  We propose a modification of special relativity in which a physical energy,
which may be the Planck energy, joins the speed of light as an invariant, in
spite of a complete relativity of inertial frames and agreement with Einstein's
theory at low energies. This is accomplished by a non-linear modification of
the action of the Lorentz group on momentum space, generated by adding a
dilatation to each boost in such a way that the Planck energy remains
invariant. The associated algebra has unmodified structure constants, and we
highlight the similarities between the group action found and a transformation
previously proposed by Fock. We also discuss the resulting modifications of
field theory and suggest a modification of the equivalence principle which
determines how the new theory is embedded in general relativity.
