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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?,
i.e.
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.
$)$.

Follow-up:
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"?

Community
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user12262
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2 Answers2

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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?

Alfred Centauri
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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.

Kaz
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