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In some PSE questions or answers such as here (and comments below) there appears the notion of "accelerating frame" or (more or less equivalently) "noninertial frame".

What's the definition of this notion?,
How are given participants (or, if you prefer, "point particles"$\,\!^{(*)}$) who "keep sight of each other" supposed to determine whether they (pairwise) belonged to the same "noninertial frame", or not?

$(*$: Cmp. the notion of "inertial frame", in distinction to "inertial coordinate system", of http://www.scholarpedia.org/article/Special_relativity:_kinematics

We should, strictly speaking, differentiate between an inertial frame and an inertial coordinate system, although in sloppy practice one usually calls both IFs. An inertial frame is simply an infinite set of point particles sitting still in space relative to each other.

The new (follow-up) question to be asked to fully address this question has been submitted as How should observers determine whether they can be described as being "defined on a Lorentzian manifold"?

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This is a question that could be answered by a quick search engine search. The wikipedia entry for non-inertial reference frame comes up as top-3 hit on at least Google, Bing, Yahoo and DuckDuckGo. I recommend the question is closed. –  Thriveth Jun 26 '13 at 21:28
@Thriveth Would you please point out one of the numerous references of "noninertial frame" (or, indeed, "non-inertial frame") as definitive; so I could refer to its terminology in case of further questions. BTW, presently there doesn 't seem to be a section Definition at en.wikipedia.org/wiki/Non-inertial_reference_frame –  user12262 Jun 26 '13 at 21:48
@user12262, you might consider telling us what you think it might be, having done some research and all, and then ask about any specific concept you don't "get". –  Alfred Centauri Jun 26 '13 at 21:48
@user12262 It doesn't say the word "definition:" in front of it, but for example the very first sentence in the Wikipedia article is pretty much spot on. –  Thriveth Jun 26 '13 at 21:51
possible duplicate of Inertial frames of reference –  Ben Crowell Jun 27 '13 at 23:41
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marked as duplicate by Ben Crowell, AlanSE, Qmechanic Jun 28 '13 at 19:50

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

2 Answers

What's the definition of this notion?

From Wiki:

A non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will in general detect a non-zero acceleration.

Now, that's pretty straightforward and easy to find so, assuming the above doesn't satisfactorily address your inquiry, what is it that you're asking?

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Thanks; well ... Is any set of "accelerometers [while they] detect a non-zero acceleration" therefore a "non-inertial reference frame"?, for instance. (Please note the word "same" in my question, which has been present, and emphasized, there from the outset.) –  user12262 Jun 26 '13 at 22:09
@user12262, I'm still not clear on what your essential question is. Are you satisfied with the definition of non-inertial reference frame? If so, is your question how two observers might determine if they share the same non-inertial reference frame? –  Alfred Centauri Jun 26 '13 at 22:18
"Are you satisfied with the definition of [NIRF]?" I believe I can comprehend what you stated. Trying to do so, however, I can imagine sets of "accelerometers [each detecting] non-zero a" which are so obviously not "sitting still relative to each other" (cmp. footnote) that I wonder whether they are generally referred to as "(non-inertial) frame". (That's, of course, presuming some particular operational notion of pairwise "sitting still relative to each other"; leading to the part on determination.) –  user12262 Jun 26 '13 at 22:40
@user12262, no, I wouldn't think of such a general set as defining a "frame" at all. It might be that you're not clear on the notion of "frame of reference" or "observer". –  Alfred Centauri Jun 26 '13 at 23:20
What's missing in this answer is the distinction between an inertial frame as defined in Newtonian mechanics and an inertial frame as defined in relativity. In the former, the earth's surface is nearly inertial. In the latter, it's noninertial. –  Ben Crowell Jun 27 '13 at 18:01
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In classical mechanics, an inertial frame of reference is one in which a free point mass floating in space does not experience any outside force. If it is moving relative to the frame, it traces a straight line in that frame in accordance with the laws of motion.

A frame that is not inertial is either accelerating or rotating, or some combination of the two, or else it is bathed in a gravitational field (and is not free falling in that field).

For instance, a frame that is fixed with regard to the surface of the Earth appears to be one which accelerates at 9.81 $m/s^2$ away from the center of the planet.

The frame does not consist of its contents; the frame is a the coordinate system selected for tracking the positions of whatever is of interest that frame. It is itself not an object, but a frame can move relative to other frames, accelerate and so on.

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A free falling frame "bathed" in a gravitational field is (locally) an inertial frame of reference, i.e., the accelerometers read zero. A frame fixed to the surface of the Earth is not free falling and that's why acceleration is felt. –  Alfred Centauri Jun 26 '13 at 23:26
@AlfredCentauri Ah, yes, that needs to be rolled in. –  Kaz Jun 27 '13 at 0:13
@Kaz Same question as regarding Alfred Centauri's answer: Is any set of participants (or if you prefer, "point masses") who are "not free falling" therefore a "non-inertial frame"? (Perhaps, any two "free" protagonists don't necessarily belong to one and the same "inertial frame", either?) Also: is it helpful or even necessary to invoke dynamics (such as mentioning of "force", and of "free ness") at all? (In contrast, Alfred Centauri's answer appeared to be restricted to geometry/kinematics.) –  user12262 Jun 27 '13 at 5:15
The masses are not the frame. The frame is the coordinate system with respect to which you measure the position of the masses. –  Kaz Jun 27 '13 at 5:29
@user12262 : A frame is a coordinate system with an origin and an orientation. For each observer (or point mass, or participant), you have to define a different frame, where the position of the observer (or point mass, or participant) is just zero. –  Trimok Jun 27 '13 at 11:37
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