Gravity is understood as a geometrization of spacetime. But spacetime is also
the manifold of the boundary values of the spinless point particle in a
variational approach. Since all known matter, baryons, leptons and gauge bosons
are spinning objects, it means that the manifold, which we call the kinematical
space, where we play the game of the variational formalism of an elementary
particle is greater than spacetime. This manifold for any mechanical system is
a Finsler metric space such that the variational formalism can always be
interpreted as a geodesic problem on this space. This manifold is just the flat
Minkowski space for the free spinless particle. Any interaction modifies its
flat Finsler metric as gravitation does. The same thing happens for the
spinning objects but now the Finsler metric space has more dimensions and its
metric is modified by any interaction, so that to reduce gravity to the
modification only of the spacetime metric is to make a simpler theory, the
gravitational theory of spinless matter. Even the usual assumption that the
modification of the metric only involves dependence of the metric coefficients
on the spacetime variables is also a restriction because in general these
coefficients are dependent on the velocities. In the spirit of unification of
all forces, gravity cannot produce, in principle, a different and simpler
geometrization than any other interaction.Comment: 10 pages 1 figure, several Finsler metric examples and a conclusion
section added. Minor correction
