# We have two particles A and B flying with different speed. Now the rest frame for A

We have two particles $A$ and $B$ flying with different speed. Now the rest frame for $A$ and $B$ is not the same. But is the inertial frame the same? Or would be the inertial frame the same if we have a third fix point $C$ and we would observe them both from $C$?
For me it seems logical to have $3$ frame of references. From the point of view of $A$, from the point of view of $B$ and from an independent point of view $C$. Is this correct?
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Mollie Roberts
You write about the rest frame and the inertial frame, but there are infinitely many such frames. The more dimensions we have, the more possibilities. Even with only 1 dimension, frames can differ in the position of their origin, in their speed, their acceleration, and higher rates of change of position.
A "rest frame" is one in which a particular object is at rest. Unless we are restricted to motion in 1 dimension, its axes can point in any direction, so there is not one "rest frame" for each object.
An "inertial reference frame" is one in which Newton's Laws of motion are true : in particular, an object not acted on by any forces remains at rest or moves in a straight line with constant speed. Any reference frame which is moving with constant velocity relative to an inertial reference frame is also an inertial reference frame.
A "rest frame" will not be an "inertial frame" if the object is accelerating, which includes rotating in a circle or spinning on its axis.
It is not clear what you are asking in your last paragraph. Even with 3 points or objects, there are infinitely many possible frames of reference.