Notes on covariant quantities in noninertial frames and invariance of radiation in classical and quantum field theory

A local observer can measure only the values of fields at the point of his own position. By exploring the coordinate transformation between two Fermi frames, it is shown that two observers, having the same instantaneous position and velocity, will observe the same values of covariant fields at their common instantaneous position, even if they have different instantaneous accelerations. In particular, this implies that in classical physics the notion of radiation is observer independent, contrary to the conclusion of some existing papers. A "freely" falling charge in curved spacetime does not move along a geodesic and therefore radiates. The essential feature of the Unruh effect is the fact that it is based on a noninstantaneous measurement, which may also be viewed as a source of effective noncovariance of measured quantities. The particle concept in Minkowski spacetime is clarified. It is argued that the particle concept in general spacetime does not depend on the observer and that there exists a preferred coordinate frame with respect to which the particle number should be defined.