180 THE QUANTUM THEORY 



multiply energy by time. We often divide energy by 

 time. For example, the motorist divides the output of 

 energy of his engine by time and so obtains the horse- 

 power. Conversely an electric supply company multi- 

 plies the horse-power or kilowatts by the number of 

 hours of consumption and sends in its bill accordingly. 

 But to multiply by hours again would seem a very odd 

 sort of thing to do. 



But it does not seem quite so strange when we look 

 at it in the absolute four-dimensional world. Quantities 

 such as energy, which we think of as existing at an 

 instant, belong to three-dimensional space, and they need 

 to be multiplied by a duration to give them a thickness 

 before they can be put into the four-dimensional world. 

 Consider a portion of space, say Great Britain; we 

 should describe the amount of humanity in it as 40 

 million men. But consider a portion of space-time, say 

 Great Britain between 19 15 and 1925; we must describe 

 the amount of humanity in it as 400 million man-years. 

 To describe the human content of the world from a 

 space-time point of view we have to take a unit which is 

 limited not only in space but in time. Similarly if some 

 other kind of content of space is described as so many 

 ergs, the corresponding content of a region of space-time 

 will be described as so many erg-seconds. 



We call this quantity in the four-dimensional world 

 which is the analogue or adaptation of energy in the 

 three-dimensional world by the technical name action. The 

 name does not seem to have any special appropriateness, 

 but we have to accept it. Erg-seconds or action belongs 

 to Minkowski's world which is common to all observers, 

 and so it is absolute. It is one of the very few absolute 

 quantities noticed in pre-relativity physics. Except for 

 action and entropy (which belongs to an entirely different 



