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I have read answers on this site as well as the Wikipedia article, but they all add to the confusion. Some people suggest that a freely falling frame is an inertial frame. I learnt in classical mechanics that the frame attached to the surface of the earth is approximately inertial. Are there different definitions of it? The concept of inertial frames seemed easy and intuitive at first, but became complicated as I read more. So I am wondering wether you have to be well versed in general relativity to really understand this concept? If not, can anyone please explain the concept of the inertial frames, and how do we determine wether some real world frame is inertial?

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    $\begingroup$ Just to add one point when you try later to learn GR. GR basically talks about how much the deviation from an inertial frame when you have gravity, en.wikipedia.org/wiki/Geodesic_deviation thats basically all there is to the effect of a non vanishing Riemann tensor. $\endgroup$ – lalala Mar 20 at 11:41
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    $\begingroup$ No this should not be necessary. Already in Newtonian mechanics the concept of inertial frame exists. $\endgroup$ – mathreadler Mar 20 at 18:35
  • $\begingroup$ Agree with @mathreader. In fact, I would try to think about the Newtonian concept first, before moving on to General Relativity; I'd even apply this to the whole physics, not just inertial frame. $\endgroup$ – JosephDoggie Mar 20 at 18:44
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    $\begingroup$ Related: physics.stackexchange.com/q/15349/520 $\endgroup$ – dmckee Mar 21 at 0:43
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The principle is surprisingly simple. Suppose you are holding an object and you let go of it. What happens to that object? If the object just floats next to you without moving then you are in an inertial frame. If the object accelerates away from you then you are in a non-inertial frame.

Where general relativity comes in is that in GR inertial frames can be surprising. For example if you are sitting in your chair typing on your computer than this seems like it should be an inertial frame. After all, you aren't going anywhere. But if you hold out your pen and let go the pen accelerates downwards away from you, and this shows you are not in an inertial frame. You are in an accelerated frame, where the acceleration is equal to the gravitational acceleration of the Earth.

Now suppose you've just jumped off a cliff and are plummeting downwards (ignore air resistance). This seems like an accelerating frame, but if you now hold out your pen and let go the pen won't move away because both you and the pen are falling with the same acceleration. So this is an inertial frame.

General relativity explains why frames can look inertial to some observers but not to others. The explanation is very simple but involves some maths that won't be familiar to most people so I won't go into it here. The bottom line is not to worry about anything outside your immediate vicinity. You can always tell whether your frame is inertial or not by observing what happens to an object you drop.

If you're interested in finding out more about this I go into more detail in my answers to Two meanings of acceleration in gravitational fields? and Can we determine an absolute frame of reference taking into account general relativity?

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    $\begingroup$ In your example where you and the pen are falling together w/ same acceleration, isn't that a non-inertial frame? $\endgroup$ – 8protons Mar 20 at 19:15
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    $\begingroup$ @8protons No. Because actually, you're travelling in a straight (inertial) line through spacetime, which happens to cause you to intersect with the planet. The planet – and everything on it – is accelerating towards you, and not the other way around. $\endgroup$ – wizzwizz4 Mar 20 at 19:58
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    $\begingroup$ But this does not answer why we also use the term "inertial frames" in the case of myself sitting on a chair, when speaking out of the context of GR. Indeed, why the term even existed prior to GR. I'm siding with Paul below, that the definition depends on what is a fictitious force, with gravity being one in GR but not virtually anywhere else. In Newtonian mechanics, for example, it is but an external field that penetrates the frame and affects motion in it, on top of inertia. $\endgroup$ – The Vee Mar 21 at 7:29
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    $\begingroup$ I'm quite confused with the given example; assume that I'm in an inertial frame, and I, somehow, have an electron in my pocket; I pull it out and let if go. If there is an electric field in the region where I'm, the electron will accelerate even though I'm an inertial frame, by assumption. Similarly, for a general case, if you and the object are accelerating at the same rate wrt to an inertial frame, when you let that object go, you will see that the object is floats, but still you are not an inertial frame. $\endgroup$ – onurcanbektas Mar 28 at 5:34
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    $\begingroup$ @TaeNyFan in GR gravity isn't a force so it's hard to answer your question. $\endgroup$ – John Rennie Jul 23 at 8:02
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The basic definition is, that physics has to be the same in every inertial frame (Classical Mechanics). As one gets fictitious forces in accelerated frames (e.g. Centrifugal, Coriolis force), these frames are not inertial. But if the forces in phenomena you want to observe are way bigger than the fictitious forces, you may approximate your frame (on the surface of earth) as inertial. SR and GR further build on this concept but aren't necessary to understand it.

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    $\begingroup$ A great answer ! And a key difference between GR and Newtonian physics is that in GR gravity is a fictitious force like centrifugal force etc. If you need to introduce a gravitational force to account for the movement of objects close to you ("local" objects) then this is a sign that you are not working in an inertial (=free-falling) frame of reference. $\endgroup$ – gandalf61 Mar 20 at 15:29
  • $\begingroup$ Long time since I took physics, but I wouldn't want to think of gravity as fictitious myself! $\endgroup$ – JosephDoggie Mar 20 at 18:45
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    $\begingroup$ @JosephDoggie It may seem counter-intuitive, but a key lesson of physics is that our intuition, based on a limited range of human experiences, is often false. Wikipedia's article on "Fictitious force" says "Einstein was able to formulate a theory with gravity as a fictitious force and attributing the apparent acceleration of gravity to the curvature of spacetime. This idea underlies Einstein's theory of general relativity." $\endgroup$ – gandalf61 Mar 21 at 11:42
  • $\begingroup$ @gandalf61 Thanks. That's interesting. But when traveling near cliffs (etc) please stick to Newtonian physics! $\endgroup$ – JosephDoggie Mar 21 at 12:21
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    $\begingroup$ @JosephDoggie Agreed - fictitious forces can still be really bad for you ! $\endgroup$ – gandalf61 Mar 21 at 13:02
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No, you do not need to understand GR to understand inertialframes. An inertial reference frame is one in which Newton's first law holds. Newton's first law is a core concept in classical mechanics that you probably learned about in high school.

The surface of the Earth is approximately inertial, so long as you treat gravity as a force. An example of a non-rotating frame would be if you're on a merry-go-round: Newton's first law does not hold; free objects appear to move (thanks to centripetal force).

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