The wisdom of classicalunified field theories in the conceptual framework of Weyl, Eddington, Einstein and Schrodinger has often been doubted and in particular there does not appear to be any empirical reason why the ...The wisdom of classicalunified field theories in the conceptual framework of Weyl, Eddington, Einstein and Schrodinger has often been doubted and in particular there does not appear to be any empirical reason why the Einstein-Maxwell (E-MJ theory needs to be geometrized. The crux of the matter is, however not whether the E-M theory is aesthetically satisfactory but whether it answers all the modern questions within the classical context. In particular, the E-M theory does not provide a classical platform from which the Dirac equation can be derived in the way Schrodinger's equation is derived from classical mechanics via the energy equation and the Correspondence Principle. The present paper presents a non-dualistic unified field theory (UFT) in the said conceptual framework as propounded by M. A. Tonnelat. By allowing the metric form ds2=g,dx dx and the non-degenerate two-form F=(1/2t)rdx dx to enter symmetrically into the theory we obtain a UFT which contains Einstein's General Relativity and the Born-Infeld electrodynamics as special cases. Above all, it is shown that the Dirac equation describing the electron in an 'external' gravito-electromagnetic field can be derived from the non-dualistic Einstein equation by a simple factorization if the Correspondence Principle is assumed.展开更多
文摘The wisdom of classicalunified field theories in the conceptual framework of Weyl, Eddington, Einstein and Schrodinger has often been doubted and in particular there does not appear to be any empirical reason why the Einstein-Maxwell (E-MJ theory needs to be geometrized. The crux of the matter is, however not whether the E-M theory is aesthetically satisfactory but whether it answers all the modern questions within the classical context. In particular, the E-M theory does not provide a classical platform from which the Dirac equation can be derived in the way Schrodinger's equation is derived from classical mechanics via the energy equation and the Correspondence Principle. The present paper presents a non-dualistic unified field theory (UFT) in the said conceptual framework as propounded by M. A. Tonnelat. By allowing the metric form ds2=g,dx dx and the non-degenerate two-form F=(1/2t)rdx dx to enter symmetrically into the theory we obtain a UFT which contains Einstein's General Relativity and the Born-Infeld electrodynamics as special cases. Above all, it is shown that the Dirac equation describing the electron in an 'external' gravito-electromagnetic field can be derived from the non-dualistic Einstein equation by a simple factorization if the Correspondence Principle is assumed.
