The spacetime framework for most physical measurements, in particular those involving radiation and scattering processes, consists of inertial frames, or frames which become nearly inertial by virtue of the limited magnitude of their spatial and temporal extent. Indeed, the asymptotic ``in'' and ``out'' regions of the scattering matrix as well as the asymptotic ``far-field'' regions of a radiator reflect the inertial nature of the spacetime framework for these processes.

Should one extend these processes to accelerated frames? If so, how? Let us delay answering the first question and note that Einstein, in his path breaking 1907 paper [#!Einstein1907!#], gave us the answer to the second: View an accelerated frame as a sequence of instantaneous locally inertial frames. Thus a scattering (or any other physical) process observed relative to a lattice of accelerated clocks and equally spaced detectors can be understood in terms of the lattice of inertial clocks and equally spaced inertial detectors [#!detectors!#] of one or several of these instantaneous locally inertial frames. Accelerated frames seem to be conceptually superfluous! Acceleration can always be transformed away by replacing it with an appropriate set of inertial frames. To make observations relative to an accelerated frame comprehensible, formulating them in terms of a sequence of instantaneous inertial frames seems (at first sight) to be sufficient.

The introduction of these inertial frames into physics was one of the two historical breakthroughs [#!Einstein1907b!#] for Einstein, because mathematically they are the tangent spaces, the building blocks from which he built general relativity.

However, characterizing an accelerated frame as a one-parameter family
of instantaneous Lorentz frames was only an approximation, as Einstein
himself points out explicitly[#!Einstein1907!#] in his 1907
article. The approximation consists of the fact that the Lorentz
frames *never have relativistic velocities* with respect to one
another. Thus Einstein approximated a hyperbolic world line in of
Figure 1 by replacing it with a finite segment having the approximate
shape of a parabola. If Einstein had not made this assumption, then
he would have found immediately that associated with every uniformly
linearly accelerated frame there is a *twin* moving into the
opposite direction, and causally disjoint from the first. Nowadays
these twins are called Rindler sectors and as in Figure 1.

These two Rindler coordinatized sectors together with their past
and future form a *double-slit
interferometer*[#!Gerlach1999!#] relative to a spatially homogeneous
but expanding coordinate frame. The two Rindler sectors and
comprise the double slit portal through which wave fields propagate
from to . During this process the wave field interacts with
sources, which due to their acceleration, are confined to, say,
Rindler sectors and/or . The interference between the waves
coming from these two sectors is observed in . There the field
amplitude is sampled in space and in time.

Consider the field which is due to accelerated sources in or in . A single inertial radio receiver which samples the field temporally is confronted with a metaphysically impossible task: Track and decode a signal with a Doppler chirp (time dependent Doppler shift) whose phase is logarithmic in time. The longer and more violent the acceleration of the source, the more pronounced the initial blueshift and/or the final redshift at the receiver end. Tracking the amplitude and the phase of such a chirped signal becomes a debilitating task for any receiver.

Suppose, however, the field gets intercepted by a set of mutually
receding radio receivers. If they, in concert, sample the field
spatially at a single instant of ``synchronous'' time, then there is
no Doppler chirp whatsoever. An accelerated source which emits a sharp
spectral line will produce an equally sharp spectral line in the
spatial Fourier domain of the sampled space domain (in Figure
1:
) of the expanding set
of radio receivers. In brief, *a signal emitted by an accelerated
point source is intercepted by a set of mutually receding phased radio
receivers with 100 % fidelity*. We shall refer to this result as the
*fidelity property* of Rindler's spacetime geometry.

The physical reason for this result is given in Section III, the mathematical formulation in Section VIA.

The application of the fidelity property to the power emitted from an accelerated dipole oscillator is given in Section VII. This application consists of Larmor's formula[#!Landau1962!#] augmented due to the fact that the oscillator is in a state of uniform acceleration.

The fidelity property applies to the radiation from a source accelerated in Rindler as well as to a source accelerated in Rindler . If the two sources have the same frequency and are coherent, then the phased array of radio receivers measures an interference pattern which is mathematically indistinguishable from that due to a standard double slit. This result is spelled out in Section VIC.

It is worth while to reiterate that the fidelity property and its two applications are statements about the Rindler coordinate neighborhoods considered jointly, with the event horizons, , integral building blocks of these concepts. Some workers in the field [#!MTWch1!#], who view spacetime only in terms of ``coordinate patches'' or ``coordinate charts'' (i.e. comply with Einstein's approximation mentioned above), tend to compare the locus of events in Fig. 1 to the coordinate singularity at the North Pole of a sphere or the origin of the Euclidean plane. Such a comparison leads to a pejorative assessment of Rindler's coordinatization as ``imperfect'',``singular'', or ``poor'' at [#!MTWch1!#]. This is unfortunate. As a result, this comparison diverts attention from the fact that (1) waves from and interfere in and that (2) as a consequence, the resulting interference patterns serve as a natural way of probing and measuring scattering and/or radiative sources as well as gravitational disturbances in regions and .

The Rindler double-slit opens additional vistas into the role of
accelerated frames and . They accommodate causally disjoint
but correlated radiation and scattering centers whose mutually
interfering radiation is observed and measured in . These
measurements are mathematically equivalent to having two accelerated
observers in Rindler and respectively. From these
measurements one can reconstruct in all detail the location and
temporal evolution of all accelerated radiation sources. The aggregate
of these sources comprises what in Euclidean optics is called an
object, one in Rindler the other in Rindler . What is observed
in is the interference of two coherent diffraction patterns of
these two objects. These measurements are qualitatively different
from those that can be performed in any *static* inertial frame. They
yield the kind of information which can be gathered only in
accelerated frames with event horizons. One of the virtues of the
Rindler double-slit interferometer is that it quite naturally avoids
an obvious metaphysical impossibility[#!MTW1973a!#], namely, have
accelerating observers in Rindler sectors and which (a) have
the physical robustness to withstand the high (by
biological-technological standards) acceleration and/or (b) the
longevity and the propulsion resources to co-accelerate for ever and
never cross the future event horizon.

From the perspective of implementing measurements, the Rindler double-slit has advantages akin to those of a Mach-Zehnder interferometer [#!Born_and_Wolf!#]: it permits an interferometric examination of regions of spacetime whose expanse is spacious enough to accommodate disturbances macroscopic in extent, and it permits one to achieve this feat without putting the measuring apparatus into harm's way. However, in order to use the Rindler interferometer as a diagnostic tool one must first have the necessary conceptual infrastructure. This article provides four of its ingredients:

- Expanding free float frame
- Fidelity property of the Rindler spacetime geometry
- Augmented Larmor formula
- Double slit interference due to a pair of accelerated sources