So the existence of a set of equivalent "inertial frames" is imposed from the start by Newton's laws.
It also follows that any other frame of reference moving uniformly relative to an inertial frame is also an inertial frame.
The serious defect in the notion of inertial frame is not that it makes an arbitrary distinction among coordinate systems for the distinction is quite as genuine as the distinction between flat and curved spacetime but that it extends indefinitely over spacetime a structure that, in our universe, only corresponds approximately to very small regions.
In the absence of such a criterion the speed of light cannot be, as Lorentz supposed, empirically measured against the background of an inertial frame; in that case the only empirically sound definition of an inertial frame is the one that appeals to the speed of light.
Let this relation be represented by κ, let the statement that events p and q are simultaneous be represented by S p,q), and let the given inertial frame be specified by the world line, O, of some inertial observer.
Next, the terms in the acceleration in the inertial frame are related to those in the co-rotating frame.
Let the location of the particle in the inertial frame be (r(t), ϕ(t)), and in the co-rotating frame be (r(t), ϕ′(t)).
Another way of putting the same point is to say that, in Newtonian mechanics and special relativity, rotation is "absolute" because the transformations between inertial frames (Galilean or Lorentzian) preserve rotational states.
Decaying homogeneous isotropic turbulence (HIT) in inertial and rotating frames is considered for this investigation.
It simply makes no sense, according to Galilean relativity, that any velocity should appear to be the same in inertial frames that are in relative motion.
