# What's an inertial frame of reference?

The Earth is an approximately inertial reference frame since it's acceleration with respect to the stars is very small. But if a group of stars is accelerating with respect to another group of stars which group is the inertial frame? Or thinking on an even larger scale, if a universe is accelerating with respect to another universe which one is the inertial and the non-inertial frame? Is there an absolute way to determine this?

I know that an inertial frame is one in which the law of inertia holds. It holds on Earth. Will it not hold in a universe that is accelerating with respect to ours?

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The first postulate of special relativity says there is no test that lets you distinguish one inertial frame from another. Noninertial frames, though, can be identified because a body rest in it does not remain at rest and a body in uniform motion does not remain in uniform motion, even though there are no net forces acting to cause those accelerations.

Consider the case of being in a car turning left. Your body moves to the right (in the car's reference frame) in the absence of a net external force. That's an apparent violation of the first law. That tells you you are in a noninertial reference frame.

Or think about car stopping. The bag of groceries on the seat was a body at rest in the car but now it flies forward in the absence of a net external force. Again, that apparent violation of the law tells you the car is not an inertial reference frame.

The Earth is not an inertial frame because it moves in a curved path around the sun. The acceleration, though, is so slight that only a very careful experiment will detect apparent violations of the first law. Unless you are conducting a sufficiently precise experiment, you can treat it an inertial reference frame.

I know my understanding of this is a little rough. Kip Thorne, in Black Holes and Time Warps, has an engaging discussion about how a freely falling reference frame is inertial. Since the Earth is in free fall with respect to the sun, that suggests it is an inertial frame...but there is something about being inertial locally that I am less sure of.

I think my first four paragraphs are a good first approximation that I will post with that proviso (especially since no one else has answered you yet). Perhaps someone else will clarify the questions I raise in the fifth paragraph.