192 ANNUAL REPORT SRHTHSONIAN INSTITUTION, 1951 



eclipse, when one can see stars near the darkened sun, that started the 

 great fame of the Relativity Theoiy and its creator. Another dif- 

 ference between the two theories concerns the motion of planets around 

 the sun. The discrepancy between results deduced by the two theories 

 is small, yet detectable in the case of Mercury, the planet nearest the 

 sun. Whenever such disagreement exists, and whenever experiment 

 can pronounce its verdict, it seems (to put it cautiously) to favor Ein- 

 stein's theory of gravitation. But the importance of Einstein's 

 achievement lies rather in the beauty and simplicity of his theory 

 than in the discovery of new phenomena. 



The gravitational field in Einstein's theory is characterized by 

 10 functions changing in space and time. They play a role similar 

 to that of the six functions in Maxwell's theory. Einstein's gravi- 

 tational equations tell us how these functions change in space and 

 time. 



We remember that in the electromagnetic theory, we have a mixture 

 of field and particle concepts. The field is produced by the electrons 

 and their motion. Similarly, in Einstein's original theory, the gravi- 

 tational field is produced by the bodies (stars and nebulae) and their 

 motion. Thus, comparing Maxwell's and Einstein's theories, we have 

 the following analogy : 



Electromagnetic field < — > Gravitational field 



Charged particles * — * Gravitational masses 



Motion of charged particles < — > Motion of gi^avitational masses 



Our analogy is not complete, and in some respects even misleading. 

 We must now mention one novel feature of Einstein's field equations. 

 The appearance of any form of energy is accompanied by a gravi- 

 tational field. The gravitational field is influenced not only by the 

 moving gravitational masses but also by the electromagnetic field 

 itself, because such a field represents energy. Tlius the sources of a 

 gravitational field lie in moving masses, in moving charges, and in 

 the electromagnetic field. A pure gravitational field can exist without 

 an electromagnetic field. But a pure electromagnetic field cannot 

 exist without a gravitational field. 



PHTSICS AND GEOMETRY 



Let us now adopt the view of 1920 (when the structure of Rela- 

 tivity Theory was finished), without which we cannot understand 

 what happened later. We see one essential difference between the 

 gravitational and the electromagnetic field: the gravitational field 

 is a geometrical field; the electromagnetic field is a physical field. 



The understanding of the gravitational field as a geometric field 

 is the result of one of the greatest and most revolutionary ideas that 



