What's an inertial frame of reference?

[MarekS]

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?

 

[Fewmet]

The first postulate of special relativity says there is no test that let's 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.

 

[naiveObserver]

This link may be useful:
http://en.wikipedia.org/wiki/Inertial_reference_frame

 

[MarekS]

Thank you for the link.

I found the following paragraph in the article:
"This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking, inertial frame is a relative concept."

So, are accelerating frames inertial also as long as they are accelerating in a straight line with respect to an inertial frame? It seems to me that all the fictituous forces one needs to introduce for a non-inertial frame have to do with it rotating. Am I wrong?

 

[rwisz]

An inertial frame of reference is a coordinate system in which Newton's first law of motion holds true. This law states that an object at rest will remain at rest and an object in motion will continue in a straight line at a constant speed unless acted upon by an external force. In other words, in an inertial frame, there is no net force acting on an object.

In the context of the Earth, it can be considered an approximately inertial frame because its acceleration with respect to the stars is very small. However, if we consider a group of stars that are accelerating with respect to another group of stars, it is not clear which group would be considered the inertial frame. This is because both groups are accelerating and therefore, the law of inertia may not hold true in either frame.

On a larger scale, if we consider two universes that are accelerating with respect to each other, it is again unclear which one would be considered the inertial frame. This is because the concept of an inertial frame is relative and depends on the observer's perspective.

In terms of an absolute way to determine an inertial frame, it is important to note that the laws of physics, including the law of inertia, are consistent in all inertial frames. Therefore, if we observe the same physical phenomenon in two different frames and the results are consistent, then both frames can be considered inertial. However, if the results are not consistent, then one of the frames may not be inertial.

In conclusion, the concept of an inertial frame is relative and depends on the observer's perspective. While the Earth may be considered an approximately inertial frame, it may not hold true in other accelerating frames. And on a larger scale, it is difficult to determine an absolute inertial frame as it depends on the consistency of physical laws in different frames.