Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

On the experimental foundation of Maxwell’s equations 303
tional constancy, the isotropy, of and Kennedy–Thorndike–experiments
[15, 16] and experiments like that of Alväger and coworkers [27] the independence
of from the velocity of the laboratory and of the source.
According to Robertson [28] from the Michelson–Morley and Kennedy–
Thorndike experiments together with experiments yielding the time dilation
factor one can derive Special Relativity. The most
modern version of these experiments give for the
isotropy of light [14] and for the independence of the
velocity of light from the velocity of the source [16].
Since the properties of the used interferometer arms or cavities are influenced
by the electromagnetic field, too, one has to be careful about the
interpretation of these experiments: It could be shown [17] that within
the model (19) under certain conditions no effect in these experiments
can be detected though there is an anisotropic speed of light. However,
these conditions, though being not exotic, are not fulfilled by the above
mentioned experiments so that the usual interpretation is still valid.
4.5. SUPERPOSITION PRINCIPLE
For a non–linear theory like the Heisenberg–Euler or Born–Infeld theory
the superposition principle is no longer valid. That the effective
underlying theory for the electromagnetic field should be non–linear has
been demonstrated through inelastic photon–photon scattering [29]. But
also other effects should occur: In the frame of the Heisenberg–Euler
theory the effect of birefringence of a propagating weak electromagnetic
wave in strong electromagnetic fields has first been calculated by Adler
[30]. This effect now seems to be in the range of detectability [31]. Also
in the case of the Born–Infeld theory the dispersion of propagating waves
has been derived and shown to be measurable [32, 33].
5. ASTROPHYSICAL OBSERVATIONS
Although in astrophysical observations the observer cannot manipulate
the creation of electromagnetic waves and the boundary conditions
and cannot move arbitrarily in space but is rigidly attached to the earth,
strong estimates can be drawn on those terms describing deviations from
the usual Maxwell equation. The main point is that if the source emits a
unique signal, then this signal usually is distributed over all frequencies
and polarizations. In this case we can make two kinds of observations
relevant for our analysis: First we compare the time–of–arrival of the signal
in one frequency range with the time–of–arrival of the same signal
in another frequency range, that is we compare the velocities connected
with the two frequencies, and second we compare the ar-