It is an argument that the privileged states of motion should not be mere artifacts of our choice of coordinates, i.e. that they should be coordinate-independent.
Owing to the choice of coordinates, the proton sector remains Lorentz invariant and does not contribute to any changes in the propagating medium22.
This choice of coordinates allows the 3D Helmholtz equation, subject to boundary conditions specified on non-planar surfaces, to be solved with relative ease.
The Cramér-Rao kernel is thus one of the cornerstones for experiment design formulations that do not depend on the choice of coordinates.
This is so because, after all, a metric represents a physical view point and by principle of covariance, the essential physical picture should not depend on the choice of coordinates.
By a proper choice of coordinates, a universal correction term is shown to be applicable to flow in essentially all practical field-flow fractionation (FFF) channels, which are characterized by a large aspect ratio.
The derivation of the underlying nonlinearity contents via the geometric approach helps the analysis not to rely on a specific choice of coordinates and allows taking profit of the vector structure of the equations for further investigations.
Combined with the equivalence principle, however, it implies that a central Newtonian idea that gravity is a force causing deviations from uniform rectilinear motion is based on an arbitrary choice of coordinates.
By the equivalence principle, however, free-fall trajectories satisfy all empirical criteria for being inertial trajectories, and so the distinction between the two types of trajectory depends on the mere choice of coordinates.
Since (k[V]^*) is the algebra of formal power series in (V), a choice of coordinates in (V) specifies a formal loop as an (n -tuple of formal power series in -tupleariables, where (n=dim V) is nof necessarily formal.
