196 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1951 



So Einstein tried to remove the fault of a double dualism from our 

 theories ; the dualism of field-matter and the dualism of physics-geom- 

 etry — that is, the dualism of electromagnetic versus gravitational field. 

 He believed that a search for a simple geometry of our universe, but 

 more general than that of Riemannian geometry, would lead us to pure 

 field equations that describe electromagnetic and gravitational phenom- 

 ena. More than that, such a theory, if successful, should disclose to us 

 the properties of elementary particles from which atoms are built, and 

 at the same time explain the motion of planets, stars, and galaxies. 



THE END OF THE SEARCH? 



Einstein believes that he may have solved this great problem. In- 

 deed, his new theory is fully a unitary theory. In it only the field 

 appears, no sources of the field. The existence of matter will have to 

 be deduced from the field equations by finding solutions that repre- 

 sent great concentrations of the field. The new theory is a purely 

 geometrical theory. Whereas the electromagnetic field is character- 

 ized, in Maxwell's theory, by 6 functions; whereas the gravitational 

 field is characterized in Einstein's old theory by 10 functions — in the 

 new theory, the metrical field is characterized by 16 (10 + 6) func- 

 tions. To put this in technical language: the electromagnetic field 

 is characterized by an antisymmetric tensor with 6 components, the 

 gravitational field by a symmetric tensor with 10 components, and 

 the geometry of the new Einstein world by a general tensor of the 

 second order with 16 (6 + 10) components. 



In General Relativity Theory, the Einstein field equations char- 

 acterized the Riemannian geometry of our world. But the geometry 

 of our world, according to Einstein's new theory, is a non-Rieman- 

 nian geometry, and Einstein's new field equations characterize this 

 new non-Riemannian geometry of our world. Every concept that 

 appears in the new theory has its geometrical image. The distinc- 

 tion between purely physical concepts and those with a geometrical 

 interpretation is gone. The distinction between matter and field is 

 gone too. There is only the field that is both geometrical and physical. 

 There are only the field equations that represent the geometry of 

 our world and the laws of physics. 



THE TEST OF THE NEW THEORY 



For weak fields, we regain from the new theory the laws of the 

 old theories — that is. Maxwell's and the gravitational equations. This 

 must be so, because every new theory must explain the phenomena 

 that the abandoned theory explained. As always, so here, the dis- 

 carded theory appears as a first approximation to the new one. 



