THE ORIGIN OF THE TROUBLE 181 



class of physical conceptions) all the quantities promi- 

 nent in pre-relativity physics refer to the three-dimen- 

 sional sections which are different for different observers. 



Long before the theory of relativity showed us that 

 action was likely to have a special importance in the 

 scheme of Nature on account of its absoluteness, long 

 before the particular piece of action h began to turn up 

 in experiments, the investigators of theoretical dynamics 

 were making great use of action. It was especially the 

 work of Sir William Hamilton which brought it to the 

 fore; and since then very extensive theoretical develop- 

 ments of dynamics have been made on this basis. I 

 need only refer to the standard treatise on Analytical 

 Dynamics by your own (Edinburgh) Professor*, which 

 fairly reeks of it. It was not difficult to appreciate the 

 fundamental importance and significance of the main 

 principle; but it must be confessed that to the non- 

 specialist the interest of the more elaborate develop- 

 ments did not seem very obvious — except as an ingenious 

 way of making easy things difficult. In the end the 

 instinct which led to these researches has justified itself 

 emphatically. To follow any of the progress in the 

 quantum theory of the atom since about 19 17, it is 

 necessary to have plunged rather deeply into the Hamil- 

 tonian theory of dynamics. It is remarkable that just 

 as Einstein found ready prepared by the mathematicians 

 the Tensor Calculus which he needed for developing 

 his great theory of gravitation, so the quantum physicists 

 found ready for them an extensive action-theory of 

 dynamics without which they could not have made head- 

 way. 



But neither the absolute importance of action in the 

 four-dimensional world, nor its earlier prominence in 



* Prof. E. T. Whittaker. 



