UNIFYING PERSPECTIVE

The four Rindler sectors lend themselves to a unifying perspective. The context which makes this possible is the emission and observation of radiation from a body accelerated linearly and uniformly. The requirement that signals be transmitted with 100% fidelity implies that the spacetime arena for this radiation process consist of two adjacent Rindler coordinatized sectors, such as $I$ and $F$ or $II$ and $F$.

The unifying perspective applied to two adjacent Rindler sectors is brought into a particularly sharp focus by the augmented Larmor formula, Eqs.(69) or (70). This is because the physical basis of this formula is a radiation process which starts in one of the two Rindler sectors and ends in the other. Indeed, the radiative longitudinal momentum (longitudinal flow of radiative energy) observed and measured in the expanding inertial frame in $F$ is expressed directly in terms of the behaviour of the dipole source in the accelerated frame in $I$ (or $II$).

The unifying perspective applies to all four Rindler sectors if one considers a scattering process which starts in $P$ and ends in $F$. In such a process an e.m. wave starts in Rindler sector $P$, splits into two partial waves which cross the past event horizons and enter the respective Rindler sectors $I$ and $II$. The partial wave in $I$ excites the internal degree of freedom of the dipole oscillator accelerated in $I$. There the oscillations constitute a source for the scattered radiation which propagates into $F$. The other partial wave, which propagates through Rindler sector $II$, also reaches $F$. There the resultant interference pattern is observed and measured. It is evident that this interference pattern is made possible by the properties of the four Rindler sectors combined, the Rindler interferometer of Section VID.

Thus both the Rindler interferometer and the augmented Larmor formula provide a unifying perspective. It joins adjacent Rindler coordinate charts into a single spacetime arena for radiation and scattering processes from accelerated bodies.

This perspective is at variance with a philosophy which seeks a particle-antiparticle definition in non-rectilinear coordinate systems in flat spacetime [#!Padmanabhan!#].

Such a philosophy typically focuses on one of the Rindler charts to the exclusion of all the others. The application of quantum field theory to such a chart leads to the paradox of spurious particle production in flat spacetime. As a result quantum theory remains meaningfully invariant only under a subset of classically allowed coordinate transformations.

A proposed solution is to disallow - in quantum theory - a large class of coordinate transformations, such as those leading to Rindler charts $F$ or $I$ [#!Padmanabhan!#].

However, the fault does not lie with these Rindler charts. Instead, it lies with the underlying philosophy which seeks a definition of the particle-antiparticle concept in one of the coordinate charts while ignoring reference to the others. Such a selective focus does not comply with, and hence is forbidden by the unifying perspective implied by the augmented Larmor formula and by the Rindler double-slit interferometer.