Unification of Gravity and Electromagnetism Revisited

Unification of gravity and electromagnetism based on a theory with an affine non-symmetric connection ${\mathrm{\Gamma }}_{\mu \nu }^{\lambda }\mathrm{\ne }{\mathrm{\Gamma }}_{\nu \mu }^{\lambda }$ and ${\mathrm{\Gamma }}_{\mu }={\mathrm{\Gamma }}_{[\mu \lambda ]}^{\lambda }\mathrm{\ne }0$, proposed by S. N. Bose in 1953, is revisited in the context of modern developments in high energy physics. It is shown that electrogravity unification can be achieved at a {\em premetric} stage, and that this unification based on {\em projective invariance} is broken by matter fields, opening up the possibility of a unified theory of all forces in which gravity emerges as a classical field. The theory predicts ${\alpha }_{sym}=\frac{1}{9}$ in the projective invariant limit, where $\alpha$ is the fine structure constant