are mixing and matching concepts from Newtonian mechanics and general relativity. Don't do that! Inertial frames in Newtonian mechanics and general relativity are rather different beasts.

The concept of an inertial frame is extremely important in Newtonian mechanics, not so important in general relativity. Proper and coordinate acceleration are concepts from relativity theory. In Newtonian mechanics, gravitation is a real force, but accelerometers can't measure it.

Newton's first law conceptually provides a way to test whether a frame is inertial: Simply find a test particle on which the net force is zero. Does the object appear to obey or disobey Newton's first law? The only problem: Good luck with this search!

That approach works nicely in general relativity. In fact, Gravity Probe B used exactly this approach. An accelerometer that registers zero acceleration does make for a local inertial frame in GR. Gravity Probe B flew low, so it was subject to drag. It had a free-floating test mass in its core. It used its thrusters to force the main part of the probe to accelerate just so and keep that free-floating mass centered. In doing this, Gravity Probe B was flying inertially from the perspective of general relativity. Because it was flying low, it was subject to some of the finer aspects of general relativity, and scientists could thereby use the observed motion as a test of general relativity.

• Can you please elaborate why did you write “Good luck with your search”. Is it because the whole Newtonian scheme of finding an inertial frame is circular, that is how do you know that no force is acting on the body without seeing in the first place whether the body moves in a straight line or not. Commented Jun 21, 2021 at 10:41
• @Shashaank That's part of it. Keep in mind that acceleration due to gravitation is locally unmeasurable. An accelerometer at rest on the surface of the Earth registers approximately one g acceleration, directed upward. The ground is pushing the accelerometer upward while the unmeasurable gravitational force is pulling the accelerometer downward. An accelerometer at the center of mass of a non-thrusting spacecraft orbiting the Earth registers nearly zero acceleration. This creates a problem with regard to finding that test article with no net Newtonian force acting on it. Commented Jun 21, 2021 at 12:59