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

On the experimental foundation of Maxwell’s equations 297
effective equations governing the dynamics of the electromagnetic field
is proposed [8, 9]. Despite that fact that all physical laws should be experimentally
verified with increasing accuracy, the new quantum gravity
induced modifications of the Maxwell equations give additional motivation
for testing Maxwell’s equations. Moreover, since Maxwell’s equations
are so intimately connected with the special and general relativistic
structure of structure of space–time, all tests of Special and General Relativity
are in most cases at the same time also tests of the structure of
Maxwell’s equations.
2.1. LOOP GRAVITY INDUCED
CORRECTIONS
In loop gravity, averaging over some quasiclassical quantum state, a
so–called “weave”–state, which includes the state of the geometry as well
as of the electromagnetic field, gives the effective Maxwell equations [8]
The corresponding wave equation is
The two helicity states lead to different
dispersion relations
There are two points which need to be discussed: First, with (2) also a
homogeneous Maxwell equation is modified and, second, the appearance
of higher order derivatives means that there are photons which propagate
with infinite velocity.
1 The deviation from the homogeneous Maxwell equations has the
important consequence that the unique description of charged particle
interference is no longer true. If quantum mechanical equations
are minimally coupled to the electromagnetic potential, that
is by the replacement then the phase shift in charged
particle interferometry is for a closed path C. If one
applies Stokes’ law in the case of a trivial space–time topology in
that region, then this is equivalent to with
where integration is over some 2–dimensional surface bounded by
the closed path C. The fact that the result should not depend on