Fidelity

The most striking aspect of the radiation process is the fidelity of the signal measured in $F$. To bring this fidelity into sharper focus, consider the radiation from two localized multipole sources, one localized at $\xi'=\xi'_{I}$ and the other at $\xi'=\xi'_{II}$. Their $m$th multipole moments are therefore

$$S^m_{I,II}(\tau',\,\xi')=S^m_{I,II}(\tau') \frac{\delta(\xi'-\xi'_{I,II})}{\xi'}\ ~,$$

Consequently, the multipole superposition has the form

$$\psi_F(\xi,\tau,r,\theta) = \left[ \frac{2S^0_I(\tau+\sinh^{-1}u_I)}{\sqrt{(\xi^2-\xi_I'^2-r^... ...\sinh^{-1}u_{II})}{\sqrt{(\xi^2-\xi_{II}'^2-r^2)^2+(2\xi\xi_{II}')^2 }} \right]$$

$$- e^{i\theta} \frac{\partial}{\partial r} \left[ \frac{2S^1_I(\tau+... ...\sinh^{-1}u_{II})}{\sqrt{(\xi^2-\xi_{II}'^2-r^2)^2+(2\xi\xi_{II}')^2 }} \right]$$

$$+ e^{2i\theta}\left( \frac{\partial^2}{\partial r^2} -\frac{1}{r}\f... ...\sinh^{-1}u_{II})}{\sqrt{(\xi^2-\xi_{II}'^2-r^2)^2+(2\xi\xi_{II}')^2 }} \right]$$

$$+ \quad \textrm{etc.}$$ (54)

where

$$u_{I,II}=\frac{\xi^2-\xi_{I,II}'^2-r^2}{2\xi\xi'_{I,II}}~.$$

Compare Eq.(48) with Eq.(54). The temporal evolution of every localized accelerated multipole source

$$S^m_{I,II}(\tau',\xi') \quad m=0,\pm 1,\pm 2, \cdots$$

displays itself with 100% fidelity as the correspondingly measurable amplitude

$$S^m_{I,II}(\tau \pm\sinh^{-1}u_{I,II}) \quad m=0,\pm 1,\pm 2, \cdots$$

on the hypersurface of synchronous time $\xi=const$ of the expanding inertial observation frame in $F$. There is no distortion and no spatial chirp ($\tau$-dependent redshift), regardless how violently the localized multipole source got accelerated.

As pointed out in section III, the high fidelity is due to the expanding nature of the inertial observation frame. Such a frame consists of an expanding set of free float recording clocks with radio receivers all synchronized and coherently phased to measure the complex amplitude (magnitude and phase) of the spatial amplitude profile at any fixed synchronous time $\xi>0$. Once these recording clocks have been brought into existence, they can always be used to measure, receive, and record the e.m. field with 100% fidelity.

Not so for the usual static inertial observation frame, which consist of a static lattice of free float meter rods, clocks, and radio receivers. Such a frame would be entirely unsuitable for observing the emission of radiation from violently accelerated bodies. Once the recording clocks have been assembled by the physicist/observer into such a frame, the reception, measurement, and recording of electromagnetically encoded information will always be compromised by the destructive blueshift from the accelerated source.