The Poynting integral is a quantity quadratic in the e.m. field . Recall that to determine this quantity experimentally and to validate it as a Maxwell field requires two distinct measuring processes. The first one measures the magnitude and the direction of the e.m. field quantities. This is usually done with an antenna, a radio receiver, and a volt meter. The second one ascertains the place and the time of this receiving antenna in relation to the dipole source. This is usually done optically. The physicist illuminates his receiving antenna with optical radiation.
The experimental determination of the e.m. field quantities consists then of establishing a quantitative relation between the results of the two measuring processes, the optical measurements and those obtained with the receiving antenna. The augmented Larmor formula, Eq.(1), is an example of such a relation. The independent variable is measured optically. The dependent variable (flow of radiant energy into the direction of acceleration) is measured with the receiving antenna. The -measurements consist of identifying the relationship between observation events in and the tickings of the expanding reference clock AB in Figure 9. This clock also serves to make the -measurements of the source events in , but only after their coordinates have been transferred (by means of the ``radar map'') from to as illustrated in Figure 13.
An obvious feature of Eq.(1) is that it differs from the standard Larmor formula by a significant contribution. However, one should not conclude from this that there is any contradiction with established knowledge. This is because the prominent assumption that went into the derivation of Eq.(1) is that the measurement of the e.m. Poynting integral is done in an inertially expanding coordinate frame. By contrast, the standard Larmor radiation formula assumes that the measurement of the e.m. Poynting vector is done in a free-float (``inertial'', ``Lorentz'') coordinate frame.
The difference between the standard and the augmented Larmor formula goes with the difference between a free-float and an inertially expanding reference frame. These two frames are incommensurable. An attempt to evade this difference by, for example, invoking a coordinate transformation between Minkowski and boost coordinates or by resorting to ``covariance'' would be like trying to transform apples into oranges. The two coordinate frames reveal entirely different aspects of nature, and the radiation from an e.m. source is one of them.