  A five-dimensional theory of relativity is presented which suggests that
gravitation and electromagnetism may be unified using a degenerate metric.
There are four fields (in the four-dimensional sense): a tensor field, two
vector fields and a scalar field, and they are unified with a combination of a
gauge-like invariance and a reflection symmetry which means that both vector
fields are photons. The gauge-like invariance implies that the fifth dimension
is not directly observable; it also implies that charge is a constant of
motion. The scalar field is analogous to the Brans-Dicke scalar field, and the
theory tends towards the Einstein-Maxwell theory in the limit as the coupling
constant tends to infinity. As there is some scope for fields to vary in the
fifth dimension it is possible for the photons to have wave behaviour in the
fifth dimension. The wave behaviour has two effects: it gives the photons mass,
and it prevents them from interacting directly with normal matter. These
massive photons still act as a source of gravity, however, and therefore they
are candidates for dark matter.
