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302 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
tric potential there is no electric field. That means that another
metallic sphere inside the sphere of potential should have the same
potential. This is only possible if the potential for a charged point particle
has the form that is, if the potential is a harmonic function. If
the equation, namely the Poisson equation which determines
the potential from the charge distribution and the boundary conditions,
has a different form, then the solution is different from and does not
show up this property.
The most recent experiment of this kind has been carried through by
Williams, Faller, and Hill [23]. Until now, the theoretical interpretation
of this kind is experiments is restricted to three models only, namely (i)
to the model of a scalar photon mass see [23, 24] and references
therein, which gives a potential of the form
(ii) to a specific ansatz for a deviation from the Coulomb law,
and (iii) to the context of a vector valued photon mass [25]. No
deviation from Coulomb’s law has been found and from the accuracy
of the apparatus one gets the estimates or
and
Behaviour of atomic clocks. Any modification of the solution for
the potential of a point charge should modify the properties of atoms, especially
the energy eigenvalues. As a consequence, the Rydberg constant
will be modified. Not much has been calculated in that context. The
modification for a pure Yukawa modification of the Coulomb potential
(20) leads to modified transition frequencies. If one compares a transition
for small quantum numbers, and large quantum numbers N,
M, then the Rydberg constant may be different, since the strength of
the electric field near the atomic core is different from the strength far
from it. This difference is calculated to be [26]
where is Bohr’s radius. From corresponding spectroscopic experiments
one derives for
4.4. TESTS OF SPECIAL RELATIVITY
The main experiments for Special Relativity test the constancy of the
speed of light: Michelson–Morley–experiments [13, 14] test the direc-